Strategy on monotone boards can be reasonably unique and I've gotten a few viewer requests for some remixes of strategy pack solutions on monotone flops so I decided to release 20 new monotone board flop solutions for free. To create these 20 solutions, I took 5 game trees, one from each of my strategy packs to date and ran 4 different monotone boards on each .

With a GTORB flop subscription this type of remixing is now very easy to do, you can just open any strategy pack solution, hit the back button, change the board cards and click solve. You can queue up as many such calculations as you want and the GTORB cloud will solve them all in parallel depending on server availability (these 20 calcs were all done within about 25 minutes).

And as a Christmas Special, for anyone who purchases a 6 Month GTORB Flop license between now and Jan 1st 2016 will get a free strategy pack of their choice (that I created) and 500 bonus flop calculations for free. Just purchase a license from the website as usual and email gtorangebuilder@gmail.com to let me know what strategy pack you'd like to get access to and it will be added to your account within 24 hours.

Here are the monotone solutions enjoy:

OOP C-betting -- UTG vs BTN

IP C-betting -- CO vs BB

Blind vs Blind

3bet -- SB vs CO

C-bet Defense -- CO vs BB

## Wednesday, December 23, 2015

## Thursday, December 10, 2015

### 18bb 184 flop HUSNG Solution

I've released a new video showing an 18bb HUSNG solution computed with SimplePostflop's 184 board abstraction. You can check out the video below. The solution is freely available to the community (thank you SPF team for being so generous!) for anyone with a free SimplePostflop account. You can buy their preflop solver and get bonus calculations as a GTORB reader with this link: https://simplepostflop.com/en/?source=gtorangebuilder. Enjoy :)

Just download Simple Postflop here, then go to File --> updates and replace the link with: http://simplepostflop.com/preflop_x64/.

Go to the SaaS tab in the top menu, login in (register for free if needed) and then go to the HU Preflop tab. Open the "Cloud" menu and chose "Preflop Situations" and the scenario will be available for free download. The "download flops" button will download all the flop solutions which you can then open in SimplePostflop at your convenience.

SimplePostflop is offering all GTORB members a small bonus on preflop points (3.5%) just purchase the preflop version after clicking this link: simplepostflop.com/en/?source=gtorangebuilder

Just download Simple Postflop here, then go to File --> updates and replace the link with: http://simplepostflop.com/preflop_x64/.

Go to the SaaS tab in the top menu, login in (register for free if needed) and then go to the HU Preflop tab. Open the "Cloud" menu and chose "Preflop Situations" and the scenario will be available for free download. The "download flops" button will download all the flop solutions which you can then open in SimplePostflop at your convenience.

SimplePostflop is offering all GTORB members a small bonus on preflop points (3.5%) just purchase the preflop version after clicking this link: simplepostflop.com/en/?source=gtorangebuilder

## Monday, December 7, 2015

### GTORB Flop Demo Video

I made a quick demo video illustrating how to use the new GTORB Flop solver and in particular I show around 2:45 minutes in how to load up a solution from a strategy pack or the flop library, tweak it and solve the modified version. Whenever I release a strategy pack I often get requests to run the calculations with slightly modified ranges / additional board textures / additional exploitative variations so I wanted to show exact how with the new system you can run these variations on your own with just a few clicks.

## Friday, December 4, 2015

### GTORB On Demand Flop Calcs Released

I'm happy to announce that private on demand GTORB flop calculations are now available for sale. You can purchase them for $69.99/month or $299.99 for 6 months here: http://gtorangebuilder.com/#buy-now. The license includes 100 flop calculations per month, unlimited turn and river calculations and unlimited access to the GTORB flop library.

You can also load any library or strategy pack solution, open it for editing with a single click and then alter a hand range / bet size / etc and calculate a new solution, so my hope is that this will be a great companion to our strategy packs and flop library that will allow people to easily experiment and further analyze strategy pack solutions.

All calculations are run server side and you can submit multiple calculations that will be run in parallel. Depending on server traffic and calculation size calculations can take anywhere from a few minutes to up to an hour.

Also from now through December 25th, anyone who purchased the GTORB Pro Bundle in the last 3 months will also be eligible for an upgrade discount and can get a 6 month flop license for $199.99, just purchase it from our site at the regular price and email gtorangebuilder@gmail.com and I will refund $100 to you within 24 hours.

You can also load any library or strategy pack solution, open it for editing with a single click and then alter a hand range / bet size / etc and calculate a new solution, so my hope is that this will be a great companion to our strategy packs and flop library that will allow people to easily experiment and further analyze strategy pack solutions.

All calculations are run server side and you can submit multiple calculations that will be run in parallel. Depending on server traffic and calculation size calculations can take anywhere from a few minutes to up to an hour.

Also from now through December 25th, anyone who purchased the GTORB Pro Bundle in the last 3 months will also be eligible for an upgrade discount and can get a 6 month flop license for $199.99, just purchase it from our site at the regular price and email gtorangebuilder@gmail.com and I will refund $100 to you within 24 hours.

## Sunday, November 22, 2015

### Solving GTO Preflop Video Released

Today I released a new video on solving unabstracted preflop scenarios for GTO play. The video examines a 7bb game tree used in Will Tipton's, Expert Heads Up No Limit Hold'em Play: Strategies For Multiple Streets (Volume 2) and compares the results of various abstracted solution techniques to a full real solution computed with the brand new Simple Postflop Preflop solver. You can check out the video below:

The full preflop solution is available for free download via the Simple Postflop client and as with any SPF preflop solution, you can also download the flop solutions for every possible resulting flop. Just download Simple Postflop here, then go to File --> updates and replace the link with: http://simplepostflop.com/preflop_x64/.

Go to the SaaS tab in the top menu, login in (register for free if needed) and then go to the HU Preflop tab. Open the "Cloud" menu and chose "Preflop Situations" and the scenario will be available for free download. The "download flops" button will download all the flop solutions which you can then open in SimplePostflop at your convenience.

Currently the SPF preflop solver only solves scenarios that are HU at the start of the hand, however in the future it will also be possible to start the solver after certain preflop actions, eg after the action has folded to the BTN, who has opened to 2.5x with a fixed range and the SB has folded and to solve for the remaining BB vs BTN action in a 6 max scenario from that point in the game tree on.

SimplePostflop is offering all GTORB members a small bonus on preflop points (3.5%) just purchase the preflop version after clicking this link: simplepostflop.com/en/?source=gtorangebuilder.

The full preflop solution is available for free download via the Simple Postflop client and as with any SPF preflop solution, you can also download the flop solutions for every possible resulting flop. Just download Simple Postflop here, then go to File --> updates and replace the link with: http://simplepostflop.com/preflop_x64/.

Go to the SaaS tab in the top menu, login in (register for free if needed) and then go to the HU Preflop tab. Open the "Cloud" menu and chose "Preflop Situations" and the scenario will be available for free download. The "download flops" button will download all the flop solutions which you can then open in SimplePostflop at your convenience.

Currently the SPF preflop solver only solves scenarios that are HU at the start of the hand, however in the future it will also be possible to start the solver after certain preflop actions, eg after the action has folded to the BTN, who has opened to 2.5x with a fixed range and the SB has folded and to solve for the remaining BB vs BTN action in a 6 max scenario from that point in the game tree on.

SimplePostflop is offering all GTORB members a small bonus on preflop points (3.5%) just purchase the preflop version after clicking this link: simplepostflop.com/en/?source=gtorangebuilder.

## Friday, November 6, 2015

### GTORB Engine Upgrade -- Free flop calcs with a GTORB Pro Bundle Purchase

We're preparing to release on demand custom flop calculations sometime in December, and we've already released the turn / river component of our new solver code. As a result all GTORB turn and river calculations should run substantially faster and to a higher accuracy than before.

I'll make a more detailed announcement when the on demand flop calcs are officially released but we are planning to expand the existing Library+ license to also include up to 100 flop calculations per month at a slightly increased price. Existing Library+ license holders will be able to upgrade or continue with the same service they currently have.

We are also offering anyone who purchases the GTORB Pro Bundle between now and December 1st

I'll make a more detailed announcement when the on demand flop calcs are officially released but we are planning to expand the existing Library+ license to also include up to 100 flop calculations per month at a slightly increased price. Existing Library+ license holders will be able to upgrade or continue with the same service they currently have.

We are also offering anyone who purchases the GTORB Pro Bundle between now and December 1st

**early beta access**to the flop solver and 100 free flop calculations to be used during the beta period, which we're hoping to start in a few weeks time. Pro Bundle license holders will also be able to upgrade to the flop solver when it is released at a discount.## Friday, October 16, 2015

### Using Bulk GTO Calculations and EV aggregation to improve preflop ranges

Today I'm going to build upon some of the work I did both in my previous post on using bulk GTO calcs to make statistical inferences and on some of the results from my OOP C-betting strategy pack to show how to use GTO postflop calcs to improve a preflop range, even in a preflop spot that is not 2-handed. I'm going to do this using SimplePostflop's new EV aggregation feature which will automatically solve a given postflop scenario on every possible unqiue flop, then weight those results by how often each flop occurs, and present average EVs for making a preflop call with each combo in the hand range. Our goal is going to be to use these calculations to work backwards from the average postflop EVs to create a stronger preflop range.

The key concept that we'll need to apply is an idea that I call marginal range building, and I'm going to take a look at how we can use this concept to iteratively strengthen an existing preflop range. As in my OOP C-betting strategy pack I'm going to be looking at improving a flatting range for a Button caller against an UTG preflop 3x open. I'm going to start with a range that is already very solid that is used by a student of mine who plays mid/high stakes 6-max on Stars and work on finding a range with an identical number of combos that will have a higher average postflop EV when we call. The same method can be used to see if we can profitably widen our flatting range by calling a range that includes more combos overall.

The final range that I end up with only differs on about 10 hand combos, but averages about 1.5bb/100 more profit than the initial range, It is played very similarly on almost all flops, it just has slightly more diversified board coverage which yields a higher average EV.

I go through all of this in the video below, and at the bottom of this post I've included links to all of the SPF files I used to do this analysis (10,000+ flop calculations!) for you guys to pour over on your own. Enjoy!

You can download the solution files here: https://s3.amazonaws.com/GTOBlogData/utgvsbtn-iterations.zip

If you want to run your own calculations you will need the desktop version of SimplePostflop, its a bit pricey but GTORB readers can get $70 off: here.

The key concept that we'll need to apply is an idea that I call marginal range building, and I'm going to take a look at how we can use this concept to iteratively strengthen an existing preflop range. As in my OOP C-betting strategy pack I'm going to be looking at improving a flatting range for a Button caller against an UTG preflop 3x open. I'm going to start with a range that is already very solid that is used by a student of mine who plays mid/high stakes 6-max on Stars and work on finding a range with an identical number of combos that will have a higher average postflop EV when we call. The same method can be used to see if we can profitably widen our flatting range by calling a range that includes more combos overall.

The final range that I end up with only differs on about 10 hand combos, but averages about 1.5bb/100 more profit than the initial range, It is played very similarly on almost all flops, it just has slightly more diversified board coverage which yields a higher average EV.

I go through all of this in the video below, and at the bottom of this post I've included links to all of the SPF files I used to do this analysis (10,000+ flop calculations!) for you guys to pour over on your own. Enjoy!

You can download the solution files here: https://s3.amazonaws.com/GTOBlogData/utgvsbtn-iterations.zip

If you want to run your own calculations you will need the desktop version of SimplePostflop, its a bit pricey but GTORB readers can get $70 off: here.

## Wednesday, October 14, 2015

### GTORB LeakBuster Integration

I'm excited to announce that GTORangeBuilder calculations are now integrated into LeakBuster. Leakbuster will automatically scan your hand histories for potential leaks and allows you to examine specific hands that its algorithm detects may have been played sub-optimally.

You can then instantly load that hand into GTORangeBuilder with ranges for both players automatically provided by the LeakBuster AI, making your GTO analysis a one click process. You can of course also tweak the ranges for both players, apply your own hand ranges, edit the bet sizing options as you see fit, etc.

This add-on to LeakBuster is available for purchase now starting at $9.99/mo here: http://www.acepokersolutions.com/Rangebuilder-Leak-Buster/

If you play on Bovada and need to get hand histories so that you can build a database to analyze you can also use the LeakBuster card catcher to save and analyze your Bovada Poker hand history files.

You can then instantly load that hand into GTORangeBuilder with ranges for both players automatically provided by the LeakBuster AI, making your GTO analysis a one click process. You can of course also tweak the ranges for both players, apply your own hand ranges, edit the bet sizing options as you see fit, etc.

This add-on to LeakBuster is available for purchase now starting at $9.99/mo here: http://www.acepokersolutions.com/Rangebuilder-Leak-Buster/

If you play on Bovada and need to get hand histories so that you can build a database to analyze you can also use the LeakBuster card catcher to save and analyze your Bovada Poker hand history files.

## Friday, October 2, 2015

### OOP C-Betting and IP Calling Strategy Pack Released

I'm very excited to announce the release of latest strategy pack on OOP c-betting vs an in position caller which focuses on c-betting / c-bet defense after raising preflop and getting flatted by an in position caller. With ~2hrs of video and 30+ GTO solutions this pack provides an indepth analysis of one of the most commonly misplayed situations in poker.

I've included some exciting new material on calculating pre-flop call EVs for an entire range by running postflop calculations on every possible flop (and full SPF solution files for every possible flop are included for download). I'll be releasing a blog post with more details on the marginal range building techniques shown in the video later this month.

In addition this strategy pack shows that while on many boards against a BTN caller an UTG preflop raiser should always check, on other boards it is essential to bet. Correctly identifying which boards an OOP player should c-bet on and which boards they should always check is a key to both playing these situations correctly and to identify how to exploit opponents who do not have a strong understanding of OOP c-betting in EP vs LP situations.

For more info you can check out the free preview on youtube below and you can purchase the strategy pack in our GTO Dojo.

I've included some exciting new material on calculating pre-flop call EVs for an entire range by running postflop calculations on every possible flop (and full SPF solution files for every possible flop are included for download). I'll be releasing a blog post with more details on the marginal range building techniques shown in the video later this month.

In addition this strategy pack shows that while on many boards against a BTN caller an UTG preflop raiser should always check, on other boards it is essential to bet. Correctly identifying which boards an OOP player should c-bet on and which boards they should always check is a key to both playing these situations correctly and to identify how to exploit opponents who do not have a strong understanding of OOP c-betting in EP vs LP situations.

For more info you can check out the free preview on youtube below and you can purchase the strategy pack in our GTO Dojo.

## Wednesday, August 26, 2015

### Preflop Range Analysis Using Bulk GTO Flop Calcs

Today I'm going to present some data that I gathered that compares the EV of different flatting frequencies from the big blind against a small blind preflolp raise (after the rest of the table has folded) in 6-max situations. This analysis uses some of the ranges from my Blind vs Blind Strategy pack and I will be adding a few additional solutions to the library using the alternate ranges from this analysis. In general the postflop strategy changes due to the alternate range are minimal on most boards. For example, as you can see in this solution on QT2 we shift from a 45% c-bet to 44.8% and a 52% call c-bet to 51.8% (on the A75 board there is a 2% c-bet shift and the largest shift was 6% on TT6) so the main point of interest is the preflop EV comparison, not the post flop strategy shifts.

While the exact data and ranges are specific to 6-max the technique of using postflop EV calcs to compare the quality of two different preflop ranges can be used in any game type so I think learning and understanding the methodology will be valuable to players of all game types.

For all of these calculations I used the Simple Postflop desktop version, which GTORB readers can get for $70 off using this link: http://simplepostflop.com/en/?source=gtorangebuilder. At the moment the workflow for doing this analysis in Simple Postflop requires a lot of tedious manual work but I am working with the creators of the program to get them to add tools to automated most of the process so that these types of comparisons can be done easily and quickly by anyone.

Because of the manual work required with the current interface I only used a smaller sample size in my analysis which means that the results are not conclusively statistically significant. Once they have improved the interface enough to make the process easy I will make a free youtube video on my youtube channel showing how to quickly set up these types of calculations and I will increase the sample size on this calculation to improve the statistical significance so stay tuned.

Range 2 (R2 - 58.26%): [25]43o, 64o, 76s, 85o, 87s, 98s, J6o, JTs, K2-K3o, KTs, Q3-Q4o, QTs, T6o, T9s[/25], [50]43s, 54, 65s, 75o, 88, A9s, AJo, KQo[/50], [75]62s, 64s, 72-73s, 75s, 77, 82-83s, 86s, 92-93s, 97s, A2-A5s, ATo, J9s, K9s, KJo, Q9s, T2-T3s, T8s[/75], 22-66, 32s, 42s, 52-53s, 63s, 65o, 74s, 76o, 84-85s, 86o+, 94-95s, 96, 97o+, A2-A5o, A6-A8, A9o, J2-J6s, J7-J8, J9o+, K2-K3s, K4-K8, K9-KTo, Q2-Q4s, Q5-Q8, Q9o+, T4-T6s, T7, T8o+

How can we mathematically compare which range is higher EV against a fixed "standard" opponent opening range? In this case I am going to be assuming an SB opening range of 52% and a 3x open.

Note that in both cases we are 3-betting 11.4% so with R1 we are folding (1 - .5222 - .114) = 36.38% vs (1 - .5826 - .114) = .3034% with R2

Note that these ranges give a total defense rate of about 65% vs 70%.

To start with let talk about the central limit theorem. There are actually many central limit theorems but in general they all state that if you have a reasonably "well behaved" random sample that is "large enough" then the average of that sample will be normally distributed, centered around the true expected value.

The key thing to determine is what "well behaved" means and what "large enough means". In this case the conditions for being "well behaved" are easily satisfied as there are a fixed number of discrete flops that can be dealt. What a "large enough" sample means is more complex.

Lets start by considering a case where an incredibly large sample is required to be considered large enough that the average would be normally distributed.

One of the simplest distributions there is is called the binomial distribution and it can represent any probability distribution with only two outcomes. One of the most basic limit theorems is that the binomial distribution can be well approximated by the normal distribution for a large enough sample. However, how large a sample is required depends on the probability of each of the two outcomes and their relative payoffs.

For example, imagine two games. In game one you flip a coin and if its heads you get a dollar if its tails you lose a dollar and that you play 100 rounds. The EV of the game is 0 per round.

In game two there is a 1 in a million chance of winning 10 million dollars and the rest of the time you get nothing and you play 100 times. The EV of this game is 10 per round.

In game one the odds that over 100 rounds your average per round payoff would be more than say $0.30 away from 0 are very low and the expected error is symmetric (you are as likely to overestimate the EV of the game by X as to underestimate it by X).

In game two most of the time your sample will contain no winning draws and you will estimate the average EV of the game as 0. In the case that you happen to get a winning draw you will estimate the average EV of the game as at least 100,000. The odds that your sample average are within $0.30 of the true mean are actually 0! Its impossible to get an accurate sample out of 100 trials. If your sample is large enough the result will still be normal but you would need to average over millions of trials.

As it turns out there are two key factors here.

While the exact data and ranges are specific to 6-max the technique of using postflop EV calcs to compare the quality of two different preflop ranges can be used in any game type so I think learning and understanding the methodology will be valuable to players of all game types.

For all of these calculations I used the Simple Postflop desktop version, which GTORB readers can get for $70 off using this link: http://simplepostflop.com/en/?source=gtorangebuilder. At the moment the workflow for doing this analysis in Simple Postflop requires a lot of tedious manual work but I am working with the creators of the program to get them to add tools to automated most of the process so that these types of comparisons can be done easily and quickly by anyone.

Because of the manual work required with the current interface I only used a smaller sample size in my analysis which means that the results are not conclusively statistically significant. Once they have improved the interface enough to make the process easy I will make a free youtube video on my youtube channel showing how to quickly set up these types of calculations and I will increase the sample size on this calculation to improve the statistical significance so stay tuned.

### The Problem

The problem I am interested in examining here is trying to estimate what frequency we can successfully defend against a static small blind opening range if both players achieve the GTO EVs postflop and/or if we are able to gain some additional exploitative EV postflop. In particular I am going to consider a fixed 3-betting range of about 12% and look at expanding our flatting range by comparing the EVs of two flatting ranges. The first range is a range from my BvB strategy pack that a student and I estimated that we believe is reasonably representative of "standard" play in mid-stakes cash games on Stars. The second range is the same as the first but with about 6% more hands so in this case Range 1 is a subset of Range 2.

Range 1 (R1 - 52.22%): [25]64o, 76s, 87s, 96o, 98s, JTs, K4o, KTs, Q6o, QTs, T9s[/25], [50]43s, 54, 65s, 75o, 88, A9s, AJo, K5o, KQo[/50], [75]62s, 64s, 72-73s, 75s, 77, 82-83s, 86s, 92-94s, 97s, A2-A4, A5s, ATo, J9s, K9s, KJo, Q9s, T2-T4s, T8s[/75], 22-66, 32s, 42s, 52-53s, 63s, 65o, 74s, 76o, 84-85s, 86o+, 95-96s, 97o+, A5o, A6-A8, A9o, J2-J6s, J7-J8, J9o+, K2-K5s, K6-K8, K9-KTo, Q2-Q6s, Q7-Q8, Q9o+, T5-T6s, T7, T8o+

Range 2 (R2 - 58.26%): [25]43o, 64o, 76s, 85o, 87s, 98s, J6o, JTs, K2-K3o, KTs, Q3-Q4o, QTs, T6o, T9s[/25], [50]43s, 54, 65s, 75o, 88, A9s, AJo, KQo[/50], [75]62s, 64s, 72-73s, 75s, 77, 82-83s, 86s, 92-93s, 97s, A2-A5s, ATo, J9s, K9s, KJo, Q9s, T2-T3s, T8s[/75], 22-66, 32s, 42s, 52-53s, 63s, 65o, 74s, 76o, 84-85s, 86o+, 94-95s, 96, 97o+, A2-A5o, A6-A8, A9o, J2-J6s, J7-J8, J9o+, K2-K3s, K4-K8, K9-KTo, Q2-Q4s, Q5-Q8, Q9o+, T4-T6s, T7, T8o+

How can we mathematically compare which range is higher EV against a fixed "standard" opponent opening range? In this case I am going to be assuming an SB opening range of 52% and a 3x open.

Note that in both cases we are 3-betting 11.4% so with R1 we are folding (1 - .5222 - .114) = 36.38% vs (1 - .5826 - .114) = .3034% with R2

Note that these ranges give a total defense rate of about 65% vs 70%.

### EV Formula

The EV formula for the comparison that we want to make is quite simple. Since we are 3-betting the same range regardless of our flatting range in this example, all we need to consider is the changes to our EV that come from folding less often with R2 and the changes that come from a reduction in postflop EV do to R2 having generally weaker hands. To normalize the EV change into something that we can use for overall bb/100 calculations we need to multiply it by (1-.114) = .886 as in those cases we will be 3-betting.

Mathematically we want to look at

.886 * ([how often we call] * [average payoff of calling] + [how often we fold] * [payoff of folding])

for each range and compare the values. If we call P[R] the postflop EV of R (the number of chips from the pot that we win on average after flatting with range R) then this can be written as

.886 * (.5222 * (P[R1] - 3) + .3638 * -1) vs ..886 * (5826 * (P[R2] - 3) + .3034 * -1)

So far this is pretty simple, assuming that we actually know P[R1] and P[R2] so we just need to figure this out. This is where the GTO postflop calculations come in.

### Computing Average Postflop EVs

In general there are two approaches to computing the average postflop EV of a range vs a fixed opponent range.

Method 1 is to compute the postflop EV of the range on each of the 1755 possible strategically different flops and compute the weighted average of those 1755 EVs based on the frequency of each type of flop conditional on the blocker effects that the ranges impose on the board.

Method 2 is to randomly select a reasonable sample size of flops by simulating randomly dealing cards and to then do a statistical estimation of the true postflop EVs using standard statistical techniques.

In general Method 1 is superior for things like 3-bet pots where it is relatively feasible to compute 1755 postflop solutions, while Method 2 is more practical for situations with wider ranges and higher SPRs were computing all 1755 possible outcomes might take weeks.

Because in this case we are looking at a single raised BvB scenario with wide ranges I chose Method 2 and because the ranges are so wide I did not incorporate the blocker effects of the ranges on the random sampling of the board. With very wide ranges these effects are minimal but with something like a 4-bet pot range they are crucial (because for example an A is much less likely to be dealt than a 2 when both players have extremely strong ranges).

I chose to use a sample size of 100 per range which means that I had Simple Postflop run a total of 200 flop solutions to "low" accuracy which took about a day (running 1755 x 2 = 3510 would have taken a few weeks). The low accuracy usually gets to between 0.75% and 0.5% of the pot in exploitability. Since we are averaging the EVs of the 100 solutions together "low" accuracy is appropriate as the nash distance errors are likely to average out over a large sample. Note that I used the same 100 random boards for both ranges.

The only major challenge that comes with Method 2 is that we need to perform an accurate statistical analysis which is something that, particularly in poker, is often done incorrectly and should always be done with a great deal of care.

The next section will be purely about statistics and will likely be a bit dry so if you aren't interested in the math feel free to just scroll down to the results below.

### Statistical Analysis of Flop EVs

Once we have all of our EV data we have to come up with a measure of the statistical noise that will be expected due to our random sampling of flops. Suppose that with R1 we get an average EV of X and with R2 we get an average EV of Y. How much bigger must Y be than X before we can say with a high probability that R2 is actually a stronger range (rather than it being the case that the 100 randomly chosen boards were just better flops for R2 than for R1)?

To start with let talk about the central limit theorem. There are actually many central limit theorems but in general they all state that if you have a reasonably "well behaved" random sample that is "large enough" then the average of that sample will be normally distributed, centered around the true expected value.

The key thing to determine is what "well behaved" means and what "large enough means". In this case the conditions for being "well behaved" are easily satisfied as there are a fixed number of discrete flops that can be dealt. What a "large enough" sample means is more complex.

Lets start by considering a case where an incredibly large sample is required to be considered large enough that the average would be normally distributed.

One of the simplest distributions there is is called the binomial distribution and it can represent any probability distribution with only two outcomes. One of the most basic limit theorems is that the binomial distribution can be well approximated by the normal distribution for a large enough sample. However, how large a sample is required depends on the probability of each of the two outcomes and their relative payoffs.

For example, imagine two games. In game one you flip a coin and if its heads you get a dollar if its tails you lose a dollar and that you play 100 rounds. The EV of the game is 0 per round.

In game two there is a 1 in a million chance of winning 10 million dollars and the rest of the time you get nothing and you play 100 times. The EV of this game is 10 per round.

In game one the odds that over 100 rounds your average per round payoff would be more than say $0.30 away from 0 are very low and the expected error is symmetric (you are as likely to overestimate the EV of the game by X as to underestimate it by X).

In game two most of the time your sample will contain no winning draws and you will estimate the average EV of the game as 0. In the case that you happen to get a winning draw you will estimate the average EV of the game as at least 100,000. The odds that your sample average are within $0.30 of the true mean are actually 0! Its impossible to get an accurate sample out of 100 trials. If your sample is large enough the result will still be normal but you would need to average over millions of trials.

As it turns out there are two key factors here.

- High variation in payoffs increases the required sample size.
- Huge asymmetry in the probability of the various outcomes increases the required sample size to apply a normal approximation.

Lets now consider how our flop EV calculations perform according to the two metrics above. First note that no matter what two ranges we are estimating the highest postflop EV possible in a 3x raise case is to win the entire 6bb pot and the lowest EV possible is to lose the entire pot and get 0. Thus something like winning thousands of hands worth of EV in a single low probability case is not possible. Furthermore, in this case R2 is a subset of R1 so a player could always chose to fold all the hands in R2 that are not in R1 and play according to the GTO strategy when you hold R1 with the rest of his range.

This would get him the R1 EV with .5222/.5826 of his range and 0 with the rest so a maximum difference between the R1 EV and the R2 EV on any board is actually about 10% of the R1 EV.

Thus on factor 1 we are in extremely good shape, there magnitude of the variation in payoffs across different boards, particularly the magnitude of the difference between the R1 and R2 GTO EVs is bounded and is very small.

For factor two, due to suit symmetries, some strategically relevant flops are more likely than others (eg AAA is less likely than K86tt), however the magnitude of this difference is not huge and we can ignore it by dealing random flops and not bucketing by suit symmetry.

Thus for both of these variables we have good reason to believe that a normal approximation should be quite accurate over a reasonable sample. I chose to use a sample size of 100 which is a bit on the small side simply due to the magnitude of the manual work required.

The result of all this is that we can apply a two population t-test to our EV results which I will go through below.

### Data and Results

I've put the raw data that this analysis is based on up on google drive for anyone to view here. All the scenarios I ran where based on a 3x SB open and a BB call with 100BB stacks and an 80% pot bet on every street. The EVs for both players and the nash distance for every scenario is recorded in the google doc.

The data shows that the average postflop EV for the 52.22% range is 2.765 while for the 58.26% range it is 2.714.

This means that the overall EVs for both calling and folding are

For R1: .5222 * (2.765 - 3) + .3638 * -1 =

**-0.487**
For R2: .5826 * (2.714 - 3) + .3034 * -1 =

**-0.470**
This suggests that there is a 1.7 * .886 = 1.5 bb/100 EV gain for calling with the wider range. However, this ignores a key element in preflop analysis which is the rake. For postflop solutions, particularly at mid or high stakes the rake is much less relevant as for example in a 5/10 game with a 3x SB open vs a BB call the rake is already capped and in almost any case you have paid a significant chunk of the rake already and stand to win far more than the potential additional rake you might pay.

However, preflop the rake is more of a concern as we are going from a strategy that paid 0 rake with 6% of hands to a strategy that is now paying significant rake with those hands. Obviously this will cut into the strategy EV gain. The exact magnitude and cap of the rake will depend on what site/stakes you play at and how many people are dealt into the hand. For this analysis I will use Stars 4.5% rake and assume that the entire average postflop EV is raked, Note that this is really worst case as some of our postflop EV comes from winning large pots where the rake would of capped out. The true impact of the rake is difficult to estimate and varies greatly across stakes / number of players dealt into the hand so this should be considered a worst case and for most players the true outcome would be somewhere in-between this case and the rake free case.

The rake changes our EV equations and resulting EVs as follows:

The worst case rake cuts our gain by almost half down to .9bb/100 and as we can see significantly deters otherwise potentially +EV high preflop calling strategies (eg something like an 80-90% defense would likely get hammered by the rake).

Finally I also considered assuming that we have a non-trivial postflop edge above the GTO EVs that would make calling additionally profitable. As I discussed in my BvB strategy pack, many people c-bet poorly in these situations and the OOP player can pretty easily achieve a higher EV than GTO against such an opponent. Assuming a moderate edge of 5bb/100 we can adjust our equations like so.

Without rake we get a 1.7 bb/100 difference:

One final comment on these numbers is that in all the above cases, the standard deviation was about 15% higher with the wider defense range, so the potential EV gains do come at the cost of higher variance. Of course this is to be expected in any strategy where you switch from folding a set of hands (0 variance) to playing out the hands postflop and potentially winning or losing a significant sum.

Anytime you do this type of analysis it is not sufficient to just compare averages.

To determine if these results are statistically significant we can do our two population t-test. I did so using this free calculator. The results suggest that to really be confident that these EV gains are not due to chance that we would need to significantly increase our sample size. The p-value of a test indicates the probability of the resulting increase being due to random chance and in this case the p-values range from ~.2 without the rake to ~.3 with the rake (.233 with no rake/no edge, .193 with no rake/ yes edge, .317 yes rake / no edge, .271 yes rake / yes edge). So at the moment the best we can say is that incorporating the rake there is about a 70% chance that the wider defense range is higher EV.

My plan is to follow up on this analysis once the technology behind the process has improved so that we can revisit these numbers and hopefully get more conclusive results. In the mean time the jury is still out but the evidence weakly suggests that a slight widening of the "standard" defense range would be +EV.

However, preflop the rake is more of a concern as we are going from a strategy that paid 0 rake with 6% of hands to a strategy that is now paying significant rake with those hands. Obviously this will cut into the strategy EV gain. The exact magnitude and cap of the rake will depend on what site/stakes you play at and how many people are dealt into the hand. For this analysis I will use Stars 4.5% rake and assume that the entire average postflop EV is raked, Note that this is really worst case as some of our postflop EV comes from winning large pots where the rake would of capped out. The true impact of the rake is difficult to estimate and varies greatly across stakes / number of players dealt into the hand so this should be considered a worst case and for most players the true outcome would be somewhere in-between this case and the rake free case.

The rake changes our EV equations and resulting EVs as follows:

For R1: .5222 * (2.765 * 0.955 - 3) + .3638 * -1 =

**-0.551**
For R2: .5826 * (2.714 * 0.955 - 3) + .3034 * -1 =

**-0.541**The worst case rake cuts our gain by almost half down to .9bb/100 and as we can see significantly deters otherwise potentially +EV high preflop calling strategies (eg something like an 80-90% defense would likely get hammered by the rake).

Finally I also considered assuming that we have a non-trivial postflop edge above the GTO EVs that would make calling additionally profitable. As I discussed in my BvB strategy pack, many people c-bet poorly in these situations and the OOP player can pretty easily achieve a higher EV than GTO against such an opponent. Assuming a moderate edge of 5bb/100 we can adjust our equations like so.

Without rake we get a 1.7 bb/100 difference:

For R1: .5222 * (2.765 + 0.05 - 3) + .3638 * -1 =

**-0.460**
For R2: .5826 * (2.714 + 0.05 - 3) + .3034 * -1 =

**-0.441**

With rake we get a 1.2 bb/100 difference:

For R1: .5222 * ((2.765 + 0.05) * .955 - 3) + .3638 * -1 =

**-0.527**
For R2: .5826 * ((2.714 + 0.05) * .955 - 3) + .3034 * -1 =

**-0.513**One final comment on these numbers is that in all the above cases, the standard deviation was about 15% higher with the wider defense range, so the potential EV gains do come at the cost of higher variance. Of course this is to be expected in any strategy where you switch from folding a set of hands (0 variance) to playing out the hands postflop and potentially winning or losing a significant sum.

### Statistical Significance of Results

Anytime you do this type of analysis it is not sufficient to just compare averages.

To determine if these results are statistically significant we can do our two population t-test. I did so using this free calculator. The results suggest that to really be confident that these EV gains are not due to chance that we would need to significantly increase our sample size. The p-value of a test indicates the probability of the resulting increase being due to random chance and in this case the p-values range from ~.2 without the rake to ~.3 with the rake (.233 with no rake/no edge, .193 with no rake/ yes edge, .317 yes rake / no edge, .271 yes rake / yes edge). So at the moment the best we can say is that incorporating the rake there is about a 70% chance that the wider defense range is higher EV.

My plan is to follow up on this analysis once the technology behind the process has improved so that we can revisit these numbers and hopefully get more conclusive results. In the mean time the jury is still out but the evidence weakly suggests that a slight widening of the "standard" defense range would be +EV.

## Monday, August 24, 2015

### HUSNG Top Winners and GTO

HUSNG.com released their weekly top winner report for all HUSNG games here and 307th, who teamed up with currrr14 to create the GTORB Spin-n-Go Strategy Pack managed to take the number one spot with $37.6K in winnings for the week. Currrr14 also made the winners list as did several other GTORB players.

Its awesome to see the impacts of GTO theory and computation playing out in the highest levels of HUSNG play and its definitely been an interesting to observe the transition in how the games have been played since Will Tipton's first book starting to really bring solid GTO theory and practice to the mainstream years ago all the way to now and 307th's rapid climb up the ranks has been very impressive to watch so a big congrats to him.

## Saturday, August 15, 2015

### New Strategy Pack: GTO and Exploitative Blind vs Blind Play + Discount Offer

I'm very excited to announce the release of latest strategy pack on latest strategy pack on OOP c-betting in Blind vs Blind play which focuses on c-betting after raising from in position and getting called by an out of position player. The second half of this strategy pack has some pretty excited new material comparing GTO and "standard" OOP c-betting ranges and noting weaknesses and exploitation opportunities that exist in standard play. It also addresses the differences in the importance of balancing your checking range as an OOP vs IP c-bettor both from a theoretical and practical perspective.

This pack features 25 GTO and exploitative flop solutions that are carefully constructed and over 105 minutes video analysis. The first ~10 minutes are available on youtube for free, you can check it out below.

Through September 15th 2015 we are also offering $50 any of the existing Alex Sutherland strategy pack when you purchase the new Blind vs Blind pack at the regular price ("In Position C-betting", "GTO Play in 3-Bet Pots" or "GTO Flop C-bet Defense"). Just purchase both packs at the regular price and email us at gtorangebuilder@gmail.com and we'll refund $50 to your account within 48 hours.

You can also get all four of my strategy packs at a steep discount with our new GTO Pro Bundle.

This pack features 25 GTO and exploitative flop solutions that are carefully constructed and over 105 minutes video analysis. The first ~10 minutes are available on youtube for free, you can check it out below.

Through September 15th 2015 we are also offering $50 any of the existing Alex Sutherland strategy pack when you purchase the new Blind vs Blind pack at the regular price ("In Position C-betting", "GTO Play in 3-Bet Pots" or "GTO Flop C-bet Defense"). Just purchase both packs at the regular price and email us at gtorangebuilder@gmail.com and we'll refund $50 to your account within 48 hours.

You can also get all four of my strategy packs at a steep discount with our new GTO Pro Bundle.

## Thursday, July 9, 2015

### GTORB / Simple Postflop Integration and Discounts

Over the past month, I've been working with the Simple Postflop creators to integrate our functionality and today we're launching the first major step in that process. If you compute a flop scenario using the Simple Postflop desktop version or a turn/river scenario using their free version, you can now view and share your solution via GTORB by going to File-->Share in the menu. I've made a quick tutorial video that walks through this process here:

Sharing/viewing solutions that are computed using their SaaS license will be available soon as well, hopefully within the next week.

As part of this launch, the Simple Postflop team are also offering the GTORB community a 50% discount on a month of their SaaS version (100 flop calcs for $35) or $70 off their desktop client. Just click this link before you make your purchase and your GTORB discount will be applied automatically: http://simplepostflop.com/en/Buy?source=gtorangebuilder

Hopefully you guys enjoy this new integration! If you have any feedback on how we could improve the experience or add additional integration features let me know in the comments below.

Sharing/viewing solutions that are computed using their SaaS license will be available soon as well, hopefully within the next week.

As part of this launch, the Simple Postflop team are also offering the GTORB community a 50% discount on a month of their SaaS version (100 flop calcs for $35) or $70 off their desktop client. Just click this link before you make your purchase and your GTORB discount will be applied automatically: http://simplepostflop.com/en/Buy?source=gtorangebuilder

Hopefully you guys enjoy this new integration! If you have any feedback on how we could improve the experience or add additional integration features let me know in the comments below.

## Tuesday, July 7, 2015

### GTORB Flop Library Highlights #2

Its been a while since my last highlights post and the flop library has more than doubled in size, so I expect it will hit 1,000 solutions sometime this month. In this post I am going to take a look at two interesting results that come from some analysis done by our community. The first result comes from 6-max 3-bet pot scenarios but applies to all game types. As always you can get access to all our Library solutions starting at just $20 on our buy now page. The second result is an example of a good usage of our new minimally exploitative solutions that I use heavily in my latest In Position C-betting strategy pack.

### Ah9h5c vs Ac9h5h

An important, and often overlooked concept on high card two-toned boards is that in general the board texture where the top card is the same suit as one of the other cards is fundamentally different from boards where the top card is the only one of its suit.

The reasons for this is very simple, lets consider a 3-bet pot in 6-max as an example. On Ac9h5h, top pair + nut FD is a very common and highly strategically relevant hand, whereas on Ah9h5c it is not a possible holding. In addition, if neither player has A9o in their range then there are 3 possible top 2-pair combos on Ah9h5c vs 2 such combos on Ac9h5h.

The result of this is that in a SB vs BTN 3-bet situation where the SB 3-bets 15.5% linear and the BTN calls with 20.1% of hands, in terms of EV Ah9h5c is much closer to A95 rainbow than it is to Ac9h5h. In fact, with the same game tree and starting ranges the strategy EV for the SB on Ac9h5h vs Ah9h5c is about 25bb/100 higher (approximately 8x the nash distance) while Ah9h5c and A95r are within 7bb/100 (~2x the nash distance).

The three relevant solutions are here:

- Ac9h5h: http://gtorangebuilder.com/#share_calc=Ac9h5h_5540f7cad85603e1102bd74dee8bfdfd
- Ah9h5c: http://gtorangebuilder.com/#share_calc=Ah9h5c_66600ac7d1b05419e18806c5717a9150
- Ac9h5d: http://gtorangebuilder.com/#share_calc=Ah9c5d_63c972bf63574f86cd1383795ad4c850

In order the EVs for the SB are 10.7 (Ac9h5h), 10.44 (Ah9h5c), 10.37 (Ac9h5d).

Now lets consider taking that same setup but changing the A to a K, which is in general always going to be more favorable for the SB. It turns out that we get a similar (but slightly smaller) effect where Kc9h5h is more favorable for the SB than Kh9c5h which is turn more favorable than Kh9h5c. However, in this case it turns out that the rainbow version of the scenario is by far and away the best version for the hero.

The reason for this is quite interesting and is a concept that comes up somewhat frequently in GTO calculations. As I noted before the K high boards are in general more favorable for the hero than the A high boards and this is reflected by a significant increase in c-betting frequency on all of the two-toned flops. In general the SB is c-betting around 40% on the two toned A high flops whereas he is c-betting around 70% on the K high flops.

It turns out that on the rainbow K high board, the SB hits a break point where suddenly his range is strong enough relative to his opponents that he can effectively bet his entire range, because when all FD possibilities are removed from the BTNs range his positional advantage decreases and his range disadvantage increases and he suddenly no longer has enough combos to profitably defend enough to make any kind of bluff -EV. In general hitting these types of break points can be extremely strong because it means that there is no longer a requirement of balance between a betting and checking range and when these types of breakpoints are hit we can see sudden, large EV increases. In this case the rainbow board is about 60bb/100 better than the best of the two toned boards.

The relevant solutions are here:

- Kc9h5h: http://gtorangebuilder.com/#share_calc=Kc9h5h_a27c4d11ced233c9338568881b2335eb
- Kh9c5h: http://gtorangebuilder.com/#share_calc=Kh9c5h_7c1e2751499c690a78ea3c6d4978ed2e
- Kh9h5c: http://gtorangebuilder.com/#share_calc=Kh9h5c_7e8c85a8309872558f881a5f12620bae
- Kh9c5d: http://gtorangebuilder.com/#share_calc=Kh9c5d_d58af7010ecd459724dc65ef5626ff1f

There are a bunch of additional similar scenarios investigating the detailed implications of suitness on a variety of boards that you can check out in the flop library. If you filter by string for "SB 15.5% linear" they will come up.

### Minimally exploiting aggressive c-betting in 3-bet pots

One of the more notable elements of GTO solution strategies in 3-bet pots is that on A high boards the 3-bettor often has a very low c-bet frequency and takes a much more passive approach to the hand than many regulars usually take.

One GTORB user was particularly surprised by a SB vs BTN 3-bet scenario where the SB 3-bet 15.8%, the BTN defended 18.3%. On a A54r flop the SB only was c-betting 13.6% of the time for a 62% pot c-bet, even in a version of the scenario where the BTN was not allowed to raise a c-bet with a small sizing (which should favor c-betting more, not less).

Of course as poker players, we care about EV, not frequency, so this raises the question, how much EV would one lose by adopting a more aggressive c-betting frequency in this type of spot if your opponent were to minimally exploit you? It turns out the EV loss for c-betting 63% here is around 35bb/100 which is about 35 times the nash distance.

The relevant solutions are here:

C-betting to aggressively on A high boards is one of the more common leaks that many regulars have and this is a good simple example illustrating that even an opponent who will never attack you with bluff raises can still substantially exploit this approach. If a non-all in raise against a c-bet were allowed the amount of potential exploitation would only increase.

I believe that the addition of minimally exploitative calculations opens up many new avenues of study for using GTO computations to analytically improve your poker game and I leverage minimally exploitative calculations heavily myself.

That's it for today, thanks as always to our community for coming up with quality scenarios for study. For those of you who may have missed it the previous library highlights post is here: http://blog.gtorangebuilder.com/2015/04/gtorb-flop-library-highlights-1.html

## Tuesday, June 30, 2015

### July Asuth Strategy Pack Sale

For the month of July if you purchase our new In Position C-Betting Strategy Pack from the GTO Dojo you can get 50% either my GTO Flop C-bet defense strategy pack or my GTO Play in 3-bet Pots strategy pack. Just purchase both packs at the regular price via paypal and email gtorangebuilder@gmail.com and we will refund $50 of your purchase within 24 hours.

You can check out the preview for the In Position C-betting Strategy pack in the GTO Dojo.

You can check out the preview for the In Position C-betting Strategy pack in the GTO Dojo.

## Thursday, June 25, 2015

### New C-betting Strategy Pack Available in the GTO Dojo

I'm very excited to announce the release of my first strategy pack on c-betting which focuses on c-betting after raising from in position and getting called by an out of position player. The second half of this strategy pack has a lot of material that I don't think has been explored by anyone else before because it focuses heavily on using minimally exploitative calculations to identify and measure leaks in c-betting strategies. I also demonstrate how different board textures allow for different levels of flexibility to c-bet exploitative without fear of counter exploitation.

This pack features over 30 GTO and exploitative flop solutions that are carefully constructed and over two hours of video analysis. The first ~7 minutes are available on youtube for free, you can check it out below.

This pack features over 30 GTO and exploitative flop solutions that are carefully constructed and over two hours of video analysis. The first ~7 minutes are available on youtube for free, you can check it out below.

## Wednesday, June 10, 2015

### GTORB in Ivey League Session Review

One of the easiest ways to use GTORB to improve your play is to compare GTORB resutls against actual hands from your recent sessions during post session review. Ivey League pro "The Student" recently released a training video on how GTORB can best be used for session review in his latest training video here:
http://iveyleague.com/video/micro-stakes-session-review

## Friday, June 5, 2015

### New GTO Strategy Pack Release -- GTO Postflop Play in HUSNGs ft. Coffeeyay from HUSNG.com

Our latest GTO strategy pack was created in conjunction with HUSNG.com and their lead coach Coffeeyay. This strategy pack focuses on postflop play both in limped and raised pots with 20-25 BB stacks. We were able to work with Will Tipton to get the exact preflop ranges that were used to generate the charts in his book and these scenarios all use a smoothed version of those ranges.

HUSNGs are on of the game types where directly applying GTO computational solutions to improve your play is easiest and most effective and this video pack should give you insight into how one of the top coaches in the HUSNG communities leverages GTORB solutions to construct stronger ranges and win more money.

You can check out a sample segment from the strategy pack in the preview video below.

HUSNGs are on of the game types where directly applying GTO computational solutions to improve your play is easiest and most effective and this video pack should give you insight into how one of the top coaches in the HUSNG communities leverages GTORB solutions to construct stronger ranges and win more money.

You can check out a sample segment from the strategy pack in the preview video below.

## Saturday, May 9, 2015

### Get access to the GTORB Flop Library for just $20 with the new GTORB Library Pass

Yesterday we launched a new purchase option, the GTORB Library Pass which gives full access to browse our flop solution library and discuss solutions with other users for just $20 per month (with our 50% launch sale). Our flop solution library currently has almost 500 flop solutions with more being added every day, for some highlights from the library see this post: http://blog.gtorangebuilder.com/2015/04/gtorb-flop-library-highlights-1.html

You can also check out our 3 free library solutions without making a GTORB account in our GTO Dojo here: http://gtorangebuilder.com/#gto-dojo to get an idea of what a GTORB flop solution looks like. Just click the "View the GTORangeBuilder Flop Library" button and the free solutions will be right at the top with the "free" tag.

With hundreds of GTO flop solutions instantly available at your fingertips for just $20 the library pass is an incredibly effective way to study GTO play at a great price.

You can also check out our 3 free library solutions without making a GTORB account in our GTO Dojo here: http://gtorangebuilder.com/#gto-dojo to get an idea of what a GTORB flop solution looks like. Just click the "View the GTORangeBuilder Flop Library" button and the free solutions will be right at the top with the "free" tag.

With hundreds of GTO flop solutions instantly available at your fingertips for just $20 the library pass is an incredibly effective way to study GTO play at a great price.

## Tuesday, April 21, 2015

### GTORB Flop Library Highlights #1

I'm going to start making a blog post approximately once a month with highlights and takeaways from some of the more interesting scenarios from the GTORB Flop library. It has been a busy month for me as the GTORB library has almost doubled in size and is now approaching 400 solutions. My goal is to continue to rapidly expand the library with a lot of user submitted content at least until we reach around 1,000 solutions at which point I may start to focus more heavily on curating content and only adding the very best and most interesting new submissions.

For this post I am going to focus on the impact of bet sizing and game tree construction on understanding computational GTO solutions. The high level take away from our data so far is that bet sizing can significantly change ranges but is unlikely to change EVs

However, if you decide not to include a non-committing re-raise in the game tree, this is a different situation and you are actually completely removing a relevant strategic option from a players arsenal. In this case you can often get significant strategy shifts as well as EV shifts, and in general if you use game trees that are not carefully constructed to include the real world bet sizing strategies that players are likely to employ you may get awkward results.

Put another way, bet sizing doesn't matter... except when it does.

I also wanted to mention that we are creating a GTORB skype group for people to analyze existing library solution and brainstorm ideas for new submissions. If you are interested please email gtorangbuilder@gmail.com (a GTORB pro license is required).

Finally I wanted to highlight two other items. I've gotten a number of inqueries regarding when I plan to release my next strategy pack on blind vs blind play, I'm aiming for the middle of next month. I also have put together a very short survey for you guys with some questions on how you'd like me to prioritize my future work on GTORB so please take a minute to answer here.

Thanks!

For this post I am going to focus on the impact of bet sizing and game tree construction on understanding computational GTO solutions. The high level take away from our data so far is that bet sizing can significantly change ranges but is unlikely to change EVs

**so long as the available bet sizes do not omit important strategic options.**So for example, it will generally be GTO to c-bet a wider range if you c-bet 50% pot vs 70% pot and your opponent will likely want to defend significantly wider, but your EV will usually be almost identical regardless of which bet size you use.However, if you decide not to include a non-committing re-raise in the game tree, this is a different situation and you are actually completely removing a relevant strategic option from a players arsenal. In this case you can often get significant strategy shifts as well as EV shifts, and in general if you use game trees that are not carefully constructed to include the real world bet sizing strategies that players are likely to employ you may get awkward results.

Put another way, bet sizing doesn't matter... except when it does.

I also wanted to mention that we are creating a GTORB skype group for people to analyze existing library solution and brainstorm ideas for new submissions. If you are interested please email gtorangbuilder@gmail.com (a GTORB pro license is required).

Finally I wanted to highlight two other items. I've gotten a number of inqueries regarding when I plan to release my next strategy pack on blind vs blind play, I'm aiming for the middle of next month. I also have put together a very short survey for you guys with some questions on how you'd like me to prioritize my future work on GTORB so please take a minute to answer here.

Thanks!

### Community remixing gets to the bottom of a surprising 20% raise c-bet frequency in a 3-bet pot.

The first highlight I want to take a look at started with a GTORB user submitting this scenario: http://gtorangebuilder.com/#share_calc=TcTd4s_faff00f970bc3c07746865b1e5ed31b7.

The situation is a 3-bet pot, SB vs BTN with a 15.8% linear SB 3-bet range vs an 18.3 % BTN call range. In this spot, BTN opens to 2.5bbs, SB 3-bets to 8.5bbs, BB folds and BTN calls. The solution was immediately interesting because it had the BTN raising a half pot c-bet from 90 to 225 nearly 20% of the time. Another user quickly noted that in practice many players don't raise a flop c-bet at all here and so he ran a minimally exploitative version of the scenario where the option to raise the flop c-bet was removed, which is here: http://gtorangebuilder.com/#share_calc=TcTd4s_2f1e030ffe8967608e003842ed907222

It turned out that due to the IP player never raising a flop c-bet the OOP player gains 0.7 chips, (this is far outside the nash distance of the scenarios which were all in the neighborhod of 0.1-0.2 chips) or 7bb/100. While not enormous this appears to be a significant mistake. However, another GTORB user made an important observation. The initial game tree did not include the option for a non-committing re-raise from the c-bettor. To investigate if it was possible for the SB to regain at least some of that 7bb/100 by being able to threaten a flop raise with a semibluff reraise he submitted a new scenario where the SB can make a small reraise. http://gtorangebuilder.com/#share_calc=TcTd4s_0dc2c56662b730628b7c563673ea9762

It turns out that giving the SB this option reduces the BTNs flop c-bet raise frequecny down to 1% and allows the SB to capture almost the full minimal exploit EV that he achieved against an opponent who never raised! Adding this one single node to the game tree basically eliminated what at first glance had seemed like an important part of the BTNs defense strategy. It also allowed the SB to c-bet significantly more aggresively, upping his c-bet frequency from 75% to 83% now that he no longer needed to fear facing a bluff raise. Note that the solution accuracy in this spots is generally on the order of 1-2 tenths of a chip or 0.05-0.15% of the pot so they are extremely accurate.

As a final iteration on this scenario, another use noted that the same flaw in the game tree existed from the BTNs perspective. When the hero check raised, there was no option for the BTN to respond with a non-committing reraise which meant that after checking the hero was raising nearly 50% of the time!

As a result a final version of the scenario was submitted with the option for a small reraise over a check raise here: http://gtorangebuilder.com/#share_calc=TcTd4s_52bb1b4a56284543f1ea489c7b9e379f.

As it turns out this change did not allow the BTN to capture much additional EV, instead it caused the SB to c-bet even more, including a number of the hands that it was no longer higher even to check raise.

I believe the final iteration of this solution represents strong play and pretty accurately models the real world no-limit version of this situation so it was very cool to see the community come together and build/improve on each others work. It is also impressive to see what a strategical difference we can see in GTO play between the first iteration of the scenario and the last.

The final EV impact of incorporating these strategic options seemed to be a shift of about 5bb/100 for the hero (in a spot like this it would be common for winrates to be on the order of 250bb/100 so this represents about 2% of your overall winnings in these spots as the SB), but it made me wonder about the following.

Suppose someone were to play according to the original version of the scenario and decided to start raising the flop in these spots 20% of the time with the initial GTORB range that assumed your opponent could not make a small reraise. How big of a mistake in terms of EV would this actually be?

This is a bit of a complex question to answer. The first approach to answering it would be to lock in the BTNs response to a flop c-bet and to then do a minimally exploitative calculation (I show how to do this using simple postflop in this post). To do this, I first ran the version of the game tree that did not include the small flop reraise, I then locked in the response to a c-bet, added the small flop 3-bet and reran the scenario. I then compared it to the EV for the SB in the same situation without a locked strategy (where the BTN chooses to only raise a flop c-bet 1%). The EV difference for the hero between these two scenarios was about .12bb per hand or 12bb/100. The minimally exploitative strategy used the small 3-bet option exclusively when it did not fold and shifted its c-betting frequency to nearly 100%.

This full minimally exploitative strategy involves altering our c-betting significantly so I also wanted to look at a downstream only minimally exploitative strategy. In a downstream only calculation we only alter our response to the c-bet raise, we do not actually shift our c-betting range (or our play on any other parts of the game tree) at all. In this case the EV gain for the hero was only slightly reduced to about 11bb/100.

I've put all the simple postflop files I used for this analysis up for download here. To view them you will need to download simple postflop. Note that the simple postflop scenario expresses all quantities in big blinds not in chips. Also, I did not manually make the turn and river trees identical in gtorb and in simple postflop and the nash distance in the simple postflop calcs is a bit higher than the gtorb calcs (although both are extremely accurate to < 0.1% of the pot) so there are minor strategy and EV difference in the GTO vs GTO strategies between GTORB and simple postlop that are within the nash distances of the respective programs.

I think the main take away from all this is that you should always take the time to preview and inspect your game tree using the GTORB tree editor and you should be sure to manually edit sizes and add/delete nodes as needed to make sure that all core strategic options such as non-committing reraises are available to each player even if the exact sizings don't seem to matter as we'll see in our next example.

It is well worth your time to think carefully and manually construct a great game tree so that you can study the results with confidence. I often spend 30 minutes or more on the ranges and game trees that I use in my strategy pack videos.

### In both MTTs and Cash c-bet sizing deep stacked shifts optimal ranges but not EVs

The second example that struck me from this month's submissions were some scenarios that were created by a MTT player who decided to remix some of the scenarios from my flop c-bet defense strategy pack using MTT hand ranges and looking at situations that are 50bbs deep with antes.

One might think that GTO play would look substanially different in a 50bb deep MTT situation on K86ss vs a 100bb deep 6-max situation on K86ss but it turns out that both optimal play and the equilibrium EVs for both players are shockingly similar.

In my flop c-bet defense strategy pack I looked at this BTN 2,5x open vs BB call scenario with a 2/3rds pot c-bet on a Kh8d6h flop. http://gtorangebuilder.com/#share_calc=Kh8d6h_e726a4f8e41f993987b4d5e073e8143f

The MTT player decided to run 3 versions of the same scenario using MTT ranges with 50bb stacks and antes, each with a different c-bet size for the IP player. Links to each are below:

In this case in the 540 chip pot, the BTNs EV with a 50% pot c-bet is 331.3 and with a 75% chip c-bet it is 331.6 and the nash distance on both of those calculations is about 1 chip, just under 0.2% of the pot. The EV difference between the 2 is so small as to not be measurable within our accuracy (and the solution accuracy is very good in these scenarios).

The 33% pot c-bet EV was 329.0 which does seem very slightly lower but the the nash distance on this solution was 1.4 chips meaning that it is just barely detectably different from the 50% pot c-bet EV. It appears that a 33% size may be slightly too small but that it is quite likely that a strategy with equal EV can be constructed using any sizing between 40% and 75% or higher.

Of course while the EVs are more or less the same in all these spots, the strategies vary significantly. with a c-bet percentage ranging from 60% at the smallest size to 46% at the largest and a fold to c-bet ranging from near 30% to near 50% depending on the sizing.

From a players perspective this means that you have a fair amount of freedom to choose whatever c-bet size you like without impacting your EV significantly, even if your opponent responds optimally to your sizing. You can pick a size that your opponent is likely to respond poorly to, as if they defend a range that is optimal vs a 50% size when you are c-betting 75% pot they will be making major mistakes with much of their range.

What also struck me was that even though these MTT scenarios used different ranges and different stack sizes from the scenario in my flop c-bet defense strategy pack (which was focused on 6-max), the % of the pot captured by each player was almost identical. 62.0% for the BTN in the 6-max case vs 61.4% in the MTT case. It appears that players preflop ranges must be extremely well honed in both cases to perform very similarly, at least on this flop texture.

Finally I should mention that the finding that the c-bet size has little to no impact on EV in deep stacked single raised pots matches the results from my flop c-bet defense strategy pack where I ran two CO vs BB scenarios with a 50% pot c-bet and a 66% pot c-bet.

In this case the EVs for the c-bettor wer 33.74 with the 66% c-bet and 33.77 with the 50% pot c-bet, with the 0.03 chip EV difference being within the margin of error of the ~0.1 chip nash distances.

## Friday, April 10, 2015

### The Perfect Complement to the GTORB Flop Library: Simple Postflop

By now most of you have had a chance to check out the GTORB Flop Library which is a great place to find precomputed, instantly-accessible, curated and community-recommended GTO flop solutions. The GTORB Flop Library lets you discuss flop solutions with the community and our pros, and share solutions and build new ones based on the game trees and ranges others have created.

As a compliment to what the library has to offer, I'd like to recommend a new tool called Simple Postflop that allows you to solve your own GTO flop scenarios privately either on our own desktop or in the cloud. I've been using Simple Postflop to test and prototype solutions that I plan to use in my videos or add to the library because it can solve most flop scenarios in well under an hour (and for simple things like 3-bet pots it often just takes a few minutes).

You can paste ranges from GTORB directly into SimplePostflop and we are working on letting you paste in full scenario configurations. We are also looking into using the Simple Postflop engine to run scenarios for the GTORB Flop Library and strategy packs.

What really got me excited about this program is that they are the first to implement the ability to run minimally exploitative calculations which I am going to be using in my next few strategy packs. I've also made a new youtube strategy video using minimally exploitative calculations to measure the magnitude of the leak of a 1-alpha c-bet defense here: http://blog.gtorangebuilder.com/2015/04/minimally-exploitative-play-measuring.html.

For anyone interested in giving Simple Postflop a try definitely check out my tutorial video below and if you have any questions on the software feel free to ask in the comments below. The creators of the software are Russian so English is not their first language and thus I have offered to help answer any questions about the software and to also teach people how to use it.

Note for full disclosure that I have worked out a partnership with Simple Postflop and thus I am financially incentivized to encourage people to buy it.

As a compliment to what the library has to offer, I'd like to recommend a new tool called Simple Postflop that allows you to solve your own GTO flop scenarios privately either on our own desktop or in the cloud. I've been using Simple Postflop to test and prototype solutions that I plan to use in my videos or add to the library because it can solve most flop scenarios in well under an hour (and for simple things like 3-bet pots it often just takes a few minutes).

#### GTORB readers can get 10% off a Simple Postflop desktop license by clicking here.

You can paste ranges from GTORB directly into SimplePostflop and we are working on letting you paste in full scenario configurations. We are also looking into using the Simple Postflop engine to run scenarios for the GTORB Flop Library and strategy packs.

What really got me excited about this program is that they are the first to implement the ability to run minimally exploitative calculations which I am going to be using in my next few strategy packs. I've also made a new youtube strategy video using minimally exploitative calculations to measure the magnitude of the leak of a 1-alpha c-bet defense here: http://blog.gtorangebuilder.com/2015/04/minimally-exploitative-play-measuring.html.

For anyone interested in giving Simple Postflop a try definitely check out my tutorial video below and if you have any questions on the software feel free to ask in the comments below. The creators of the software are Russian so English is not their first language and thus I have offered to help answer any questions about the software and to also teach people how to use it.

Note for full disclosure that I have worked out a partnership with Simple Postflop and thus I am financially incentivized to encourage people to buy it.

## Friday, April 3, 2015

### Minimally Exploitative Play --- Measuring leaks with Simple Postflop

In my latest free youtube strategy video I go through what minimally exploitative play is and how to calculate it using the Simple Postflop solver. All GTORB readers can get 10% off the standalone version of Simple Postflop just by clicking this link. Minimally exploitative play is also now built into GTORB directly and you can access it buy going to "Customize game tree" and locking in a strategy at a decision node.

Minimally exploitative play can be calculated by locking a certain portion of a players strategy (that represents the leak we wish to exploit) and solving the game tree for a GTO solution conditional on that specific part of the strategy being locked. This results in a strategy that is unexploitable, so long as the specific leak that we are exploiting exists.

The video above examines OOP c-bet defense on a K86ss board that I analyzed in my Flop C-bet Defense strategy pack which is available in the GTO Dojo. I've made the K86 solution freely browseable by anyone (with or without a GTORB account or license) and you can check it our here: gtorangebuilder.com/#share_calc=Kh8d6h_MC0cb81ppNmrbITbU52U4JCnSaq3IBqaZ

It turns out that on this board GTO c-bet defense involves folding to a 2/3rds pot c-bet about 50% of the time which is significantly higher than the often used "1-alpha" minimum defense. In the C-bet defense strategy pack I explained in depth why minimum defense frequencies rarely apply to flop play, but In this video I use minimally exploitative play to measure the exact magnitude of the error of playing according to a 1-alpha defense which is something that many very strong midstakes players do. The magnitude of the leak ends up being about 4.5bb per hundred conditional on defending your blind, and in the video I show how to actually compute the minimally exploitative strategy that is guaranteed to extract this 4.5bb/100 value against a player who sticks to a 1-alpha based defense.

For anyone interested in learning to use Simple Postflop to calculate minimally exploitative play you can also check out my Simple Postflop Tutorial. This functionality will also be built into GTORB itself in the coming months.

Minimally exploitative play can be calculated by locking a certain portion of a players strategy (that represents the leak we wish to exploit) and solving the game tree for a GTO solution conditional on that specific part of the strategy being locked. This results in a strategy that is unexploitable, so long as the specific leak that we are exploiting exists.

The video above examines OOP c-bet defense on a K86ss board that I analyzed in my Flop C-bet Defense strategy pack which is available in the GTO Dojo. I've made the K86 solution freely browseable by anyone (with or without a GTORB account or license) and you can check it our here: gtorangebuilder.com/#share_calc=Kh8d6h_MC0cb81ppNmrbITbU52U4JCnSaq3IBqaZ

It turns out that on this board GTO c-bet defense involves folding to a 2/3rds pot c-bet about 50% of the time which is significantly higher than the often used "1-alpha" minimum defense. In the C-bet defense strategy pack I explained in depth why minimum defense frequencies rarely apply to flop play, but In this video I use minimally exploitative play to measure the exact magnitude of the error of playing according to a 1-alpha defense which is something that many very strong midstakes players do. The magnitude of the leak ends up being about 4.5bb per hundred conditional on defending your blind, and in the video I show how to actually compute the minimally exploitative strategy that is guaranteed to extract this 4.5bb/100 value against a player who sticks to a 1-alpha based defense.

For anyone interested in learning to use Simple Postflop to calculate minimally exploitative play you can also check out my Simple Postflop Tutorial. This functionality will also be built into GTORB itself in the coming months.

## Wednesday, March 18, 2015

### The GTORangeBuilder Flop Library is Live

I'm happy to announce the release of the GTORB Flop Solution Library which currently contains almost 200 pre-computed flop solutions from a variety of game types with many more to come. The solution library is searchable, and there are discussion threads for every solution where you can join our community in analyzing GTO play.

Anyone can browse the contents of the library for free, even if they do not have a GTORangeBuilder account and we have made 3 of the solutions freely available to the public. The other solutions can only be viewed license holders and only license holders can submit new scenarios that they would like to see added to the library.

Regarding licenses, all existing turn license holders have automatically been upgraded to GTORangeBuilder Pro licenses and will receive full library access for free. We also have removed the 250 monthly cap on turn calculations, you can now run as many as you want. Finally, we have removed the option to purchase a monthly GTORangeBuilder license and have instead replaced it with a 6 month license with no recurring charge or activation fee.

Anyone can browse the contents of the library for free, even if they do not have a GTORangeBuilder account and we have made 3 of the solutions freely available to the public. The other solutions can only be viewed license holders and only license holders can submit new scenarios that they would like to see added to the library.

Regarding licenses, all existing turn license holders have automatically been upgraded to GTORangeBuilder Pro licenses and will receive full library access for free. We also have removed the 250 monthly cap on turn calculations, you can now run as many as you want. Finally, we have removed the option to purchase a monthly GTORangeBuilder license and have instead replaced it with a 6 month license with no recurring charge or activation fee.

## Monday, March 9, 2015

### GTO Play in 3-Bet Pots strategy pack is now available in the GTO Dojo

I just finished my second video pack on GTO play in 3-bet pots, which features a bunch of theory on equity realization with lower stack to pot ratios. One of the more interesting results is that the standard theory of only betting when you can be called by worse or fold out better doesn't hold up and that often times in larger pots, aggression with a merged range is optimal because it is the most efficient way to lock in equity when the stack to pot ratio is small and you are out of position.

This pack includes about 80 minutes of video as well as 21 pre-computed GTORB flop solutions that examine both in position and out of position play in 3-bet pots on a variety of boards. I've put the first ~10 minutes of the video up on youtube for free, you can check it out below, the entire pack is available in the GTO Dojo.

This pack includes about 80 minutes of video as well as 21 pre-computed GTORB flop solutions that examine both in position and out of position play in 3-bet pots on a variety of boards. I've put the first ~10 minutes of the video up on youtube for free, you can check it out below, the entire pack is available in the GTO Dojo.

## Sunday, March 1, 2015

### The GTORB Flop Solution Library is coming!

We’re happy to announce the upcoming release of the GTORB Flop Solution Library which we're hoping to

release a week from Friday (March 13th). Here’s a breakdown of how it works:

release a week from Friday (March 13th). Here’s a breakdown of how it works:

- 100+ (and growing) precomputed, instantly browseable, high-quality flop calcs. These calcs are tagged by game type and are fully searchable so that you can quickly find solutions that apply to specific real world conditions from your games.
- Discussion threads and up/down voting on each flop calc so the GTORB community can help you find and understand our best content.
- We’ll continue to add solutions to the library driven by your requests. Tell us what you want to learn about and we’ll add it!

**Be sure to comment below with your thoughts and what you’d like to see in the library.**

We’re also working on more GTORB Strategy Packs which combine precomputed flop calcs with video and mathematical analysis. Our first pack on Flop C-bet Defense is enormously popular so we’ll be following it up with a pack on in and out of position post-flop play in 3-bet pots very soon!

GTORB Flop Solution Library pricing is still being determined but we plan to automatically add free library access to all GTORB Turn licenses.

## Friday, February 13, 2015

### GTO Flop c-bet defense strategy pack is now available in the GTO Dojo

I've been working very hard on adding to the GTO Dojo and the first big step came today. I just released my first strategy pack, which explores optimal defense frequencies / ranges OOP against c-bets on the flop. The main goal is to understand how defense frequencies vary across board textures, how relevant (or not) models like 1-alpha defense and the [0,1] game are to C-bet defense and how we can use actual real-world GTO solutions to win more money in these spots.

While the theoretical analysis should be largely applicable across game types, the strategy pack focuses on single raised pots with 6-max cash stacks/ranges and includes 12 fully browseable GTORB flop solutions.

You can browse strategies for both the in-position c-bettor and the out of position defender on the flop and on every possible turn / river situation/runout across seven different boards / bet sizes / game trees. The pack also includes about 90 minutes of video commentary, and a few pages of mathematical notes and calculations.

I've put the first ~8 minutes of the video up on youtube for free, you can check it out below, the entire pack is available in the GTO Dojo.

This is my first time releasing a pack like this so definitely let me know what you think!

While the theoretical analysis should be largely applicable across game types, the strategy pack focuses on single raised pots with 6-max cash stacks/ranges and includes 12 fully browseable GTORB flop solutions.

You can browse strategies for both the in-position c-bettor and the out of position defender on the flop and on every possible turn / river situation/runout across seven different boards / bet sizes / game trees. The pack also includes about 90 minutes of video commentary, and a few pages of mathematical notes and calculations.

I've put the first ~8 minutes of the video up on youtube for free, you can check it out below, the entire pack is available in the GTO Dojo.

This is my first time releasing a pack like this so definitely let me know what you think!

## Tuesday, February 3, 2015

### Verifying a GTORangeBuilder Flop Solution with CREV

As I showed in my Epsilon equilibrium blog post, simple turn and river GTO strategies are generally quite easy to verify with CREV using the standard epsilon distance measurement.

However, it turns out that flop solutions with real world hand ranges are too far too big to actually enter into CREV. In the video below I demonstrate how to verify an individual slice of GTORB flop solution using CREV and also offer a sneak peak of a fully browseable GTORB flop solution (a GTORB turn license is required to view it). The CREV file is also below.

Here is the GTORB Solution from the video:

And here is the CREV file download:

https://s3.amazonaws.com/GTOBlogData/25bb+3bet+KT7r+bet+call+from+flop.stx

However, it turns out that flop solutions with real world hand ranges are too far too big to actually enter into CREV. In the video below I demonstrate how to verify an individual slice of GTORB flop solution using CREV and also offer a sneak peak of a fully browseable GTORB flop solution (a GTORB turn license is required to view it). The CREV file is also below.

Here is the GTORB Solution from the video:

And here is the CREV file download:

https://s3.amazonaws.com/GTOBlogData/25bb+3bet+KT7r+bet+call+from+flop.stx

Subscribe to:
Posts (Atom)