Thursday, February 4, 2016

GTO Brainteaser #10 -- Flipping coins

While this problem isn't directly related to game theory, it does bring up some very interesting concepts from probability which is another essential mathematical topic in poker.  Its also a really great brainteaser so I decided to go ahead and post it even if it is 100% GTO related.  Disclaimer, I didn't not make this problem up, its a very old problem often taught in statistics that I was recently reminded of by reddit.

Problem:

You go to a casino and see that they've introduced a new game.

They are flipping a fair coin and to play you must make a $100 bet.  They will start flipping the coin and keeping track of the outcomes of heads or tails.  They will keep flipping until they either get the sequence heads, heads, tails or heads, tails, tails over their last 3 flips.

If heads, heads, tails comes first the game ends and you lose your bet of $100 for a loss of $100.  If heads, tails, tails comes first the game ends and you win $105 (plus you get your $100 back) for a profit of $105.

So for example if they get:

HTHTHTT

Then you win.  On the other hand if it comes

THTHHT

then you lose.

Is the game positive EV?  What is the EV of the game?

Bonus:  On average, when you win how many flips does this game take?  What about when you lose, what is the average number of flips in that case?

Also, just incase you missed some of my past brainteasers here are links to the past problems (except the true/false quizzes).

Monday, February 1, 2016

New SimplePostflop HUSNG Preflop Solution Pack is Available

I'm excited to announce that I've worked with SimplePostflop to release a preflop strategy pack that has HUSNG solutions at every stack size from 5BB up to 25BB in 1BB increments.  All the solutions use 184 board flop subsets, include overbets and standard bet sizes in the postflop game tree, and have very low nash distances, making the pack for more precise than existing approximations.

You can learn more and buy the pack here: simplepostflop.com/en/Solutions_Library?source=gtorangebuilder.  By using that link you will also get a $17.50 discount.  You need to download the free version of SimplePostflop to view and browse the preflop solution files, but no other license is required, you can just buy the pack and you're good to go.

I believe this is the most comprehensive HUSNG solution pack out there and the results are pretty fascinating.  Some highlights of interest:

  1. Between 18bb and 25bb stacks we see a slow steady shift from limping to minraising from the SB, with the limping frequency decreasing about 3% for each 1bb increase in effective stack size.  At the same time the SBs EV advantage steadily grows as stack depth increases.
  2.  At stack sizes of 20bb+ a 2.5x raise against a limp is almost never used and a large size is favored.  However in the 12-16bb range a mix of using two different raise sizes against a limp is favored.
  3. 13bb is about the lowest stack size at which the SB should ever use a minraise as part of his strategy.
And of course there is much more.  To fully study and learn the full GTO strategy from this pack would take weeks or months and it contains everything you need to implement GTO play in HUSNG.

I've also gone ahead and put up 5 free GTORB postflop solutions that use the minraising and calling ranges from the preflop solution pack at 25bbs.  You can explore them at the links at the bottom of the post.

I've also found it very interesting to compare the results in this pack to the results from Coffeeyay's SB vs BB Spins pack (where the SB is OOP) as it allows us to measure the value of position and to analysis its effects.  That pack is also available here and GTORB users can get $10 off with this link: http://simplepostflop.com/en/Solutions_Library?source=gtorangebuilder


Free GTORB Postflop Solutions


Enjoy!

Thursday, January 28, 2016

Why and how to learn GTO -- The GTO Learning Path

One of the most common questions that I get from players who are looking to get started with learning GTO and integrating GTO concepts is "where do I start?".  Over the last year or two I've put out so many videos / blog posts / strategy packs, etc that it can be difficult to know where the jump in, whether you are completely new to GTO or whether you already have a strong fundamental understanding of GTO concepts.

At the bottom of this post I'm going to put links to all of our relevant GTO articles, videos, strategy packs, quizzes and brainteasers so that hopefully this post can be a one-stop place to learn everything you need to do to master GTO concepts and apply them to your game.

But before I lay out the curriculum I want to start by answering one of the most common and fundamental questions that every player should ask themselves before learning GTO theory and strategy.

Why should I learn GTO?


The core answer is simple very simple, to win more money!  How exactly understanding GTO theory does this however is more complex and often very misunderstood so I want to directly state the core values of learning GTO strategy and dispel some of the misinformation that is out there.  Perhaps the biggest misconception is the idea that the goal of learning GTO is so that we can play the GTO strategy 100% of the time and abandon exploitative play completely.  As we'll see below that is of course ridiculous, and in fact, an understanding of GTO is an invaluable tool in identifying and exploiting leaks in our opponents play.

At the poker table we are going to encounter a variety of players of various skill levels who play a wide variety of strategies.  At various times we will be playing in a situation where we have no read whatsoever on our opponents, or against a player who we know is stronger than us.  At other times we will be playing against weaker players who have clearly defined strategy errors that we believe they are unlikely to correct and that we can exploit.  

Our ability to win in the long run requires that we can both play fundamentally strong poker that is difficult for our opponents to exploit in situations where we are readless or against strong opposition, while also being able to quickly identify and attack leaks in our opponents' strategies in ways that do not open us up to counter exploitation.  Both of these goals are nearly impossible to achieve without a strong understanding of GTO strategy.

Lets begin by considering how to identify and attack leaks in our opponents.  Lets imagine that you are facing an opponent in a 100bb cash game who raised UTG to 3x and you flatted from the button and the other players folded.  He c-bets 80% of the pot on a AT3r flop.  You look at your HUD and note that this players OOP c-bet frequency in single raised pots is 62% and that he opens UTG about 17%.  How should we react to his c-bet with various parts of our range?  

It turns out that without a reasonable knowledge of GTO strategy the question above is very difficult to answer and in fact that for years "standard" play approached this situation incorrectly.  We first might want to ask, is a 62% out of position c-bet frequency too high (and thus should be exploited by calling or raising a much higher % than usual and by betting near 100% after he checks a flop) or to low which of course would be exploited differently..  This is impossible to know without knowing what the correct, unexploitable c-bet frequency is in out of position pots.

With GTO computation we can actually directly asses what an appropriate c-bet frequency on this board is (about 15%) and browse the entire GTO strategy and compare it to how we think our opponent plays.  You can see an example of that here: http://gtorangebuilder.com/#share_calc=AhTc3s_817242a1f8d8ce5f75f7b848fcf709b0.  We can then lock in our opponents incorrect c-betting strategy and optimize our play computationally against that.

For a long time many players, who at the time were considered quite good,  c-bet a very high frequency here.  They got away with it because no one had the tools or knowledge to correctly identify and exploit the leak.

However, we now know that there are very few boards where c-betting more than 50% of the time as an UTG raiser vs a BTN call is GTO, so c-betting 62% on average is way too high.  This player is c-betting far too aggressively so we should attack his c-bet.  If we have enough of a read to know that this play might c-bet 62% on this specific flop texture we could use a minimally exploitative strategy calculation (which you can learn about below) to determine that even if our opponent plays the turn and river perfectly we can probably raise this bet with as much of 20% (~3x as often as we would raise against a GTO c-bettor) of our range and we should only fold the about a third of our range, netting an EV gain of about half a big blind in a single hand.  

If we believe our opponent at least recognizes that AT3r is a board that should be c-bet from OOP  less often than an average board we might exercise a bit more caution but we can again estimate his c-betting range and determine that we should raise/call far more than usual.  

Without knowing what the GTO c-betting strategy is like is this spot we cannot identify strategy errors.  We can note that some players c-bet in a spot more or less than the population average but we have no way to be sure if that is a mistake or actually play that is better than the population and history shows that significant population level strategy errors can exist in "standard" play for years before they are exploited and fixed.

Similarly consider the situation where we open a 17% UTG range and get flatted by an unknown player in the BTN (or a very tough player).  Since GTO play will grind out a steady profit against sub-optimal players and because we have no specific read on the exact leaks in the BTNs game, our best bet in this spot is generally going to be to c-bet according to GTO.  By having a fundamentally solid and well structured c-betting range in this spot we will increase our win-rate against unknowns and prevent stronger players from exploiting errors in our play.  We can neither prevent leaks from appearing in our own game, nor can we systematically identify and exploit leaks in other players games without knowing what exactly "leak free" GTO play looks like.

So hopefully that gives you guys motivation to put in the study time and become GTO experts.  Here's how you can do it.


GTO Resources / Learning Path






Thursday, January 21, 2016

Get a free strategy pack when you buy two --- through February 1st

By popular request I'm going to be offering a special strategy pack sale from now through February first.  Anyone who buys two strategy packs at the regular price between today and February 1st 2016 can get a third strategy pack that was created by me (Alex Sutherland) of their choice for free!  Just email gtorangebuilder@gmail.com once you've purchased two packs and tell me which free pack you'd like and I'll add it to your account within 24 hours.

As usual you can preview and purchase all of our strategy packs in our GTO Dojo at: http://gtorangebuilder.com/#gto-dojo

Enjoy!

Wednesday, January 20, 2016

SPF launches Preflop Solution Packs -- Discount for GTORB Readers

I'm excited to announce that SimplePostflop has released their first two preflop solution packs which are available for sale here: http://simplepostflop.com/en/Solutions_Library?source=gtorangebuilder . If you go to the site using that link you will automatically get a 5% discount of off all solution packs.  The packs give you full access to large pre-computed preflop solutions at a greatly reduced cost compared to constructing and calculating the solutions yourself (the existing two packs are in the $100-$200 range).

 No SPF license is required to purchase and use preflop solution packs, all you need is a free SPF account.

Right now there are only two packs available, one by Coffeeyay with SBvsBB solutions for spin-n-go situations and one with SBvsBB solutions at 50/75/100/150 stack depths for cash players.  Currently the cash solutions do not include rake but rake support as well as many more solution packs will be coming over the next few months. I'll also be personally constructing some preflop packs soon so keep your eye out for an announcement in the coming weeks.

Monday, January 4, 2016

GTO Betsizing Strategy Pack Released

I'm very excited to announce the release of latest strategy pack on GTO Bet Sizing which contains both pure theory on bet sizing and in depth analysis of optimal bet sizing on various board textures in 3-bet pots, single raised pots and on the river.  With ~2hrs of video and 80+ GTORB solutions this pack provides an indepth demonstration of how to study and analyze optimal bet sizing with modern computational tools.

This is also the first new strategy pack I've put out since the launch of the GTORB flop solver, which (in addition to letting you solve custom scenarios of your own design) lets you open any strategy pack solution, tweak the ranges / board / bet sizes as you see fit, and resolve the scenario, all in just a few clicks.

To encourage people to try this out I'm offering a special discount where anyone who buys the new GTO Bet Sizing pack before February 1st 2016 can get a month of GTORB flop access with 200 flop calcs for just $20.  Just purchase the strategy pack from the GTO Dojo and a monthly subscription from the GTORB buy now page and email gtorangebuilder@gmail.com and I'll refund $25 to you within 24 hours.

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, December 23, 2015

Christmas Discount Special + 20 Free Monotone Flop Solutions

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