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 email@example.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.
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.