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
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