EDIT: I mean 852 two tone and 754 two tone!



I am very curious about these two outputs. The ranges are the same and the boards seem similar. Yes, BB has six combos of 65s on 974 but it has 4 combos of 43s on 852. BB has 6 combos of 86s and 76s.

While the 30% Cbet sizing frequencies are almost the same (34-35% of the time), UTG checks far less on 852 (42% of the time compared to 56%).

This is because UTG does a 150% overbet 23% of the time instead of 10% (48 combos instead of 22). Why is there such a big difference?

On both boards, sets are overbet a minority of the time, and top pair 17% to 20% of the time. But:

• Overpairs are overbet far more on 852 - 17% of the time or 6 combos compared to 1 combo. There are 36 combos of overpairs instead of 30 on a 9 high instead of an 8 high board, but 99 is bet infrequently anyway (0.7 out of 6 combos, all of them with a spade.) The real difference is in AA-KK, which get overbet 33% of the time instead of 7% and QQ which gets overbet 22% of the time instead of never.
• Flush draws get an overbet 38% of the time compared to 23% (7.5 combos to 4.5)
• Overcards also get an overbet 38% of the time compared to 10% (33 to 12). Some of this is the FDs above, but we have a similar number of those. It's also hands like AQo, AJo, ATo, QJo being bet far more whether or not they have a BD draw.
• 2 card BD flush draws are overbet 14% of the time rather than 4% (3 to 1)
• In total it's 49 combos to 22.

Could it be how BB reacts to the overbet? When I look at BB reaction, we see a lot of folding on 852 - 62% of the time. But it's 63% on 974. The raise and call frequencies are virtually identical, too. Either way, they never fold their two pair, sets or (almost never) flush draws and they fold a lot of the rest.

So what explains such a big overbet frequency? Tombos's excellent article on flop overbets didn't quite explain it here for me, as his explanations work about as well on either board. https://blog.gtowizard.com/overbetti...in-cash-games/ I would be very interested in some theories.

I have now re-run 852 to make the 5 a diamond and the overbet frequency falls right down to the same as 974. So it seems like the potential for top pair plus FD hands in villain range is making the difference? The solver loves raising an overbet with these hands on both 8s5d2d and 9s7d4d.

any experiment can be cool and interesting but keep in mind this question is merely theoretical and has no application or usefulness to playing poker

Thank you for the kind words but this article was written by my colleague Steven Zahr

I was just gonna suggest it probably has something to do with Top Pair + Flush Draw being possible. Solvers will often play these FD boards differently compared to the other FD counterparts.

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I think it has something to do with villain's bluff-catcher region having more polarity against your nutted hands.

Yup, overbets don't work very well when villain has a large region of high-equity draws. Pair+flush draws, and even naked flush draws to some extent will discourage IP from betting too large. Which is why we see more overbetting when the board is rainbow.

It sounds counterintuitive, but the idea behind overbetting is not to "charge the flush draws". Rather, it's to build the pot against hands like JJ/TT, that are drawing almost dead against our value region. Think about it: when you overbet with a hand like AA, would you rather BB call with a weaker overpair, or some kind of flush draw?

Here's an excellent article that explains this concept in more detail. Or you can watch this video if you prefer something more visual:

This isn't universally true, though.

BTN vs BB we do a little bit more overbetting on flush draw boards than rainbow boards.



Weighted average sizing on flush draw boards is 0.61x pot.
Weighted average sizing on rainbow boards is 0.54x pot.

It’s true on low boards, where the betting range is more polarised (mostly overpairs and bluffs).

On higher boards, we have more marginal hands (eg middle pair, underpairs) that bet more often when the board is rainbow. Which is what drives the small betsize.

The stronger hands like TP and overpairs actually want to go bigger on rainbow boards. It’s just that many of them end up betting small along with our marginal hands, so we don’t see many leftover big bets.

Great article and video, kwuwai - thanks.