single cbet size outperforming multiple bet sizes?
hello everyone,
i recently ran an aggregate report for a specific spot over 19 representative flops. my aim was to identify the "best" bet size for a one-bet-size strategy (easiest to implement + as little EV regret as possible compared to multiple bet size solution). so i built a model where IP could choose from 4 different bet sizes or check back when checked to. then i ran the same report with the only difference being that IP is forced to range bet 33% when checked too (all other parameters, aswell as bet sizings on future streets etc. were the same). worked perfectly: on 4 out of 19 flops b33 range has less than 1% pot EV regret compared to multiple bet size solutions and on all other flops b33 range looses significant EV.
now comes the weird part:
i did the same for check/b75 when checked to. this strategy OUTPERFORMED the 4 bet size solution on ALL the 19 flops! how is this possible? i would've thought that the EV for IP with a stronger range would increase monotonically with the amount of possible bet sizes since solver can balance them perfectly and thus realize equity better with more bet sizes.
the only "explanation" i can think of is that it has something to do with board coverage/information advantage if IP splits its range early into the hand...
I am a beginner so maybe I am completely overlooking or misunderstanding something. any help/explanation would be most welcome.
thank you all
8 Replies
What accuracy did you run it to?
Multiple sizes will always have higher EV (however tiny), otherwise the solver wouldn't use them.
hello everyone,
i recently ran an aggregate report for a specific spot over 19 representative flops. my aim was to identify the "best" bet size for a one-bet-size strategy (easiest to implement + as little EV regret as possible compared to multiple bet size solution). so i built a model where IP could choose from 4 different bet sizes or check back when checked to. then i ran the same report with the only difference being that IP is forced to range bet 33% when checked too (all other parameters,
What accuracy did you run it to?
Multiple sizes will always have higher EV (however tiny), otherwise the solver wouldn't use them.
I would imagine OP is specifically talking about a HU hand ran in PIO or similar for a cash game hand. Zamadhi is correct in those instances and it is likely due to not running the sim long enough.
I did not know that though @plexiq. Do you have any simple toy game examples to illustrate this if you have time? or real examples?
I did not know that though @plexiq. Do you have any simple toy game examples to illustrate this if you have time? or real examples?
Tombos wrote an article about it.
In ICM, there is no guaranteed minimum EV if you play GTO, like there is in chipEV. This happens because EV can leak to the rest of the table.
So playing GTO vs a fish can have lower EV than playing GTO vs GTO!
And, yes, removing betting options can increase EV!
I would imagine OP is specifically talking about a HU hand ran in PIO or similar for a cash game hand. Zamadhi is correct in those instances and it is likely due to not running the sim long enough.
I did not know that though @plexiq. Do you have any simple toy game examples to illustrate this if you have time? or real examples?
For the most basic toy game example, consider how removing the "swerve" action of one player in "game of chicken" changes the equilibrium. (Game of Chicken / Wiki)
This comes up occasionally as support question when users test out multiple sizings in ICM or bounty spots, it's really not that rare.
I've actually read the gtowizard article, I guess I just forgot about it. I don't play MTTs so it is not something I've given much thought to.
Thanks for the links.
Thank you all very much for the replies!
I did only run the sims to 1% accuracy and all the EV-deviations in the single-bet-size sims compared to the baseline multiple-bet-size sim are within 1%.
I am wondering about two other things aswell tho:
1.) Is my approach here good? My goal is to develop cbet strategies for 6max. I would like to use a one-bet-size strategy on as many boards as possible. So my approach was to run an aggregate report with 3 bet size options (33, 50, 75) and then compare the EV to single bet-size-strategies to see on which flops I can simplify down to a single bet size. If the EV regret of a one-bet-size solution on a given board is within 1% of the pot I will study only that bet size on that given flop. Does this make sense? Is there anything to consider here I might not be seeing? I don't wanna do all this work just to find out later that the process is flawed.
2.) I am using a pretty simple game tree. On every node there is just a default bet of 66% (except the cbet size for IP which is the focus of the study). With only 2 bets left a geometric size is used instead of the 66% default bet. That's it. Is this simple model sufficient for the solver to realize equity in a way that makes the comparison of EV of multiple-bet-size solutions to EV of single-bet-size solutions meaningful?
Thank you all
2.) I am using a pretty simple game tree. On every node there is just a default bet of 66% (except the cbet size for IP which is the focus of the study). With only 2 bets left a geometric size is used instead of the 66% default bet. That's it. Is this simple model sufficient for the solver to realize equity in a way that makes the comparison of EV of multiple-bet-size solutions to EV of single-bet-size solutions meaningful?
No option for OOP to check-raise? If so, that will influence your solvers output to a degree where your results are not applicable in real games.
