ekethio

Hey Qing,

I really like your videos and the format. On this video, you mention that PIO bets small on the flop with nutted hands to protect weak hands that want to bet small. However, I think that might not be the case. At equilibrium, a line for a given hand is only picked if it has a higher EV compared to the EV of other lines. In fact, solvers wouldn't care about how other hands would perform but rather try to maximize the EV of each hand which in turn will maximize the EV of the range. In this specific case, betting small with nutted hands has higher EV compared to betting geometrically because those nutted hands benefit from being included in a weaker range and being attacked by opponents check raising range. Plus, there are two more streets to get the money in non-geometrically. I just wanted to clarify that balance and range protection aren't concepts solvers care about but just heuristics that make their results easy to understand.

Hi Ben,

Nice video. On your videos, you commonly point out players' mistake of value betting too light and other times for bluffing with hands with good showdown(enough pot share) on the river. I was just wondering, have you ever came across a combo at equilibrium that derives its EV on the river partially from folding better hands and to some extent getting called by worse? Or are river decisions comparatively very linear that this type of stuff never happens at equilibrium.

Thanks
Ek

I think it just depends on how the ranges work. Generally, if opponents range is relatively capped nutted hands want to bet as much as possible, even 6x pot or bigger to leverage the nut advantage to deny showdown equity to villain. But if ranges are relatively symmetric and we don't have good hands in our block betting ranges we might leak EV by capping our range in those spots.

Fair enough, I'm still a bit confused about the situation then, could you try explaining to me why it is that each hand doesn't purely take the highest EV line in solver sims if we're maxing EV hand by hand rather than maxing the EV of the range as a whole? I

I think part of the way mixed strategies work is that the EV's for betting checking or whatever action are maximized at those exact frequencies. For instance when we do block bet with the nuts, if we do it with more frequency than the mixed strategy suggests the EV of betting will decrease. So the solver is maximizing the EV of checking and betting weighted by each frequency. You can correct me if I am wrong though.

Is it possible for a given hand in a range to take a sub optimal line EVwise to raise the EV of the overall range?

SPR does matter. but only up-to a threshold. 5 to 1 and 10 to 1 provide the same results. In addition, the solution my contain multiple Nash Equilibrium, most of while involve a lot of check folding by OOP.

It is very interesting to see that, it isn't only Range and Ev advantage that affect the equilibrium strategy for all streets. Being capped has huge consequences, and as stacks get deeper, capped player will have a hard time extracting value from the Equity advantage.

Hi Ben,

I have been watching most of your videos recently. Great video. I guess one way to visualize the bluff catching situations is that the maximum achievable EV by the polarized player is never above the pot size (Bluff Catcher can have a simple folding strategy otherwise) , and since betting as big as possible insures bluff catcher folds at the highest frequency while having a 0 ev call it would mean betting max also maximizes EV by denying bluff catcher its share of the pot.