Hi Guys, i made this question because i saw in the new update of the 3-bet shoving equity calculator excel paper that there is the chart with values in chips, in BB and also in $ EV. I don t understand the utility of the last one. Best regards, pazzopoli.
It's just approximating your $EV as being Prizepool*(chips you have)/(total chips in play). It's equivalent information as chipEV.
This approximation is making the assumption that you and your opponent are equally matched since it means that if you have half the chips in play (your starting stack) you win 50% of the time, and therefore 50% of the prizepool. This means it's not a great approximation if you expect to have edge vs your opponent--this concept is known as "winrate maximization". But that's a whole other conversation and not relevant to new players both because you have to prove you have an edge before assuming it and because it's a second order effect useful mostly for fine-tuning strategies.
Thanka Coffeyy for your answer,
Yeah it was exacly what i thought because i knew that in hu matche there aren t any kind of ICM considerations. But only for a theoretic interest , could you tell me an exampke in which we consider the fact that we have an edge against our opponent and we decide not to take a decision that is marginally +EV? The only one that came to my mind is for exampke if we are same stack against a very very very passive opponent and we decide not to take a flip at the begininning of the match (if we knew that will be a flip hipotetically)? Thank you for you answer!
Sure! It's actually a somewhat significant effect if you assume decent win-rate like 53%.
Let's say first hand you face an open shove in the BB, 25bb deep.
EV_chip(fold) = 0
EV_chip(call) = EquityVsShoveRange*50bb - 24bb
=>EV_chip(call) > EV_chip(fold) when EquityVsShove>24/50=48%
However, if we look at win-rates things are a bit different. Assume we expect 53% winrate at start of match. This means the winrate of a 25bb stack is 53%.
EV_Winrate(fold) = Winrate(24bb)
Winrate(24bb) ~ Winrate(25bb) - 1/50 (since we know that each bb in our stack is worth more than the chip EV estimate of 1/50 this is a reasonable approximation that likely underestimates our winrate by a little bit)
=> EV_winrate(fold) = Winrate(24bb) ~ 51%
Assume no ties when calling a shove, since these happen rarely
EV_winrate(call) = EquityVsShoveRange (since we win the match with probability equal to our equity and have 100% winrate, or lose with probability (1-Equity) and have 0 winrate)
=>EV_winrate(call) > EV_winrate(fold) when EquityVsShove>51%.
That's a 3% difference in results! Even if we were a little off with approximating the winrate of a 24bb stack (there are more sophisticated ways to approximate it) you can see that it's a very clear effect and changes how much equity you need to make calling better then folding by a fairly large margin (3% is huge when all-in, as evidenced by Nash push ranges shoving 54s even 20+bb while shoving 54o only extremely shallow).
Calling shoves is the place where this effect is the biggest, which is why I used it as my example since it's most obvious there. But this process does effect all of our decisions, just usually it's a much smaller size of an effect. One of the models I ran showed me that if you assume a 53% win-rate then open-shoving 22 when 25bb deep is ~.3bb worse (as far as I remember off the top of my head) when looking at winrate maxing (and then translating them back into chips) then a pure chipEV estimate using an open shove math tool like CoffeeCalcs or ICMizer would show. It ends up impacting every decision we make, whether it's pre-flop or post-flop (ex: calling shoves on river needs a bit more equity then pot odds would tell you as well).
It's pretty subtle stuff, but it is a noticeable effect and can be a way for very strong players to squeeze out more (win-rate) edge (though sometimes this can be at the expense of hourly!). It's also interesting (at least to me) that it's actually depends on actual stack as well as effective stack--the effect will be slightly different when you are the big stack then if you are the small stack. The reason for this is folding as a big stack brings the two stacks closer to even which is where you have the biggest edge, while folding as the small stack brings your stack closer to 0bb where you have 0% win-rate and therefore no edge, This difference in effect is very small though so best not to get too hung up over it :) Still it's kind of cool that in full theory even effective stacks aren't actually the end-all be-all of EV :D
Thank you soo much for your answer!
Really appreciate your explanation, very clear and very interesting! Thank you Coffeyay!