I believe its a pretty interesting question.

Lets say we got 10 blinds and our fishy vpip90 pfr 30 opponent (stats for sb) limps.

And we hold some kind of a hand (doesn't matter but could be K9o for example).

We could push here and then our equity would depend on opponents range to call our allin after doing a limp and that [limp/call range] equity against K9o.

But if we check how do you think would be most appropriate to approximate our hand EV? I guess it has to be some kind of forumula using our hand, current blinds and our chances against percieved opponents range, but which one suits better you think?

Thanks

empirical evidence is probably best.
lacking that you can try to make some sort of clever approximation. It probably ends up being .1->1BB depending on hand but that's a guess.

Use SAGE and you need not think about it, otherwise you are not knowing what to do on the flop. Get it in good pre flop with the wind at your back and be happy with about the way you played the hand.

So with K9 (10BB) I am shoving, hoping for a fold or a double up, I am happy with both outcomes really.

if he is passive im shoving pre hands like Ax Kx pocket pairs if he is thigt we can shove suit-conn type hands but we can also check and stab OTF so we dont risk our entire stack

Hey guys, im actually asking in a software developer role here. No need for SAGE cause everything is calculated precisely.

Im just thinking which algorithm should be better used when we compare push ev (easily calculated) and check ev (hard to calculate) here to get EV diffrence for such situation.

Pretty sure there's no way you could come up with a formula to compute the EV of checking back. There's just too many variables in a poker hand.

Empirical evidence is the only practical way to figure this out. If you play with the filters in PT3/HEM, you could get a pretty good idea of your own numbers if you have a large enough sample. Then you would need other people to give you their data so you can get an average number among winning players.

I agree with you. Analyzing a HUGE database could give us some insight into this.

However lets pretend this option is unavailble. And we need approximate (probably very approximate) algorithm here. Just to have some kind of a baseline to compare push with. Since effective stack size, our hand and opponent hand are like 3 variables, also with uneven distribution of player types etc , I think empirical evidence approach is super hard here.

So if we were to invent some "smart" approx formula, how do you think it would look. I suggest a kind of brainstorm here. Drop some ideas, but no emperical evidence.

Maybe if our hand is relatively good, and opponent range relatively tight we can expect higher postflop potsize? or smth like this. Formula approach I mean , thanks.

Empirical seems best. I agree.
my only thought is that may be you could use some sort of formula where your hand keeps it's flopped equity, like if it was checked post flop combined with some post flop fold Eq when villain doesn't hit anything.
I have tried to evaluate flatting that way with cardrunnersEV in the past but I wasn't convinced by the results I was getting.

Hmm, if we assume both players have no edge over eachother (therefore cancelling the effects of bluffing and value betting thinly), I guess a super loose approximation could be:

(Your hand's equity vs villain's range) * avg pot size in BBs in limped pots - BBs invested = EV of checking back

Example, K9o has 56.097% vs top 85.5% limping range. If the average potsize in limped pots is 4BBs, we win (4*0.56097 -2BB = +0.24) every time with that hand. If you want to add the effects of bluffing better/value betting thinner than villain, you add +0.xx BB to the above equation.

ya that's kind of what I had in mind. Just much better

but as you said it's a very loose aproximation. I tried to do that to calculate the EV of flatting to find out when it was better to flat or shove in end game. But the results were not even close to the empirical data.

Yeah I guess we are assuming equal skills here, for a baseline.

How should we calculate average pot size for given hand & opponent range though? If we are 100bb deep it can be different than if we are 10bb deep I think. (opponent might be more eager to take down 20% of stack then 2% as well as we in position)?

We're assuming skill differences are negated and the EV comes solely from our hand equity.

I really think you'd need to resort to empirical evidence once again to figure out the average potsize in a limped pot.

You can come up with some ridiculously loose way of approximating it.. but then I start to question how valuable the results of our calculation becomes since we're making loose approximations based on looser approximations.

Example, probability of flopping top pair * probability of villain flopping top pair = 15-20bb pot. Probability of flopping air and not improving * probability of villain flopping air and not improving = 2-4bb pot. When you factor in every possible situation with your own approximatation of the pot size, you get the avg pot size for 10bb effective stacks..

And then again, it becomes very tedious and very likely inaccurate.

edit: In the end, it just comes down to the fact that human decisions are not a mathematical calculation. The best way we have of quantifying it is empirical evidence.

this is deffo an area I need to explore, i believe many of us are missing huge +ev shoving over limp spots, on the other hand, sometimes overdoing it and making clear -ev pushses.

But yeah, its really hard to come up with an answer.. this is one of the areas that probably goes by "feel" / experience. I think its even harder to determine villain limp range at 10bb, and their calling range, its really randomized amongst average villains, and for the push EV calculations you need those ranges.

don't forget to account for your hourly though! shoving pre is really quick and a little more eV from checking back/playing postflop might not make up for the fact that the hand takes 5-10x as long to play!

if anyone maybe got some fresh ideas after a year they are still welcome

ive no idea how the above two posts are related

i mean, there's always the hard way. write out all the possible lines after a limp and check back, give Villain ranges for taking each of his actions, find the best way to play our hand in response and the EV if we do that.

Well hard way wont work I think.

We need something reasonable , with limited complexity, and what doesnt include huge sample analysis as suggested by some guys.

just approximate it as ">than folding" so start at -1, compare the shove to that, and let ppl do their own math to compare it to checking back (knowing that checking back is >-1)

This way you at least knock out some possibilities (if a shove is worse than folding you don't need to consider it at all) and leave a reference point that is clear and unambiguous.

If you do something based on hand strength it will also depend on how skilled you are as a player and how skilled your opponent is which is obviously impossible to quantify.

Yep thats a very straightforward and clear possible choice. prolly will implent it this way if noone suggests something evidently better.

it's especially nice since you already have a feature to put in an ev difference to pick out more selective ranges. so you just set your personal ev check ~.25bb and can easily check shoves after that too. It doesn't take into account hand strength but that's ok.

I could be wrong but I think cardrunners EV can calculate things like this.

You might wanna crosspots this in the Probability forum - these guys produce some weird looking formula stuff when you ask such questions.

Depends on how much you want it, sir.

even if you were holding two jokers and had 100% equity in the hand, the EV would still depend on your villain's looseness and your ability to extract value, i have no idea how you would want to quantify that in a formula.

This is just spitballing and may not be the best way, but why not compare the equity in the 2BB pot based on hand vs limp range against the equity of the shove vs perceived calling range? I know this doesn't really account for future action. But, it seems similar to Coffeeyay's approach but a bit more realistic since the loss of 1BB for a fold is not really applicable to this situation?

zero

Edit: I know this does not account for skill differences or positional advantage, but I think you have to assume that these are negligible for the sake of a calculation like this, even though it makes it less realistic.