I made the following calculation to calculate the EV of a shove preflop with a small pocket pair:

(400 *75%) + (1320 * 25% * 18.5%) - (920 * 25% * 81.5%) = 173.5

400 = chips in pot
920 = Hero's effective stack
75% = % of time we expect Villain to fold
25% = % of time we expect Villain to call
18.5% = Our equity when called

Can anyone tell me the correct methodology to calculate at what point this becomes EV neutral i.e. what % of the time Villain needs to fold to make this shove 0 EV ?

what you mean by effective stacks?

I mean that we have 920 chips left in our stack after the previous action.

unsolvable without blinds/starting stack/action

Hesitate to question you, but isn't this a maths problem so the previous action is irrelevant & it is possible to solve for = 0 ?

could be that you can do it like this, though it's way easier to solve when you know what part of the 400 chips in the pot are yours

doesnt matter howmuch is urs. all that matters is the size of the pot on the table

dont see where the 18.5% comes from. thought it should be way more. Even against overpair our equity is still 20%. we are flipping against the rest so its somewhere between 20 and 50 imo. correct me if im wrong.

Not really relevant to solving the problem but the example is 33 v QQ+ which is 18.5% equity.

in that case your variable is too strict. Variables in equations such as this should be more flexible imo...
dont get me wrong im only elaborating

let's say (theoretical) that blinds are 0/400 and we jam 920 into 400 and have 18.5% against a callingrange
in that case, having him to fold nets us 400*X with X being how often he folds; if we get it in, then we are in a 1840 pot with 18.5% equity so we lose 580 every time; this means we need to solve the equation 400x-(1-x)580=0 which means x = 59.18% (which is the FE we need)

let's say that blinds are 100/200, villain limps, we jam for 920 more, a fold will net us 400*X again; if we get it in, we will be in a 2240 pot with 18.5% equity so we lose 706 every time we get a call; this means we need to solve the equation 400x-(1-x)706 = 0 which means we need x=63.83% fold equity

Trust me its not, but as I say it is not relevant at all to solving the problem in any case.

Thanks for this, but I still don't see why the blinds have any relevance here.

i gave you 2 examples of where blinds/starting stacks are different and it came up with a different solution
how can it not be relevant?

But I don't think either are correct as when I substitute into the original formula the answer is not 0.

If you're talking about 0EV compared with folding instead, you need to indicate hero's invested chips.

If we've invested 20 chips and villain open raised to 380, that's very different than if we've invested 120 chips and villain open raised to 280. In the first, we need -t20 in expectation for the entire hand for shoving to be better than folding, in the second, we need expectation better than -t120.

Maybe I haven't phrased the question well enough. What I am trying to establish is the % of the time Villain needs to fold to make a shove breakeven. I am still struggling to understand how any past actions is terms of blinds or raise size etc. is relevant here.

I know that if Villain folds 75% of the time our EV is 173.5 chips. I also know that the play is breakeven if he folds 55.85% of the time (assuming that he is still only calling with QQ+), but I have only calculated this by trial and error substituting in the formula.

I am not a maths expert, hence the question, but I assume we can solve this with my 75 as x and 25 as 1-x in my original formula?

i give up, we tried pointing it out 2 or 3 times now wtf?

I think maybe OP is trying to say that we have 920 behind after there is 400 in the pot, not at the beginning of the hand.

If that's the case, I think the formula is something like this:

where p= probability that villain folds

400*p + 2240*.185*(1-p) - 920*.815*(1-p) = 0

Solve for p to find the breakeven point.

Sausage

I think what spamz trying to say is that there is a correlation between pre flop activity/blind level and stack sizes that will affect the out come of your calculations.

Like if we are deep, villian limps and we shove - thus when we get called we are losing more and when villian folds we win less (or risking more to win less)

However when effective stacks are shorter and villian raises and we shove then we risking less to win more (as the amount we win is a greater proportionally to our stacks).

Thus effective stacks/blinds and pre flop activity will have a direct correlation on the amount you win or lose.

Another thing that effects these calculations is villians raising range vs there 3bet calling range - if villian has a wide raising range but a tight calling range then we will make more (or lose less) than when villian has a tighter raising range but the same calling range.


I would suggest doing a few exersizes - take 2 different effective stack sizes (say 25bb's and 15bb's), and create 2 different scenario where villian minr pre and you shove and the other where villian 4x's and you shove. Now add 2 different ranges to each scenario - one where villian opens 80% and only calls with 15% and one where villian opens 50% and calls 15%.

so it will look like this;

1) 25 bb effective stacks;
A) villian minr 80% and we shove - he calls with 15%
B) villian 4x 80% and we shove - he calls with 15%
C) villian minr 50% and we shove - he calls with 15%
D)villian 4x 50% and we shove - he calls with 15%

2) 20 bb effective stacks;
A) villian minr 80% and we shove - he calls with 15%
B) villian 4x 80% and we shove - he calls with 15%
C) villian minr 50% and we shove - he calls with 15%
D)villian 4x 50% and we shove - he calls with 15%

You'll find out that these factors are pretty significant to your outcomes.

I know this doesnt really help with your questions about determining FE calcs, but its important to understand this stuff and will definitly help you exploit villians. Plus, once you understand these things then spamz and Mer's answers will make a lot more sense. GL!

OK, got it. It's important to understand that you're calculating EV in terms of being 0EV in the hand overall - not whether your actual decision is +EV. It's important to make the distinction clear. Usually, when people talk about "is shoving here +EV", they mean, "is the decision +EV", not "do I have positive expectation in the hand". You're not asking if the decision is +EV, you're asking for even more than that. Just something to understand.

For example, if you call a potsized bet on the river, most people use the term +EV to mean when you have 33% equity or better. The way you're asking the question, to have 0EV in the hand, you need to have 50% equity.

That's where spamz and I's initial remarks come from - expecting you to be talking about the EV of the decision. Hope that helps.

No, I am talking about the EV of the decision we are making and I clearly feel like I am missing something very obvious here, but it seems extremely odd to me that things that have already happened such as blind sizes and earlier bet sizes are relevant when calculating the expected value of a future action.

As I said in my earlier post I "know" that villain has to fold 55.85% of the time to make a shove 0 EV in this scenario I just don't know how to calculate that.

Definitely appreciate your answers & understand if you want to give up on this because I am missing something obvious.

Fwiw (400 *55.85%) + (1320 *44.15% * 18.5%) - (920 * 44.15% * 81.5%)
= 223.4 + 107.8 -331.0
=0.2

This is I guess what I would revert back to for you, then. Do you see why your expectation in the first scenario needs to be better than in the second scenario, despite the same pot size?

I think you have confused everyone because you haven't explained what the 1320 number means or the exact situation of the hand.

I assume that in the equation above this is what the various bits mean:
(400*75%)= villain fold
+(1320*25%*18.5%) = he calls you win allin
- (920*25%*81.5%)= he calls you lose

If that is the case then I think this is what you are looking for:

let x = fold %
then call % =1-x
then subst x and 1-x into your original equation and make it = 0
so,

400x + (1320*(1-x)*0.185)- (920*(1-x)*0.815)=0

400x + (1-x)((1320*0.185) -(920*0.815))=0

400x +(1-x)(-505.6)=0

400x -505.6+505.6x=0

905.6x -505.6=0

x=505.6/905.6= 0.558


The use of 1320 as the pot you gain when you win an allin implies that you have both put 200 into the pot up to the point that you jam and you both have 920 left.

Just because there is a 400 pot does not mean that you have both equally contributed. The blinds could be 50/ 100 and you could be in the BB facing a 3x open, you have have put in 100, your opponent 300.
In this case you would use 1120 (400 in the pot plus the 720 more villain needs to call jam) instead of 1320 to determine your break even point.

Thanks for your patience.

I have finally realised why the previous contributions to the pot matter in terms of solving this as a poker problem as it will effect the amount that both Hero & Villain will need to contribute to the future pot, therefore giving different answers. The problem for me was that I was thinking of this as a maths question not as a poker question.

I will go away & try some examples using the methodology given by Spamz in his earlier response.