I am having trouble figuring how to calculate equity. Or maybe I am not. I don't know.

On Pokerstars, the casino will cash you out if you are all in, based on the equity you have in the hand, -1%.

If Hero has Aces and Villain has Kings then Hero has approx 80% equity.
hero gets paid by the casino 79% of pot.

If Hero wins the showdown, the casino keeps the remainder.

So, basically I am against this bet for a number of reasons.

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But.....I was talking to another player and we were talking about the situation when you get all in with a draw.

So here is how I calculated it, is this not right?

Hero has a nut flush draw on the flop and only the nut flush is going to win it for Hero.
Therefore we have 9 outs and basically 36% equity.

We are both all in for 200 total bb. (100 each)
Therefore if I cash out, I get paid 35% of 200bb = 70bb.
If I do that 100 times, I am +700bb

If I let the hand play out, and I play it 100 times:
I win 200bb, 36 times = +7200bb
I lose 100bb 64 times = -6400
I end up plus +800bb

divide by 100 again and the cashout is +7bb and play it out is +8bb.

So the EV for taking the cash out is -1bb.

Is that correct. (If so, BTW, should I not be shoving every time I have a nut flush draw? I don't think anyone recommends that).

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example 2:

Hero, 54s, hearts
v1 has AK, no hearts
v2 has 88 no hearts

flop is 3h6h,As

Hero = 57%
V1 = 39%
V2 = 4%

Pot 300bb

If I cash out I get 56% of 300 = 168bb
If I do that 100 times I profit 16,800

If I play it through I win 300 57 times = +17,100
I lose 100 43 times = -4300
Total EV = +12,800

Divide by 100 again
cashout EV = +168
Play it through EV = +128

EV for taking the cashout is +40bb

Is that right?

Thanks,

Magnum

Let's look at it another way. I'm assuming all of your money is in the pot before you have the option to cash out or play. So you have 0. No matter what happens in the hand, you will never lose money (your balance will not be below the 0 that it is right now).

In situation 1, if you take the cashout, you will have 70BB. If you play it out, you have 36% equity, and therefore you will get, on average, 72BB. You are losing 2BB (2/72 or 2.8%) by taking the sure thing deal.

In situation 2, again you come to the decision point with 0 in your stack. A cashout gives you 56% or 168. Playing it out nets you, on average, 171BB. You lose 3BB, or 3/171 1.8% by taking the deal.

You are always going to be better off (in the long run) by playing it out - because you are getting the true % as compared to the true % - 1. Any time someone offers less than your true odds you are losing something. But you can actually be better off in the short run because psychologically you don't want to deal with the ever present chance of getting stacked.

Thank you. I felt like I was butchering those equations.

Aside from the math, my initial reaction for exotic bets, whether it is blackjack or craps or whatever is 'why is the casino offering this bet?' The answer is always the same, of course. It is a good bet for the casino.

Thanks again, 2+2 is a great community and a great resource.

Magnum