How Do I Calculate EV?

I'm trying to calculate basic EV for some classic heads-up situations, but I'm confused about something relatively simple. The basic equation for EV is:

EV=(% chance of winning)(amount won) - (% chance of losing)(amount lost).

Let's say I have AA and $100 in front of me. I manage to get all my money in PF against one opponent, who has a random hand. My % chance of winning is ~85% in this situation. Therefore, the equation should be:

EV=(85%)($X) - (15%)($100).

My problem is this: what value should I put in for $X? Is it just the $100 I expect to win off my opponent? Or is it the total pot amount, which would be $200? (I'm ignoring dead money, the blinds, and rake). I'm leaning towards the $200 value, but some info I've seen online suggests otherwise. Help!

Cheers,
Bug

think about it logically, 85% of the time you win how much money, 15% of the time you lose how much?

So, 85% of the time I win the $200 that's in the pot, right? In other words, the money I put into the pot isn't mine anymore (i.e., it belongs to the pot) and therefore is added to the amount I can win.

This sounds so basic, but like I said, I've read some conflicting advice online.
Thanks,
Mark

No, because you don't win 200 when you win. The amount you win is what you get minus what you invested.

Just take the coinflip example, if you and villain each put $1 on the hand then 50% you're going to win $1 and 50% you loose $1, so (0.5 x $1) - (0.5 x $1) - if it were like you said then the EV would be 0.5x2 - 0.5x1, which of course can't be correct, because we know the EV for this scenario is 0.

There are two slightly different concepts here. EV usually relates to a decision (i.e. when not all of the money is in the pot yet). It sounds more like you are talking about equity. Once all the money is in the pot your equity (fair share of the pot) is your chance of winning multiplied by the size of the pot. In this case 0.85 x $200 = $170. So your equity is $170.

If you consider the case where the villain moves allin with his remaining $50, into the pot which is already $100 then your expectation (EV) for calling looks like this.

The pot + villains bet is $150.
You are risking $50 to win this $150.
85% of the time you will win $150. The remaining 15% of the time you will lose $50.

Your EV is therefore 0.85 x 150 - 0.15 x 50 = 127.5 - 7.5 = +120

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I rarely, if ever, get pms

EV = (% you win)(total pot) - (how much it cost you)

Say you have $100 and villain has $100. Villain open shoves with a random hand. You call with AA, giving you 85% equity against his range. Your EV on the call would look like:

EV = (0.85)(200) - 100
EV = 170 - 100
EV = $70

So on average, you expect to win $70 by making this call. Your formula is still correct; however, it just needs to be altered a tad. Using your formula it should look like this:

EV = (% you win)(amount you win) - (% you lose)(amount you lose)
EV = (0.85)(100) - (.15)(100)
EV = 85 - 15
EV = $70.

"Amount you win" refers to the amount you stand to win while disregarding how much you are risking.

For another example, you are trying to decide the EV of a call. The pot is $150 on the river, and villain shoves $100 (you have him covered). You figure that against his range you have 30% equity when facing his river shove. The EV of your call is:

EV = (% you win)(total pot) - (amount you lose)
EV = (0.30)(150 + 100 + 100) - (100)
EV = (0.30)(350) - (100)
EV = 105 - 100
EV = $5.

OR

EV = (% you win)(amount you win) - (% you lose)(amount you lose)
EV = (0.30)(250) - (0.70)(100)
EV = 75 - 70
EV = $5.

So in this instance, your call is barely above BE, but it is +EV. This can be referenced by looking at your equity, and the pot odds you are being given on the river shove. He is shoving $100 into a $150 pot. So you are needing to call $100 to win the $250 pot, so your getting pot odds of 2.5:1, which means you need 1 / (2.5 +1) or ~29% equity for a call to be breakeven. Well, you have 30% equity, which is barely above the needed equity, so a call is +EV, but only barely ($5 worth as shown).

Originally Posted by oskar

No, because you don't win 200 when you win. The amount you win is what you get minus what you invested.

Just take the coinflip example, if you and villain each put $1 on the hand then 50% you're going to win $1 and 50% you loose $1, so (0.5 x $1) - (0.5 x $1) - if it were like you said then the EV would be 0.5x2 - 0.5x1, which of course can't be correct, because we know the EV for this scenario is 0.

Unless you use the altered formula I described in my above response:

EV = (% you win)(total 'pot') - (amount you lose)

Which in this case you are winning the total 'pot' of $2 on average 50% of the time. And losing $1 on average 50% of the time. So the formula looks like:

EV = (0.50)(2) - 1
EV = 1 - 1
EV = $0.

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"Ev calcs iz srs bizness!" - Stax

mod title: "srz bizness"

Why do I always kill threads? A lot of responses, then I respond, and thread dies. I haz feelings too!

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