How to calculate expected value?

[DyessMan89]

Can anyone give me an explanation? I have seen this many times, but I dont get the formula.

Thanks.

[Al_Capone_Junior]

EV calculations are simple if the problem is simple. For instance, say you flip a coin, and you pay me $1 for heads, and I pay you 50c for tails, what is my EV? You take what happens during all possible events times the payoff when each of them happens then add them up...

the chance of heads or tails are both 50% or probability of 0.50, or it's easier to just say one time I win and one time I lose...

I make a buck when I win, and lose 50c when i dont

EV = 1 * 1 + 1 * -0.5 = 1 - 0.50 = 50 cents

These calculations can of course get much more complex, particularly in poker, but you get the jist I hope.

Here's a poker EV calculation

Say you have a flush draw, nine clean outs, and you know you won't win by catching anything else, like a pair or straight. Also say it's heads up with one card to come. There is $80 in the pot, it costs you $10 to call. Your opponent will not pay you off on the river if you catch the flush, and you won't pay him off if you miss. What's your EV?

chance of making a flush with one card to come = 9/46 = 0.195, which is about 4.1:1 expressed as odds [(1/0.195)-1 to 1]. It's costing you $10 to win $80, so your pot odds are 8:1, much more than your odds of winning, so obviously you are in a +EV situation here. Here is one way to calculate your EV here...

1 time I will win $80, and 4.1 times I will lose $10, so

1 * $80 - 4.1 * $10 = 80 - 41 = $39

Your EV is $39 here.

You can of course calculate these things with much more complex factors, like chance to win by bluffing on the end, chance you'll catch a pair and your opponent will be bluffing, implied odds, exposed cards, whatever, but this is usually all that is necessary to understand this stuff pretty good.

al

[DyessMan89]

Thanks a lot. [img]/images/graemlins/grin.gif[/img]