Mathematical Expectation?

[The Nutz85]

Ive read in TOP about EV i understand the concept behind the coin flip scenario but cannot put it into use.
Can i see example of practical use and the math part broken down piece by piece when it comes to calculating you expected value on a play?
I beleive that could help me out allot

[UATrewqaz]

There is a 15% chance that it will rain more than 1 inch, a 45% chance that it will rain but be less than an inch, and a 40% chance of no rain at all.

We make the following agreement, if it rains more than an inch you give me $3, if it doesn't rain at all I give you $2. if it rains but less than an inch we push.

Your expected value on this wager

(.15 * -3.0) + (.45 * 0.0) + (.40 * 2.0) = 0.35


You expect to make about 35 cents on this prop bet int he long run.

The formula is just the sum of (probability of event * result of event) over all possible events (the sum of the probabilities should equal 1.0).

Does this help at all??

Here's an actual poker example, let's say you hold

4 /images/graemlins/diamond.gif 5 /images/graemlins/diamond.gif

Board is

6 /images/graemlins/spade.gif 2 /images/graemlins/heart.gif A /images/graemlins/spade.gif J /images/graemlins/club.gif

The pot has $200 and it's you and an opponent heads up, he bets $40 and then let's assume he's a drunk idiot flips over his pocket aces and is like "beat this you loser".

We now have all the information we need to make a proper EV decision.

We have 4 cards that will make us a straight and a winning hand over his three aces. Every other card we lose. THe odds of us catching one of our 4 cards is roughly 8% (we'll say 8.0 even to keep the math pretty).

Thus we examine our EV of calling or folding

EV of folding = 0
EV of calling = (.08 * 240) + (.92 * -40) = -17.60

(I'm not factoring in river action for simplicity).

It's clear we should fold, we simply do not have hte right odds to call the bet. You can see how this EV calculation cahnges if we had moer outs (say we had an open ended straight flush draw) or if the pot was much bigger (say $1000 with still $40 to call).

The problem with poker ist hat it's imcomplete information so your math is guess work, and you haver very odd scenarios.

For example calling may have -EV and raising has even worse -EV, but you think your opponent is weak and may fold to a raise, thus you have to try to figure out hte % chance he will fold to a raise and factor that into your raising EV calculation.

[The Nutz85]

yes thank you that does clear quite a bit up at least on the math part. but what about its uses specifically in poker.
What would it be if i was on a semi bluff raise with one card to come on a flush draw? he fold 30% re-raise 20% and fold 10% and i would hit my draw 30%? as you can see this is where i get real shady on this EV calculating

[DJ Sensei]

to calculate the EV of any particular play, we multiply individually the probability of each possible outcome by the return on that outcome (in poker terms, generally a positive or negative number of chips)

So with your flush draw semibluff, given the numbers you used (lets say the pot is 1000 chips, and you bet 500 on the turn). I'm a little confused by your percentages, so lets say he'll fold 30% of the time, reraise 20% of the time, and call 50% of the time.

EVP = the expected value of your bet
it equals EVF + EVR + EVC
EVF = .30 * (+1000) (Villain folds, you win 1000 chips)
EVR = .20 * (-500) (Villain reraises and you fold, and lose 500 chips)
EVC = .50 * (.21 * (+1500) + .79 * (-500))

EVC of course is the expected value if he calls (we'll disregard implied odds of extra bets on the river) which equals the chance of making your flush times the chip gain of that plus the chance of missing your flush times the chip loss of that.

In this example, the EV of your bet is +160 and is therefore a profitable play.

See how it works?