Expected Value (EV) in Texas Holdem..?

Question

I have read a couple articles on Expected Value. I still do not understand the concept. It would be greatly appreciated if someone could explain it to me with examples.

Answer 1

Expected Value is the average you expect to win each time if a hand was played infinite amount of times

example

flip a coin.  If it's heads you get 2 dollars.  If it is tails you give me 1 dollar.  What is your expected value?

well

50% of the time it will be heads and you win 2 dollars

so that is

.5 * 2

50% of the time it will  be tales and you lose 1 dollar

so that is

.5 * -1

(.5 * 2) + (.5 * -1) =

1 - .50 = .50

so your expected value every time you flip a coin in this instance is +$.50

same thing in cards

if it costs you 10 dollars to call, and the pot is 40 dollars, and you will win the pot 35% of the time you compute it like this

35% of the time you win 40 dollars

65% of the time you lose 10 dollars

(.35 * 40) + (.65 * -10) =

(14) + (-6.5) =

$7.50

so when you make this call, it has an expected value of +$7.50

hope that helps

Answer 2

It's been explained in sufficient detail already, but in more layman's terms, it's the idea of how much you're expected to get back based on the current odds in a situation.

A simple example in poker is the starting hand AA.  This is considered the best hand to start with because it has the highest expected value (in other words, it wins more often than any other starting hand).  Which is why you should put your money in with it.  More often than not, you will win with that hand.

Another example would be if you were holding KQ of hearts in the pocket and the flop came out:

Jh Th  4c

Say the pot is $6.  Your opponent bets $3.  He is now saying "If you want to win $9, you have to put in $3", which means you would be getting 3-1 on your money.  Is it worth it?  Let's see.  To improve you would need:

A heart (9 left)

any A or 9 (6 left; not counting the ace and 9 of hearts).

You have 15 outs, or about a 60% of hitting a nut (or near nut) hand.  In other words, you have about a 2-1 chance.  So yes, the EV in this situation is positive, it's worth a call.  On the other hand, let's say you have a KQ of hearts and the flop comes like this:

AdQs2c.

Same situation, except this time, you only have 5 outs (3 kings and 2 queens), which means you only have a 5-1 chance of hitting the best hand (assuming your opponent does not have AA, AK or AQ).  In that case, you have a negative expectation because if you call the $3 you will lose more often than you will win.

Hope that helped.