Online Poker » Poker Strategy » Math » Expected Value

When new players are first learning the game of poker everything goes. They play any face card, suited connector or small pocket pair and even chase gut-shot straight draws regardless of how much is bet into them. Now, it is obvious that playing like this is a losing strategy but it is more important to know why.

The reason why plays like this are costly is because of expected value or EV for short. Expected value will simply tell you whether the play a player is making has a long term positive or negative expectation and should be the base of any decisions that are made. By using expected value in the decision making process and making the correct mathematical play each time, a play should prove to be profitable over time regardless of any losses that may occur.

For a better understanding please read our example below.

Calculating Expected Value

One of the most common situations in poker that offer the most temptation is chasing nut flush or straight draws. And, who can really blame anyone for wanting to? In a majority of cases, a flush or straight will prove to be the best hand at showdown.

However, in most cases, everyone else at the table will see these draws and if they caught a piece of the flop, they will bet in attempt to block the draw. It is up to the player to determine if calling the bet will prove to have a positive expectation or not.

For example, let's assume that you were on the button with Ad-Kd in a $100/$200 no limit hold'em cash game. Everyone has folded to you and you raise a standard 3x the big blind up to $600 total. The small blind folds and after some thought, the big blind calls the extra $400. There is now $1,300 total in the pot, $600 from you, $100 from the small blind and $600 from the big blind.

The flop brings 10d-9d-2h giving you the nut flush draw. It is up to the big blind first to act and he leads out for two-thirds the size of the pot, or $900 with a total of $2,200 now in the pot. Now, it is up to you to act. Can you make the call and have positive expectations?

Well, the first thing that needs to be done is calculate your outs to figure out the odds of catching one of your needed flush cards. There are two diamonds on the board and two in your hand so you know that there are 9 left in the deck. So we take our 9 cards that will help us against the 38 that won't to come up with a little worse than 4 to 1 odds.

Now, you need to know how much money you are spending and what you are getting in return and apply that to your odds. So, if you call $900 you will stand to gain $2,200 in profit. This is what your equation would look like:

* (odds you miss x money spent to chase) + (odds you hit x money you win) = EV

So, we now put our numbers in to see if this play is a positive expectation or not:

* (4 x $900) + ($2,200 x 1) = -$1,400 -EV

As you can see, calling this hand will prove to have a negative expected value over a long period of time. Sure, you may hit it this one time but on average, this is a losing play, thus making you a loser if you continue to call bets with odds like these.

Ok, so can this situation show a positive expected value? Well, let's assume that the big blind decided to make a minimum bet of $200 as opposed to a two-thirds sized bet. There would be now $1,500 in the pot for you to win.

* (4 x $200) + ($1,500 x 1) = $700 +EV

Ok, so now this play has a positive expectation of $700. Using math alone without any other factors considered this is a sound call to make. In fact, any call up to about $400 or so would show some kind of profit but obviously the bigger +EV you have, the better.

For those of you that may be concerned about how much math is involved don't be. To figure this out quickly, all you will need to do is compare your pot odds to the odds of you catching your outs. As long as the odds of you catching your outs are smaller than the pot odds you are receiving, then you will be making a profit. In other words, you need to be paid more in exchange for the risk you are taking (pot odds > card odds).

Expected Value in Poker

Expected value in poker is essential to learn and understand simply because it will keep you from making the commonly bad plays that many beginners make. Since poker is a life long session, an understanding of expected value and how to employ it when making decisions will help keep you a +EV player for the length of your career.