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Calculating Expected Value of your poker hand

Many poker players, especially new ones, flinch at the mere juxtaposition of the words poker and math.  The problem is that these players use hunches when they should consider the “odds”.  So, we decided to try to simplify poker math for you.

Poker Expected Value Simplified

First of all, poker math is actually more important when you play poker online than when you play at a land-based casino.  When you play online poker, you can’t get any physical signs from your opponents so you need to rely on your wits and, dare we say it, math.

Calculus Not Involved

The math you need to play poker well is not the higher math of MIT geniuses.  Until you get good at figuring out the odds, you might need a calculator.  Online poker is perfect for this as you’ll never be mocked for pulling out the pocket calculator.

Eventually, you’ll know how to make these calculations without a calculator.

Visual versus Intellectual

We think that poker is all about watching what your opponent “tells” you.  This is a big rookie mistake.  First of all, there are few tells in poker online.  Second, tells are notoriously inaccurate when you play on land.

Decision Time

At every street in a Texas Hold’em game, you need to observe the cards, evaluate the odds, make a decision, and do what you decided to do.  There are no cold feet in poker!

So let’s make this a list:

  • Observe
  • Evaluate
  • Decide
  • Do it

Evaluate

The math all comes in on the second step: evaluate.  A lot of poker math wizards throw out MIT style math ideas but they won’t do here.  If you get so good at the basics of poker math and, if you are so inclined, you can learn all the esoteric math stuff like the Nash Equilibrium.

Those highfalutin concepts are not for us here.

Expected Value

Whenever poker players get down to the nitty-gritty of poker math, they talk about expected value or EV.  It is important to have positive EV which is written as +EV.

Think of EV as the attitude of the hand as a whole.  It is the poker way of saying this hand gives off either positive or negative vibes.  The only difference is that EV is a math concept and you calculate it using math.

To simplify EV we need to reduce it to fifty-fifty probabilities.  Let’s use a standard deck of cards.  We will win $1 every time we guess the color of the card correctly and we lose nothing if we guess right.  This type of problem never happens in poker but we are using it to introduce the concept of EV slowly.

If we take this bet ten times, we will likely win five times and lose five times.  We win $5 but we lose $0 for our losses.  So, for every time we take the bet, we can expect to win one half dollar or $0.50.  we never actually win one half dollar; that is simply the EV for this game.

EV in poker is more complicate, but it is based on the same principle. 

Continuing the example, we win $1 whenever we guess the color correctly but we have to bet 50 cents on each call.  In this case, the EV is 0.  Now, if the amount we have to bet goes even one penny above 50 cents, the game has negative EV and we would expect to lose money over time.

Calculate EV in Poker

Calculating EV in a poker hand is not nearly as simple as in the example we gave but it is also not overly complex.  The amount you would win is the amount in the pot.  If you are betting, it doesn’t include your bet; you calculate EV before you bet.  If you are calling, EV doesn’t include your call.

You count your outs.  It doesn’t matter which hand you are trying to get; you count your outs.  It is obvious that you have more outs if you’re going for a straight or a flush than if you want to get three-of-a-kind.  It is also obvious that you have more outs going for an outside straight over an inside straight.

Calculate your outs.  Now we convert that number into a percentage.   Let’s say that we are trying for an outside straight.  There are six cards that can give us the straight and there are 46 unseen cards.  So the chances of getting the straight are 6/46.  Here is where a calculator will come in handy until you get good at making this calculation. The percentage is 13%.  The chances of not getting the straight are 87%.

The EV is the amount you stand to win (based on the pot, not counting your bet or call) times the percentage of hands that you’ll win.  We subtract from this number the amount you would lose which is your bet on this street times the percentage that you’ll lose. 

We admit that it looks complicated but it isn’t.  The percentage of winning and losing the hand are the same regardless of the pot size.  So, the EV goes up as the pot is larger and the EV is worse if the pot is small.  From the EV standpoint, there might be many cases where the pot is simply too small to justify calling a relatively large bet.

What Counts?

When you calculate the EV for the amount you could win, you use the entire pot.  Once the money is out there, it is not yours even though you put some of it in the pot.  A lot of players get all wrapped up in figuring how much they put in and subtracting that amount from the pot.  This is a mathematical mistake and a very big poker EV mistake!

When you calculate the money you could lose, you use only the amount of the bet you are contemplating. 

The bottom line on EV is that is a mathematical comparison of the amount you could win or lose, the odds of winning the hand, and the size of the pot.  All three numbers work together to arrive at the EV.

One of Many

EV is only one of many math concepts useful in poker.  We will talk about other poker math ideas in upcoming articles.