Expected Value

Expected value is the key to becoming a winning player in the long run. Poker is a game of skill and luck. As there is an element of luck, the best player will not always come out ahead in a cash game and will not always place 1st in a tournament. In fact, things can change fast, on the flip of a card. Here I will explain what Expected Value or EV is and how it can be used to your advantage.

 

Every decision you make in poker has an outcome. Regardless of where you sit (in relation to the button), who you play against or how much money is involved, every decision you make can either have a neutral, positive or negative expectation, or expected value. In short, a decision that has a positive expected outcome is good (profitable in the long run) whereas a negative EV is bad, meaning you will lose in the long run if you ran the same scenario over an extended period of time.

 

How is Expected Value (EV) used

Let’s take a look at calculating the expected value on a few examples to show you firstly how it is calculated and also what it means in terms of profitability.

 

Let’s assume you are playing a game of roulette and are betting on red and black. There are three outcomes. You could hit a black number, a red number or hit 0. For the sake of illustration, let’s assume there is no 0, meaning it will either be red or black. Let’s assume that you get $5 if it comes red and you lose $5 if it lands black. If you did this 10 times, you would expect to win 50% of the time – or would have a neutral expected value (you would win 5, lose 5 so would be even, in terms of funds). Now let’s assume you are offered $10 if red hits but only lose $5 if black lands. Again, let’s run this 10 times. You win 50% so would win 5x$10=$50. You also lose 5 @ $5 a pop so would lose 5x$5=$25. After 10 spins you would have a profit of $25. This makes it good value (not that you needed math to come to this determination).

 

To calculate the EV of this scenario, it looks like this: $10 x (0.5) - $5 x (0.5) = +$2.5 EV. That means that you have a positive expected value of $2.5 on each spin, again meaning a good bet.

 

Now this is on a random bet. EV can also be calculated from a hand of poker in which you know the odds of hitting a hand against the pot odds of hitting the hand. Where the pot odds are greater than the odds of hitting a hand, you have +EV and should make the bet (or call). Let’s look at an example.

 

You hold A-10 hearts and the flop comes 5(h)-9(h)-2(s). Let’s assume you are up against 2 other players. With 52 cards in the deck, you have seen 5 cards, so there are 47 left. You need another heart to make your flush. With 13 hearts in total, you have two and there are two on the board, leaving 9 remaining. You could also hit any four remaining 10’s or four remaining aces. That makes a total of 17 outs. Let’s assume the pot sits at $50 and you are faced with a $10 bet from your opponent. What do you do?

 

You will win some 36% of the time ( (17/47)x100 ). That equates roughly into 3-1 (once every three times the hand is played). With a $10 bet into a $50 pot, you are getting 6-1 pot odds and so should be making the call, as you would be getting value to call (doubling your stake). This bet has a +EV as you are getting higher pot odds ratio to the odds of making your hand. To put it into perspective, if you made this bet 6 times, you would win twice making $120 (2x$60), whereas it would only cost you $60 to play it 6 times, giving you a profit of $60 (positive expected value).

 

Expected Value and Profitability

People play poker to make money. Regardless of how fun you find it, don’t treat your hard earned money without respect. If you only ever made plays that had a positive expected value, what do you think this would do for your profits? Short term results will see fluctuations primarily because there is the luck factor. Regardless of how good or bad you are, you will lose hands in which you were the favorite going in, and similarly you will win hands that you shouldn’t have won. This is known as swings and roundabouts. The ups and downs of the game.

 

The reason that good player make money in the long run is that they make +EV bets. Yes, in the short term they will lose hands they should have won, but in the long run, the odds make them a winner. Applying these principles and staying away from plays that have a negative or only minimal positive expectation will turn you into a positive player over the long haul.

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