For as long as the game of poker has been around, there has and will always be players who play too many hands, chase miraculous draws, and feel as if their actions are justified because for some reason 'lady luck' decided to bless them with yet again another 1-outer to take down a huge pot.
But even though they catch the few outs they have to take down a huge pot, in the long run the ends just does not justify the means. In other words, these plays just do not make any sense, as they do not have any positive expected value.
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You do know what expected value is, right? If not, do not worry because we will explain this in a minute. But in a nutshell, expected value is an amount that a player can 'expect' to win or lose in the long run if they were to make the same play over and over again. This is important to understand so that players can make educated decisions when faced with calling bets while they are only on a draw or have few outs to better their hand. To better explain, please look at our example below.
Calculating Expected Value
When calculating expected value, the goal is to make plays that will show a positive expected value, or +Ev, in the long run as this should show a profit over time. While this may not comfort you when you make the correct play and lose, at least over time you will know that if there are positive expectations for your play, the play should eventually prove to be profitable. A common occurrence is in situations where a player may face a bet and are on a flush or straight draw and are unsure whether to make the call or not.
For example, let's say that you are involved in a hand where the blinds are $100/$200 and you and an opponent have just seen a flop. There is $1,000 in the pot, you have Ac-Jc, and the flop was 8c-Kc-9 d which leaves you with the nut flush draw. Your opponent is first to act and leads out for $600 or 2/3 of the pot. There is now $1,600 in the pot and it is up to you to decide if you will make the call for $600 or not.
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To figure out the expected value, you first need to know a couple other things. First, you will need to count your outs and figure out the odds to catch one of your flush cards. In this case, 9 other cards will give you the flush which gives you roughly odds of 4 to 1. This means that for every 5 times you pay to chase your hand, you can expect to catch a needed card 1 time to win, and will miss 4 times to lose.
Next, you need to know how much you are spending in relation to what you hope to win, otherwise known as pot odds. In this situation, you will spend $600 to win a $1,600 which when simplified gives you odds of 2.6 to 1.
Now, we put all the numbers together. If you are spending $600 5 times, 4 times losing $600 for a loss of -$2,400 and winning once for $1,600, this will give you an expected value of -$800. All that you need to do is take the number of times you should lose and multiply that by the amount needed to call. To that, you will want to add the amount that you will win the one time you win the hand. It should look like this:
(# of times you lose * amount paid to win) + (# of times you win * amount in pot)
Using our example above:
(4 * -$600) + (1 * $1,600) = -$800
This shows that making this call will cost you money in the long run and that you should fold your hand. Sure, you may win once or twice, but poker is a life long game and to be a winner, you want to make plays that have life long positive expectations.
The math that is used to calculate expected value sure seems like a lot to do during the 30-second timeframe that players are given to make decisions, doesn't it?
Well, do you remember when we pointed out that you needed to know the pot odds? To quickly figure out if the play you are making is a good one or not all that you need to do is compare your pot odds to the odds of you catching one of your outs. As long as the pot odds are bigger than the odds of you catching one of your outs, then the play you are making is +EV. Using the same example from above, if you were receiving 6 to 1 on your money ($600*6=$3,600) with the same 4 to 1 odds, you can still expect to lose $600 4 times but win $3,600 once which shows a $1,200 profit (4 * -$600) + (1 * $3,600). The idea is to get more money for chasing draws with slim odds (pot odds > card odds) or (6 to 1 > 4 to 1).
Expected Value
While expected value may seem difficult to understand at first, it is actually very easy to do after a while and will become a natural part of your decision making process. By having a firm grasp on what expected value is, players can then make educated decisions that should save them money in the short run and show positive expectations in the long run.
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