Expected Value in Poker
It is not enough to have an understanding of poker outs, odds and pot odds in poker; no, players need to take all of those concepts a bit further, combine them and gain an understanding of expected value.
Now, expected value in poker is the amount that a player 'expects' to win should he or she make the same play repeatedly over a large sample size. This expected figure can be a loss or a profit and is determined on how likely it is that the player will hit their hand as well as the price they pay to attempt to do so.
To provide a bit more insight on the topic of expected value including how to use it in real poker situations, we encourage you to continue reading as we have provided an example for you below.
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How to Calculate Expected Value in Poker
A common example of where many players neglect to calculate there expected value is when they are involved in a hand where they have draws to excellent hands such as straights or flushes.
For example, let's assume that you sitting on the button with Ks-Qs, the blinds are $100/$200 and there are two limpers in front of you. You decide to call as well, the small blind folds and the big blind checks his option. There is now $900 in the pot.
The flop is Js-8s-4c which gives you the second best flush draw. The big blind leads out for $600, the other two players fold and it is now up to you act. With such a strong drawing hand, do you make the call and chase your flush or do you lay the hand down?
In my opinion, many newer or lesser-experienced players feel that this is an insta-call; no further thought needed. However, to make the correct decision, players must go through a couple steps to see if calling this bet will prove to be a profitable decision over a long period of time. After all, poker is a life long game, so all decisions that are made should be based on that idea.
So, the first thing to do here is to count how many outs you have and then convert that into odds. There are two spades in your hand and two on the board so you know there are 4 of your outs gone. Since there are 13 cards of each suit in a deck of cards, you can then figure there are only 9 outs that will better your hand to the flush. Next, take the remaining cards in the deck which should be 47 (52 minus the 3 on the flop and 2 in your hand) and divide that by the number of outs you have. This gives us 5.2 or 5.2 to 1. To make the math simple, we will just round down to 5.
The next step is to take the amount of money that is required of you to call, and multiply that by the number of times that we chase and lose. We know that we are facing a $600 bet and will lose ever 5 times out of 6 that we attempt to complete our flush which gives us a loss of $-3,000. Next, we compare the $-3,000 to the amount we will win that one time we do complete our flush. Since there is $1,500 in the pot now, you add your $600 to that and come up with $2,100 for each time you win. Now, let's look at these numbers side by side:
-$3,000 in losses versus a $2,100 win
When you do the math ($-3,000 + $2,100), you will see that over the course of 6 flush draw attempts you manage to lose $-900 in the process. What this ultimately means for you is that this is a losing proposition or negative expected value in the long run and that you should fold your hand.
This probably seems like a lot of math to do, especially when you only have 90 seconds or so to act when it is your turn. But don't worry, there is a much simpler way to find out if the call you are about to make is profitable or not.
Just compare your pot odds to your cards odds.
If you just compare the odds to hit your hand to the pot odds you are receiving, you can quickly deduce whether or not the hand is worth calling a bet with. The goal is to be receiving bigger pots odds in comparison to the odds of hitting your hand. So for example, in our hand above we were receiving about 2.5 to 1 in pot odds (3.5 to 1 including our bet) in comparison the our 5 to 1 odds of making our hand. Our pot odds would at the very least need to be 5 to 1 to break even with any number over that showing a profit. Here are a couple examples:
2.5 to 1 pot odds versus 5 to 1 card odds
This is a losing hand because our pot odds are smaller than our card odds.
5.5 to 1 pot odds versus 5 to 1 card odds
This would be a slightly profitable play because our pot odds are bigger than our card odds which just mean there is enough money to justify the risk of chasing our hand.
This is the faster way to figure it out without having to break out a calculator and the higher your pot odds in comparison the odds of you hitting your hand, the more profit you can assume that you will make.
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Expected Value in Poker
Expected value is an important concept to learn especially for new players because in theory, it should eliminate one of the biggest leaks that newer players have which is chasing too many draws. By being able to calculate the expected value of their hands over a large sample size, they can than make educated decisions based on their findings which should lead to them maximizing their wins and most importantly, minimizing their losses.
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