Expected Value In Poker

Expected Value or EV is one of the most important concepts in poker. Once you understand the concept and its implications it will change the way you think about poker. It is a basic part of human nature to be results oriented. We want to see positive results for our efforts and attempt to minimize negative outcomes. Unfortunately, sometimes our very nature works against us, especially in games of chance like poker. Many players will play good poker until they suffer a “bad beat” that throws them off their game. Why? Because they were results oriented and more focused on winning the hand than on winning expected value. In order to be successful poker player in the long term it is critically important to focus on expected vlaue.

In poker it is relatively simple to know what the expected value of a particular pre-flop All-in situation is. For example, if you are All-in preflop at a $1/2 NLHE  game for 100BB with AA vrs 22 your chance of winning the hand is approximately 80%. Your expected value in this hand assuming equal $200 stacks is going to be $120. If you win the hand your money won will rise $200 but your expected value will rise only $120. In this scenario you will be $80 above your expected value.

Where it gets more interesting is when you want to factor in fold equity. Consider at a $1/$2 poker table the BB shoves All-in versus the SB for 30BB or $60. The small blind will fold sometimes and call others. How to we figure out the expected value of this play? Assume we realize our expected value in a 100 hand sample. Out of 100 hands the BB shoves the SB calls 20 and wins 65% of the time he calls. The SB folds 80 out of 100 times. Here is the calculation

Expected Value =(80*(Raise+BB(sunk))+(%opp loses when calling*number of calls)(Amount Won)-(%opp wins when calling*number of calls)(Amount Won))/Total Number of Outcomes

Expected Value =(80(5)+(.35*20)($60)-(.65*20)($120))/100

Expected Value =($400+$420-$780)/100= $.40

Under this scenario you will win $40 in 100 shoves or 40 cents every time you shove pre-flop from the BB vrs the SB. We have taken into account the frequency of our opponents folding, calling, winning, etc. When you are studying poker decisions and trying to determine if they are profitable or not this is the way to do it. The less assumptions you are forced to make the more accurate your results will be. In this kind of pre-flop scenario it should be relatively easy to determine what an opponents steal % is and then how frequently he is calling our shoves. We should then be able to develop a profitable strategy for dealing with this opponent. By thinking about the expected value of certain decisions rather than the result your poker game will improve dramatically over time.

The best way to track your expected value  is with a program like PT4 or HM, which will display an All-in Equity line. You can compare the All-in equity line to the money won to get a sense for where you should be. Generally, if you focus on your expected value during your sessions rather than your money won it will serve as a better metric. It will also be less volatile and help you avoid the highs and lows that come with winning pots. Poker players commonly feel great after winning a big flip, but in reality their expected value has not risen. At some later date they will lose a flip back and feel bad for no reason. By focusing on the expected value rather than the result it can help to reduce tilt and keep you level headed.

Take a look at the graph on my twitter page that shows me around 1400 BB below my expected value over my most recent 15k hands https://twitter.com/PokerCapitalist/status/374584755661983744/photo/1. These kind of swings are relatively common and tend to even out over larger sample sizes. Historically, I have found some significant divergences between money won and expected value over 10-100k hand samples, but over 300-500k hands they tend to even out. However, keep in mind that PT4 does not include all hands in an All-in EV calculation. I believe it excludes 3 way pots where two players are all in. I also think that it excludes pots where Player A is all in and called by Player B and Player C. On the flop Player B bets and is called by Player C, but on the Turn Player C folds. Because it would not be fair to assign an All-in EV under these parameters, it is excluded.

Hope you guys enjoyed this post. I am going to talk about expected value in life on my next blog here. This is a topic that I think is incredibly important for a lot of people. Most of us should factor in the “EV” of a decision more frequently than we do when making life decisions like choosing a mortage, buying a house, etc. Follow me on Twitter @PokerCapitalist


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