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Learning The Art Of Expected Value

published on 11/04/10 at 7:49 am

Expected value is a very important concept in all forms of gambling. If it is possible to always make bets with a positive expected value, then in the long term one would always win. Expected value is not the only thing to consider, for instance we also need to consider variance, but expected value is where we need to start.

Expected value is the anticipated return on a bet. If you bet $1 on the flip of a coin at evens, then the excepted value of your bet is ($1 x 0.5) + (-$1 x 0.5) = 0, but if you could get odds of 2/1 then the expected value would be ($2 x 0.5) + (-$1 x 0.5) = $1.

Expected value in poker is just the same, and we use it in computing pot odds. The rule is to only draw to a hand when there is a positive expected value. Consider that you, as small blind, are holding Ace Spades and 10 Spades and the board is 8 Spades 7 spades 2 Hearts. You check the big blind bets and three other players call. What should you do next?

These are the things to consider. You only need one card to make a flush and there is a 0.35 probability that you will do so and a flush would almost certainly win the pot.

If you decide to raise, then it is likely that four players will call, so you will only be contributing 20% of the pot. If the blinds were $1:$2 then the expected value would be $.75 x (0.35 x ($5 – $1).

Of course you might hit an Ace or a 10, so you are not simply relying on a flush. And a flush is not guaranteed to win, for instance another player could get a full house. You may not be able to compute all the odds, but it is obvious that raising would be the best decision.

Quickly assessing the expected value of your bets is a skill that is well worth developing and one that will win you money in the long term.

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