Expected Values

When betting on an uncertain outcome, it helps to think in terms of the average profit that results if the same bet in the same situation is made repeatedly. It is useful to define the expected value of a bet as the average profit that results after many repetitions. Expected values can be positive, negative or zero, depending on whether the bet wins money over the long-run, loses money, or breaks even. The expected value of a bet depends on the odds against success and the payoff if the bet succeeds.

For example, consider having four cards to a flush, with one card to come, and it costs $1 to contest a $5 pot. The odds against success are 4 to 1, which means on average, four out every five times, this bet will lose. It costs $5 to make this bet five times and its one success will return $6—the $5 already in the pot, plus the $1 put in to contest it. The ratio of 6 to 5 is 1.2. That means the expected value of the bet is $1.2 -$1 or $0.20. The bet expects to return a profit $0.20 per dollar on average every time it is placed.

Consider the same situation with the cards, but with a $3 pot. It now costs $1 to contest a $3 pot. Again, it will cost $5 to make this bet 5 times, but the one success will return $4. The ratio of 4 to 5 is 0.8, so the expected value is $0.8 - $1 or -$0.20. On average, this bet will lose $0.20 per dollar each time it is placed.

The expected values is a useful concept but keep in mine the following: