Odds to 1

The relationship between probability and odds can be stated as follows:

"Odds to 1" = (1/Probability) - 1


Or, if one writes things in terms of probability, then:

Probability = 1/("Odds to 1" + 1)



Example:
Let's say you wish to convert the 2 to 1 insurance payoff into a win probability. In this example, Probability = 1/("Odds to 1" + 1) = 1/(2 + 1) = 1/3 = 0.333...

This means that you have to have an expectation of greater than 0.333... in order to make the insurance bet a profitable one.








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