Another example, odds of 4/1. Probability = 1/(4+1) = 1/5 = .2 or 20% odds against = (1/Probability) -1
For example, I might like an even money bet that pays 2-1, but it's the same as a bet that works out 2/3 of the time and pays 1-1. Odds: 2/1 Pays out as if prob of winning: 1/3 Pays out 3 P(win) = 1/2 Expected Return = 1.5 Odds: 1/1 Pays out as if prob of winning: 1/2 Pays out 2 P(win) = 2/3 Expected Return = 1.33333