Poker Wiki

Probability versus odds

The conceptual difference between probability and odds is that probability is:

successful outcomes / ALL total outcomes


successful outcomes / (successful outcomes + failure outcomes)

Odds are expressing the same relationship in a different way:

Failure outcomes : Successful outcomes .

So you do NOT want to reduce 46:9 unless you want to find the probability of a flush, which would be written 9/46 = 1/5.222222 = 0.191489 = 19.1%.

For odds, you want to reduce

non-flush cards : flush cards

which is

all unseen cards - unseen flush cards : flush cards

which is

47 - 9 : 9 or 38:9 or 4.2222222 : 1

to hit your flush ON THE TURN CARD.

Note that the odds against are always one less than the inverse of the probability. If p is 1/5, odds are 4:1. If p is 1/23, odds are 22:1.