in reply to What are "the odds"?
in thread Fastest way to calculate hypergeometric distribution probabilities (i.e. BIG factorials)?

Probability p is expressed in terms of odds is "(1-p)/p to 1 against". Notice that if p=1/4 this gives "3 to 1 against." One can also compute "odds in favor" of an event, although "odds against" seems more common. (I'm not sure why that is, but suspect it may be that gamblers often like to bet on something with big odds against which then has a large payoff.) But you are correct that "the odds are 3" isn't really meaningful although I understood what tlm meant.

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Re^2: What are "the odds"?
by tlm (Prior) on Jun 14, 2005 at 13:46 UTC

    The expression "odds" by itself (without the qualifier "against" or "in favor") usually means "odds against." Hence the common expression "long odds" to refer to low probability. Long odds == fat chance == slim chance (go figure).

    And you're right, this is "bookie talk".

    the lowliest monk