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Old 08-28-2006, 03:45 PM
AaronBrown AaronBrown is offline
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Join Date: May 2005
Location: New York
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Default Re: Odds vs Chances/Probability

There's no difference internationally, although people often misuse the terms.

Bets can be stated as X for Y or X to Y. 2 for 1 means get $2 for each $1 bet, that is the other party takes your $1 and keeps it, and pays you $2 if you win. It's how casinos think about odds. This is fair if the chance of winning is 1/2.

2 to 1 means you get $2 if you win and pay $1 if you lose, which is fair if your chance of winning is 1/3. This is how two bettors will think of a bet.

The second one is the correct use of the word "odds" in stating bets. In terms of probabilities, the odds of an event is the probability of it happening divided by the probability of it not happening. So the odds of flipping heads with a fair coin is 0.5/0.5 = 1.

Odds = Probability / (1 - Probabilitiy) to 1
Probability = Odds / (1 + Odds)

But if someone says the odds of that occurring are 10%, you know they mean "probability" instead of odds. If they say the probability is 2 to 1, they should mean odds, but it's anybody's guess what they actually mean.
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