You must have heard of the odds of winning bets. It says what kind of bet you would be willing to make. It is often confusing as there are several conventions to describe. We will see them one by one and understand the associated probabilities.
Odds in stats
A 2 to 1 odds means that out of three possible outcomes, there will be 2 of one kind and 1 of another. It means there is a probability of 2/3 (66.7%) for one and 1/3 (33.3%) for the other. The relationship is:
For p = 2/3, odds = (2/3)/(1-(2/3)) = 2/3/1/3 = 2/1.
The odds of rolling a six in a die is 1 to 5. This means one outcome will favour a six, and five do not.
In gambling
Things take a slightly different turn in gambling. The odds in gambling focus on winning the stake and, therefore, represent the amount the bookmaker pays along with the original bet. Odds of 4/1 means the bettor stands to make 4 profit on a stake of 1 (gets a total of 4 + 1 = 5). And there are four styles of betting odds:
1. Americal style
Boston Celtics: +450
Golden State Warriors: +550
Milwaukee Bucks: +800
Those mean: If you bet 100 on the Celtics, you win 450; a total payout of 550. Warriors: bet 100, win 550, payout of 650. Finally, the bucks can win you 800 and a payout of 900 for a 100 bet.
Odds with a negative sign in front mean how much money you need to bet to win 100. So -200 means you get 100 if you bet 200 (total payout = 100 + 200 = 300).
2. Decimal style
Multiply the decimal with the wager, and you get the payout. So for the Celtics case, the decimal odd is 5.5. Bet 100, and you get 5.5 x 100 = 550 as the payoff.
3. Fractional style (UK)
Like the American style, this calculates the profit and not the payout. a/b (a-to-b) means your profit is (a/b) x wagered amount. So for the Celtics, the fractional odds are 4.5/1 or 9/2.
4. Implied odds
It is the probability equivalent in the betting world. A 9-to-2 odds imply it is an underdog with a chance of 2 out of 11 for winning or 18.18%.
Sports betting odds: The Sports Geek
