This month I'm posting Mad-Cool-Math Nuggets.
Image courtesy: mkw87
O is for Odds.
Odds are used in statistics and in gambling. I'll take a wild guess and assume you'd find gambling more fun, so I'll stick to that for this discussion.
Let's start with probability. If you roll a single die, there are 6 possible outcomes. So the probability of rolling a 2, for example, is one-sixth or 16.67 %.
In betting odds, we look at this example a little differently. The odds of rolling a 2 are said to be 5/1, read "5 to 1". Why 5 and 1? Because there are 5 ways the outcome we want will not happen (rolling a 1, 3, 4, 5 or 6) and 1 way the outcome we want (rolling a 2) will happen. This is known as fractional odds, and you can use these two numbers to calculate the same probability of rolling a 2. Here's how:
The probability of an event with A/B odds is B / (A + B). In this case, the probability, or odds, of rolling a 2 is 1 / (5 + 1) = 1 / 6 = 16.67 %.
Fabulous. So how does this work with money? Bet $M on an event with A/B odds. If you win, you get M x (A/B) dollars plus your original $M back. (If you lose, say bye-bye to your $M.)
Bet me $1 that I will roll a 2 on my handy-dandy die, an event with 5/1 odds. If I roll a 2, you win, and you get 1 x (5/1) = 1 x 5 = 5 dollars, plus your original $1 back. Squee! (Don't spend it all in one place.)
If you bet $8 on the same event and win, you get 8 x (5/1) = 8 x 5 = 40 bucks plus your original $5 back.
Ready to hit Vegas? Well, maybe not. The example above is a fair game, statistically speaking. If we were to play enough times, you would win about as much money as you would lose, and so would I. Neither one of us would make a profit. In Vegas, casinos need to make money to stay in business.
Remember Hunger Games and the saying "May the odds be ever in your favor"? Yeah, right. That didn't work out so well for the players. All but one bit the dust. The same holds in Vegas. The odds are definitely in the casinos' favor, by design.
Ever been to Vegas? Play the lotto?
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