Roulette Expectation

label Mathematics
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schedule 1 Day
account_balance_wallet $5

A standard roulette wheel has 38 numbered spaces for a small ball to land in: 36 are marked from 1 to 36, half black and half red, 0 and 00 are green. If you bet $100 on a particular number and the ball lands on that number, you are paid a whopping $3600. What is the expected value of betting $100 on red 9?

Apr 21st, 2015

The probability that you win $3600 on the number is 1/38 and the probability that you lose $100 is 37/38.

So, the expected winnings are 3600*(1/38) + (-100)*(37/38) = -$2.63


Apr 21st, 2015

Thanks so much. Could you explain the answer in a way thats a little relatable?

Apr 21st, 2015

You are welcome. As for the answer, it means that when you bet many times on the number 9, you lose approximately $2.63 on each bet. Of course, it is possible that you win an occasional bet but on the average the more you bet, the more you lose. The house eventually wins. 

Apr 21st, 2015

Great! This helps me a lot.

Apr 21st, 2015

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