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A gambler who makes 100 bets of $1, each at payoff odds of 8 to 1. He wins 10 of these bets and loses 90. How many dollars has the gambler gained overall?

I don't seem to understand what "odds of 8 to 1" means. Can someone please explain this to me?

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Odds of 8 to 1 means that for every \$1 you wager, you could either

  • win \$8 in addition to receive your \$1 wager back
  • lose your \$1 wager

So from his 10 wins, he gets \$80, and from his 90 losses, he is down \$90. Net, he is down \$10.

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Odds of 8 to 1 mean you make a bet of \$1, then you win \$8. You also receive your original \$1 back, so if you win an 8 to 1 bet, you pay \$1 and receive back \$9.


In regards to your problem, the gambler pays in $\$100$, and gets back $\$90$, so all in all, he has lost $\$10$.

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