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Carnival Game Math Puzzle

How much can someone expect to gain or loose in this carnival game math puzzle?

 

Carnival Game Math Puzzle

In years gone by, there was a carnival game where the player would place his bet on a number from 1-6. He would then roll 3 dice. The payout was his bet plus 1, 2 or 3 times the bet, depending on how many times his number came up. Of course, if it didn't come up at all, he got nothing.

If the player bets $1, what is the expected gain or loss per game?

From Mathematical Puzzles of Sam Loyd

Click to find the answer to this math puzzle.

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