Rules
The player chooses rock, paper, or scissors, and the computer will do the same. Rock beats scissors, scissors beats paper, and paper beats rock. If both throw the same thing the bet is a draw for single throw bets. The player may also bet on 2, 3, or 4 game series, in which he must win every throw (ties lose) to win the bet.

Analysis
The single throw bets pay 1.9 on a win. The expected return is (1/3)*1.9 + (1/3)*1 = 2.9/3 = 96.67%.

A two throw series pays 8.7. The probability of winning is (1/3)² = 1/9. The expected return is (1/9)*8.7 = 96.67%.

A three throw series pays 26. The probability of winning is (1/3)³ = 1/27. The expected return is (1/27)*26 = 96.30%.

A four throw series pays 78. The probability of winning is (1/3)⁴ = 1/81. The expected return is (1/81)*78 = 96.30%.

Strategy
In the Playtech game the odds are the same for all three throws. However, when playing a novice human opponent always throw paper the first time! This is because most people tend to prefer rock, especially on the first throw. You can thank me later after after you see how well this works! Just don’t employ this strategy against Lisa Simpson.

Text from wizardofodds.com

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