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Last Updated: July 14, 2010

# Rock Paper Scissors

## Introduction

Rock Paper Scissors is a game found at Internet casinos using Playtech and Evoplay software. The image you see on top of this page is from the Playtech version.

## Playtech 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.

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%.

In the Playtech game the odds are the same for all three throws.

## Evoplay Rules

The Evoplay Entertainment version, called Rock Paper Scissors -- Viking Version, just goes one game at a time. Wins pay 1.92 for 1. the following table shows the expected return is 97.33%, counting ties as a resolved bet. We all know Rock Paper Scissors never ends on a tie, so if you don't count them, the return drops to 96%.

### Evoplay Rules

Event Pays Combinations Probability Return
Win 1.92 1 0.333333 0.640000
Tie 1 1 0.333333 0.333333
Loss 0 1 0.333333 0.000000
Total 3 1.000000 0.973333

## Gameplay Interactive

Gameplay Interactive has two types of Rock Paper Scissors games. Classic and Super pay 2 for 1 on a win, but 0.9 only on a push. The following return table for this classic/super version below shows a return of 96.67%.

### Gameplay Interactive — Classic/Super Rules

Event Pays Combinations Probability Return
Win 2 1 0.333333 0.666667
Tie 0.9 1 0.333333 0.300000
Loss 0 1 0.333333 0.000000
Total 3 1.000000 0.966667

Gameplay also offers another version, Lucky and Fortune, where an arrow on a wheel spins that determines how much a win pays. A tie in this version pays 0.8 of the amount bet. The following table shows the number of slices for each win on the wheel and my own sampling of 105 spins of where the arrow stopped.

### Gameplay Interactive — Average Win

Win Slices Sample
1 2 47
2 4 40
4 3 17
7 2 1
20 1 0
Total 12 105

If every stop on the wheel were random, then the average win would be 4.67. However, based on my sampling, it is closer to 1.92. The following return table shows that if we assume an average win of 1.92, the expected return is 90.79%.

### Gameplay Interactive — Classic/Super Rules

Event Pays Combinations Probability Return
Win 1.923809524 1 0.333333 0.641270
Tie 0.8 1 0.333333 0.266667
Loss 0 1 0.333333 0.000000
Total 3 1.000000 0.907937

## Real Life Strategy

When playing a novice human opponent, especially a male, always throw paper the first time! This is because most people tend to prefer rock, especially on the first throw.

• Try out at the Evoplay corporate web site.

Written by: Michael Shackleford

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