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

BetGames.tv Rules

Following are the rules as played at BetGames.tv.

1. The dealer uses a single deck of 24 cards, consisting of eight each of rocks, paper, and scissors.
2. There are two betting positions -- Silver and Gold.
3. After betting, the dealer shall deal one card each to each position.
4. The player may bet on which symbol to play against each dealer position.
5. On the Silver position, wins pay 1.9 for 1 and a tie pays 1 for 1 (a push).
6. On the Gold position, wins pay 2.5 for 1 and a tie pays 0.4 for 1 (a net loss of 60% of the bet).
7. The player may bet on one symbol only per hand.

Following is an example.

In the image above, I bet 0.1 mBTC (a mBTC equals 1/1000th of a Bitcoin) on paper for the Silver hand and Scissors for the Gold hand. The dealer drew rock on the Silver and paper on the Gold hand. This resulted in wins on both hands. Wins on the Silver hand pay 1.9 for one and on the Gold hand pay 2.5 for one. My total win was 4.4 bet units. Since my bet unit was 0.1mBTC, I got back 0.44 mBTC. Of that 0.2, was my original bets back and 0.24 in profit.

The following table shows my analysis of the bet on the Silver Hand. The lower right cell shows an expected return of 96.67%.

BetGames -- Silver Hand

Event Pays Probability Return
Win 1.9 0.333333 0.633333
Push 1 0.333333 0.333333
Lose 0 0.333333 0.000000
Total   1.000000 0.966667

The following table shows my analysis of the bet on the Gold Hand. The lower right cell shows an expected return of 96.67%.

BetGames -- Gold Hand

Event Pays Probability Return
Win 2.5 0.333333 0.833333
Push 0.4 0.333333 0.133333
Lose 0 0.333333 0.000000
Total   1.000000 0.966667

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.