# Coin Toss

## Introduction

Coin Toss is a simple game based on the toss of one or four coins.  The game is made by KingMidas.

## One Coin Rules

1. The player may bet on Heads or Tails.
2. After betting is closed, the game will pick one side to pay 1.2 to 1, if it wins. The other side will pay 0.7 to 1.
3. A coin will be flipped and winning bets paid.

## Four Coin Rules

The player may bet on any split between heads and tails as well as the 50/50 proposition on whether the total number of each side is an odd or even number. Here are the specific bets.

1. The following types of bets are available:
• 2 Heads & 2 Tails
• Odd/Even (Odd bets win if there is a 1-3 or 3-1 split between Heads and Tails, Even bets win if there is a 0-4, 2-2, or 4-0 split).
2. The game will randomly decide to boost the pay of some bets. Standard and bonus pays are shown in the table below.
3. After betting is closed, the game will flip four coins and pay winning bets.

### Coin Toss Pays

Bet Standard Pay Bonus Pay
Even, Odd 0.95 1.1
All Heads, All Tails 13.5 20

A representative with KingMidas told me the the probability any given bet getting the bonus pay in the four-coin version is configurable. Following are the ranges given to me.

### Coin Toss Bonus Pay Probabilities

Bet Minimum
Probability
Maximum
Probability
Even,Odd 0.035 0.04
All Heads, All Tails 0.12 0.17

If my rules were unclear, you may read them directly from the rule screen of the game.

## Analysis

To analyze the game, I took the average of the minimum and maximum of the Bonus Pay probabilities. The following table shows the expected value of each bet.

### Coin Toss Analysis

Bet Average
Pay
Probability Expected
Return
Even,Odd 0.955625 0.5 -0.022188
2 Heads/2 Tails 1.588000 0.375 -0.029500
All Heads, All Tails 14.442500 0.0625 -0.034844

## Screen Shots

The image above is of the one-coin version.

The image above is of the four-coin version.