Last Updated: January 7, 2019

# Thimbles

## Introduction

I think everyone has seen the game Three Card Monty at some point. It is a simple game where there are three cups, or thimbles in this case, with a ball under one of them. In street games, three cards are often used, two red and one black (or vise versa) or matchbooks. Evoplay Entertainment now brings us the game in a digital format.

## Rules

1. The game presents three thimbles (actually, they look more like half a barrel to me).
2. The player may choose one or two balls (actually, they look more like a truncated dodecahedrons to me) and a bet amount.
3. The game shuffles the thimbles. It is so fast that I don't think paying attention to the original barrel(s) with the balls will help.
4. If the player clicks either the "one ball" or "two balls" buttons, the game will replace the balls and reshuffle.
5. The player must pick a barrel.
6. If there was one ball, and the player chose correctly, he will win 2.88 for one.
7. If there were two balls, and the player chose correctly, he will win 1.44 for one.

## Analysis

The following table shows my analysis of the one-ball game. The lower right cell shows an expected return of 96%.

### One Ball Analysis

Event Pays Combinations Probability Return
Win 2.88 1 0.333333 0.960000
Loss 0 2 0.666667 0.000000
Total 3 1.000000 0.960000

The following table shows my analysis of the two-ball game. The lower right cell shows an expected return of 96%.

### Two Balls Analysis

Event Pays Combinations Probability Return
Win 1.44 2 0.666667 0.960000
Loss 0 1 0.333333 0.000000
Total 3 1.000000 0.960000