# Banca Francesa

## Introduction

Banca Francesa is a simple dice game, involving three dice and three bets. I hear it is popular in Portugal. Online, it can be found at Internet casinos using Gaming1 software.

## Rules

1. Three ordinary six-sided dice are used.
2. Players have three bets to choose from, as shown below.
3. If the total of the dice do not fall in a range that resolves a bet, then all bets push.

### Banca Francesa Bets

Bet Winning Totals Pays
Low 5 to 7 1 to 1
High 14 to 16 1 to 1
Aces 3 61 to 1

## Analysis

The following table shows my analysis of the Low bet. The lower right cell shows a house edge of 0.46%, if ties are counted as a bet resolved. If ties are ignored, then the house edge is 1.59%.

### Low Bet Analysis

Event Pays Combinations Probability Return
5 to 7 1 31 0.143519 0.143519
4, 8 to 13, 17, 18 0 153 0.708333 0.000000
3, 14 to 16 -1 32 0.148148 -0.148148
Total 216 1.000000 -0.004630

The following table shows my analysis of the High bet. The lower right cell shows a house edge of 0.46%, if ties are counted as a bet resolved. If ties are ignored, then the house edge is 1.59%.

### High Bet Analysis

Event Pays Combinations Probability Return
14 to 16 1 31 0.143519 0.143519
4, 8 to 13, 17, 18 0 153 0.708333 0.000000
3, 5 to 7 -1 32 0.148148 -0.148148
Total 216 1.000000 -0.004630

The following table shows my analysis of the Aces bet. The lower right cell shows a house edge of 0.46%, if ties are counted as a bet resolved. If ties are ignored, then the house edge is 1.59%.

### Aces Bet Analysis

Event Pays Combinations Probability Return
3 61 1 0.004630 0.282407
4, 8 to 13, 17, 18 0 153 0.708333 0.000000
5 to 7, 14 to 16 -1 62 0.287037 -0.287037
Total 216 1.000000 -0.004630