Last Updated: October 14, 2019

# Lucky Nines

## Introduction

I first noticed the Lucky Nines side bet on a baccarat machine on a bar top multi-game machine by Interblock at Binion's Las Vegas on October 13, 2019. The bet pays according to the number of nines between the Player's and Banker's initial two cards and whether they are suited.

## Rules

1. Eight decks are used.
2. Two cards are dealt to the Player and Banker hands each.
3. The Lucky Nines bet pays according to the following pay table and those initial four cards. Pays are on a "to one" basis.

### Lucky Nines Pay Table

Event Pays
Four nines 500
Three suited nines 250
Three nines 20
Two suited nines 8
Two nines 5
One nine of diamonds 2
One nine 1

## Analysis

The following table shows the number of combinations, probability, and contribution to the return of all possible outcomes. The lower right cell shows a house edge of 19.46%.

### Lucky Nines Return Table

Event Pays Combinations Probability Return
Four nines 500 35,960 0.000029 0.014619
Three suited nines 250 64,512 0.000052 0.013113
Three nines 20 1,840,128 0.001496 0.029922
Two suited nines 8 8,236,032 0.006696 0.053571
Two nines 5 28,237,824 0.022959 0.114794
One nine of diamonds 2 74,908,672 0.060905 0.121810
One nine 1 224,726,016 0.182714 0.182714
No nines -1 891,881,376 0.725148 -0.725148
Total   1,229,930,520 1.000000 -0.194605

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