# Tie Max (formerly Lucky Max)

## Introduction

Tie Max, formerly known as Lucky Max, is a pair of baccarat side bets based on the highest individual card in the event of a tie. I first heard about it in December 2015, when it appeared at the Gold Coast in Las Vegas.

## Rules

1. Standard baccarat rules are followed, which I assume the reader is familiar with. For this analysis, eight decks are assumed.
2. The game pays based on the highest point value card in the event of a tie. For example, if the Banker had K-7-2, and the Player had 10-5-4, then the highest point value among all six cards would be the 7.
3. The High Tie Max bet pays 10 to 1 if the the highest card in a tie is a 6 to 9. All other events lose.
4. The Low Tie Max bet pays 55 to 1 if the the highest card in a tie is a 0 to 5. All other events lose.

## Analysis

The following tables show the probability and contribution to the return for both bets. The lower right cells reflects a house edge of 16.45% for the Low Tie and 11.75% for the High Tie.

### Low Tie Max Return Table

Event Pays Combinations Probability Return
Low tie 55 74,570,116,880,640 0.014919 0.820534
Loser -1 4,923,828,158,622,710 0.985081 -0.985081
Total   4,998,398,275,503,350 1.000000 -0.164547

### High Tie Max Return Table

Event Pays Combinations Probability Return
High tie 10 401,057,309,592,576 0.080237 0.802372
Loser -1 4,597,340,965,910,770 0.919763 -0.919763
Total   4,998,398,275,503,350 1.000000 -0.117391