Cee Lo

Introduction

Cee Lo is a player-banked dice game. There is generally a banker who plays against the other players.

Rules

Two sides are established as the Banker and Player. The Banker will book bets on the Player side. Wins pay even money. The rules that determine the winner are as follows.

1. Three ordinary six-sided dice are used.
2. The Banker rolls first.
3. If the roll from rule 2 is any of the instant winning events listed below, the side rolling wins.
4. If the roll from rule 2 is any of the instant losing events listed below, the side rolling loses.
5. If a pair plus a singleton 2-5 is rolled, the singleton is known as the "point" of the side rolling.
6. Any other roll (three singletons other than 1-2-3 and 4-5-6) results in an immediate re-roll
7. If a point is established per rule 5, then the Player shall roll.
8. Rules 3 to 6 shall be repeated for the Player.
9. If there is both a Banker and Player point established, the side with higher point shall win.
10. If there is both a Banker and Player point established and the points are the same, it is a tie.

Instant Winning Rolls

• Three of a kind
• 4-5-6
• Any 1-5 pair + singleton 6 (for example, 3-3-6)

Instant Losing Rolls

• 1-2-3
• Any 2-6 pair + singleton 1 (for example, 3-3-1)

Analysis

The following table shows the number of combinations and probability of all rolls, assuming there was no re-roll.

Roll Resolved Probabilities

Event Combinations Probability
Three of a kind 6 0.055556
4-5-6 6 0.055556
1-2-3 6 0.055556
Pair + 6 15 0.138889
Pair + 1 15 0.138889
Pair + 2-5 60 0.555556
Total 108 1.000000

The following table shows the probability of all possible outcomes of the Banker position. The lower right cell shows an advantage of 2.47%.

Roll Resolved Probabilities

Event Pays Probability Return
Instant win 1 0.250000 0.250000
Instant loss -1 0.194444 -0.194444
Opponent instant win -1 0.138889 -0.138889
Opponent instant loss 1 0.108025 0.108025
Higher point win 1 0.115741 0.115741
Higher point loss -1 0.115741 -0.115741
Tie 0 0.077160 0.000000
Total   1.000000 0.024691