Cee-Lo

I have heard of Cee-Lo off and on for about a dozen years now. I resisted writing about it because of many rule variants as well as various different titles for the game. When I saw the game mentioned in Scarne's New Complete Guide to Gambling, it rekindled my interest. Then I saw a Wikipedia entry on Cee-Lo, which at least establishes a baseline set of rules.

This is usually played as a player-banked game. There are two sides, which I'll refer to as the Banker and Player. As long as bets are balanced between the two sides, any number of people may play. All wins are even money.

Here are the rules that determine the winning side.

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)

Here are my probabilities are all rolls, not counting re-rolls.

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

Here is my analysis of the full game on the Banker side.

Game Outcome	Pays	Probability	Return
Instant win	1	0.250000	0.25
Instant loss	-1	0.194444	-0.194444444
Opponent instant win	-1	0.138889	-0.138888889
Opponent instant loss	1	0.108025	0.108024691
Higher point win	1	0.115741	0.115740741
Higher point loss	-1	0.115741	-0.115740741
Tie	0	0.077160	0
Total		1.000000	0.024691358

Wikipedia claims a 2.7% Banker advantage. If we ignore ties as a resolved bet, then I agree with that figure.

The question for the poll is would you play Cee-Lo

This is called Strung Flowers in China because it was apparently popular with Chinese people a long time ago, but I've read it with different payout rules. I think a pair and a six is also an instant win. Also, if the two players both have a pair, the payout is a multiple of however far apart their numbers are. So, if player one has x-x-5 and the other player two has x-x-2, player two would owe player one 3 units. Some of the rolls have names, too. A pair and a 1 is called an "ace negative." A roll of 4-5-6 is Strung Flowers. 1-2-3 is called something too, but I forgot what it was.

Quote: TigerWu

This is called Strung Flowers in China because it was apparently popular with Chinese people a long time ago, but I've read it with different payout rules. I think a pair and a six is also an instant win. Also, if the two players both have a pair, the payout is a multiple of however far apart their numbers are. So, if player one has x-x-5 and the other player two has x-x-2, player two would owe player one 3 units. Some of the rolls have names, too. A pair and a 1 is called an "ace negative." A roll of 4-5-6 is Strung Flowers. 1-2-3 is called something too, but I forgot what it was.
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Good comments. I think the title comes from the Chinese words for 4-5-6. Probably Cantonese.

Wikipedia lists some other rule variants.

Here is my new page on Cee Lo. I welcome all comments.