Chemin de Fer

Last update: July 20, 2010

Introduction

Despite having been to Europe three times, I still have never knowingly seen a game of Chemin de Fer.

Rules

To avoid confusion, when addressing the hands of Player and Banker, I will use capital letters. When referring to a human player or banker, I will use lower case. The hand scoring rules in Chemin de Fer are the same as baccarat. Otherwise, the rules of Chemin de Fer are as follows.

1. Six 52-card decks are used.
2. Instead of the casino banking the game, a single player does. The turn to be the banker rotates around the table.
3. The banker always has the Banker hand.
4. The banker would indicate the maximum he was willing to lose.
5. From the banker's left, the other players would indicate how much they wanted to bet. If a player wanted to bet the maximum he could, subject to the banker's stated maximum loss, he would declare "banco," and no other players could bet.
6. The dealer would give deal two cards each as the Banker and Player hands. The Banker hand would be given to the banker, and the Player hand to the player with the largest wager.
7. The players with control of the two hands would check their cards. If either had an 8 or 9 total (known as a "natural"), he would turn them over immediately. The other hand would be turned over as well.
8. Otherwise, unlike baccarat, the player with the largest wager could choose whether to take a third card. I have read it was traditional to always hit on 4 or less, and stand on 6 or more, with the five the only Player total that was seen going either way.
9. If the player with control of the Player hand took a third card then he must turn it face up after examining it.
10. After the player with the Player hand either stood pat or took a third card the banking player then had the option to take a third card.
11. All other cards would be turned over, the hands scored, and wagers resolved.
12. I do not think there was a tie bet, but my analysis below shows what the tie bet would pay anyway at a win of 8 to 1.

Strategy

Banker Strategy when Player Draws on 5

Banker should draw on 6 or less when Player stands, and following the following table for drawing a third card after the Player draws. Note that the following table is the same as conventional baccarat, although the rule of drawing when the Player stands is not.

Banker Strategy when Player Stands on 5

Banker should draw on 5 or less when Player stands, and following the following table for drawing a third card after the Player draws. Note the only two changes are standing on Banker 3 vs. Player 9, and Banker 5 vs. Player 4.

The strategy for the Player and Banker hand depends on what the other bettor's strategy is. Much like rock paper scissors. The following is the expected profit of the Banker bet according to the four possible strategy mixtures.

• If the Player Draws on 5, and the Banker correctly predicts this, then the Banker will have an expected win of 1.3803%.
• If the Player Draws on 5, and the Banker incorrectly predicts he will stand, then the Banker will have an expected win of 1.1993%.
• If the Player Stands on 5, and the Banker correctly predicts this, then the Banker will have an expected win of 1.5501%.
• If the Player Stands on 5, and the Banker incorrectly predicts he will draw, then the Banker will have an expected win of 0.9100%.

Doing some game theory, which I won't get into, the Player should draw on 5 with probability 77.96%, and the Banker should draw on 6 with probability 42.72%, while making the adjustments of standing on 3 vs. 9 and 5 vs. 4 the other 57.28% of the time.

I get into a simplified version of this kind of game theory problem on my MathProblems.info site, problem #192.

Banker has Less Free Will Rule

According to The Doctrine of Chances: Probabilistic Aspects of Gambling by Stewart N. Ethier, in modern Chemin de Fer the Banker must stand on 6 if the Player stands. If this is the case, then the Player should always hit on 5, and the Banker should always follow the conventional baccarat rules for drawing after the player draws, specifically drawing to a 3 against a Player 9, and 5 against a Player 4.

Links

• Wikipedia page on Chemin de Fer.
• The Doctrine of Chances: Probabilistic Aspects of Gambling by Stewart N. Ethier. This college text has several pages devoted to the mathematicis of Chemin de Fer, although based on an infinite deck, which does affect the odds and strategy.

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