Trente Et Quarante Layout
How Trente et Quarante is Played at Monte Carlo and at the French Riviera
Trente et Quarante is one of the two games played in the gambling rooms at Monte Carlo, roulette being the other.
Two croupiers sit on each side of the table, one of them being the dealer; behind the two on the side opposite to the dealer a supervisor of the game has his seat. Six packs of fifty-two cards each are used; these are well shuffled, and the croupier asks any of the players to cut, handing him a blank card with which to divide the mixed packs. There are only four chances at trente et quarante: rouge or noir, known as the grand tableau', couleur or inverse, known as the petit tableau.
At Monte Carlo the stakes are placed on the divisions indicated on the table, the maximum being 12,000 francs and the minimum 20 francs which must be staked in gold. The dealer, who has placed all the cards before him, separates a few with the blank card, takes them in his left hand and invites the players to stake with the formula, 'Messieurs, faites vos jeux!' After a pause he exclaims 'Le jeu est fait, rien ne va plus!' after which no stake can be made. He then deals the cards in a row until the aggregate number of pips is something more than thirty, upon which he deals a second row, and that which comes nearest to thirty wins, the top row being always distinguished as noir, and the lower as rouge. In announcing the result the word 'trente' is always omitted, the dealer merely announcing 'un, trois, quatre', as the case may be, though when forty is turned up it is described as quarante. The words noir and inverse are also never used, the announcement being rouge gagne or rouge perd, couleur gagne or couleur perd. Gain or loss over couleur and inverse depends upon the color of the first card dealt.
If this should be also the color of the winning row, the player wins. Assuming, for example, that the first card dealt is red, and that the lower row of the cards dealt is nearest to thirty, the dealer will announce 'Rouge gagne et le couleur.' If the first card dealt is red, but the black or top row of cards is nearest to thirty, the dealer announces 'Rouge perd et le couleur.'
It frequently happens that both rows of cards when added together give the same number. Should they both, for instance, add up to thirty-three, the dealer will announce 'Trois apres,' and the deal goes for nothing except in the event of their adding up to thirty-one.
Un apres (i.e. thirty-one) is known as a refait; the stakes are put in prison to be left for the decision of the next deal, or if the player prefers it he can withdraw half his stake, leaving the other half for the bank. Assurance against a refait can be made by paying 1% on the value of the stake with a minimum of five francs. When thus insured against a refait the player is at liberty to withdraw his whole stake. It has been calculated that on an average a refait occurs once in thirty-eight coups.
After each deal the cards are pushed into a metal bowl let into the table in front of the dealer. When he has not en'ough left to complete the two rows, he remarks 'Les cartes passent'; they are taken from the bowl, reshuffled, and another deal begins.
If you are ever in a European casino and come across Trente-et-Quarante, it is an excellent and enjoyable table game that offers very good value for the slight edge that it carries.
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Introduction
Trente et Quarante is French for 'thirty and forty.' It is an old European casino game still found in Monte Carlo and other major French casinos. When I went to Monte Carlo, I didn't knowingly see the game, but I wasn't specifically looking for it either.
The game can be most closely compared to baccarat. There are two hands, and players bet on which one will have the better score. In this case, the lower the score the better.
Rules
- Six 52-card decks are used.
- Aces are valued as one point, 2s to 10s according to pip value, and face cards as 10 points.
- There are four bets available: Black, Red, Color, and Inverse. In addition, an Insurance wager is available on each of these four bets.
- After players have made their wagers, the dealer will deal cards to determine the value of the 'black' hand. A running total will start at 0 and go up as the cards are dealt from the shoe. The dealer will stop when the total points is 31 or more. The maximum possible score is 40.
- Next, the dealer will do the same thing but for the 'red' hand.
- The Black wager shall win if the black hand has fewer points than the red hand. If the red hand has fewer points, then the result is a loss. If there is a tie at 32 to 40 points, then the result is a push. If there is a tie at 31 points, then the player may choose to lose half, or 'imprison' his bet, which I explain below.
- The Red wager is the opposite of the Black wager, winning if the red hand is less and losing if it is more. The tie rules are the same.
- The Color wager acts like a Black wager if the first card dealt to the black hand is black, and like a Red wager if that first card is red.
- The Inverse wager is the opposite of the Color wager, acting like a Black wager if the first card is red, and a Red wager if the first card is black.
- The player may take out Insurance on the Black, Red, Color, or Inverse wagers. The Insurance wager must equal 1% of the primary wager and pays the loss if the outcome is a 31 tie. If the primary wager wins or loses the full amount, then the Insurance wager loses. A 32-40 tie results in an Insurance tie. In other words, Insurance pays 49 to 1 on a 31 tie, pushes on any other tie, and otherwise loses.
- If the player imprisons a wager after a 31 tie, then it is blocked off somehow. Then the next hand is played out. If that next hand results in a win for the blocked off wager, then it is returned to the player. If the next hand results in a loss for the blocked off wager, then it is lost. Any tie, including on 31, results in the blocked off wager remaining on the table until there is a win or loss to resolve it.
Odds
The following table shows the probability of each number of points for each hand.
Points Distribution
Points | Probability |
---|
31 | 0.148177 |
32 | 0.137900 |
33 | 0.127618 |
34 | 0.116876 |
35 | 0.106136 |
36 | 0.094963 |
37 | 0.083814 |
38 | 0.072255 |
39 | 0.060751 |
40 | 0.051510 |
Total | 1.000000 |
The next table shows the probability of each possible outcome between the Black and Red hands.
Points Distribution
Event | Probability |
---|
Black wins | 0.445184 |
Red wins | 0.445184 |
Tie (32-40) | 0.087705 |
Tie (31) | 0.021927 |
Total | 1.000000 |
The next table shows the return table for the Black, Red, Color, and Inverse bets. The lower right cell shows a house edge of 1.10%.
Text big hit members.
Return Table for Black, Red, Color, and Inverse
Event | Pays | Probability | Return |
---|
Win | 1 | 0.445184 | 0.445184 |
Push | 0 | 0.087705 | 0.000000 |
Lose half | -0.5 | 0.021927 | -0.010964 |
Lose all | -1 | 0.445184 | -0.445184 |
Total | 1.000000 | -0.010964 |
The next table shows the return table for Insurance, assuming the player chooses to lose half on a 31 tie. The lower right cell shows a player advantage of 18.41%!.
Return Table for Insurance
Event | Pays | Probability | Return |
---|
Win | 49 | 0.021927 | 1.074436 |
Lose | -1 | 0.890367 | -0.890367 |
Push | 0 | 0.087705 | 0.000000 |
Total | 1.000000 | 0.184069 |
The above Insurance table shows that Insurance is indeed a great bet. Aside from some Super Bowl proposition wagers, the best bet I've ever known. Unfortunately, as stated in the rules, Insurance is limited to 1% of the primary wager. The next table shows the combined effect of betting 100 units on Black, Red, Color, or Inverse and 1 unit on Insurance. The lower right cell shows an expected loss of 0.912295 units. The combined expected value between the two bets is thus -0.912295/101 = -0.00903262.
Combined Return Table on 101 Units Wagered
Primary Wager Event | Primary Wager Pays | Insurance Pays | Total Win | Probability | Return |
---|
Win | 100 | -1 | 99 | 0.445184 | 44.073184 |
Push | 0 | 0 | 0 | 0.087705 | 0.000000 |
Lose half | -50 | 49 | -1 | 0.021927 | -0.021927 |
Lose all | -100 | -1 | -101 | 0.445184 | -44.963551 |
Total | 1.000000 | -0.912295 |
Strategy
- It doesn't matter what you bet on between Black, Red, Color, and Inverse.
- Always take insurance.
- The odds between losing half and imprisoning a bet after a 31 tie are the same.
In other words, do whatever you want, as long as you take Insurance.
Trente Et Quarante
Methodology
This analysis was based on a random simulation of over 26 billion hands. A cut card was used in the simulation, placed after 271 cards.
Trente Et Quarante
Links
- montecarlocasinos.com has a page on the game rules.
- The Doctrine of Chances: Probabilistic Aspects of Gambling by Stewart N. Ethier. This book has a chapter on Trente et Quarante. My house edge for the game is 0.000018 higher than Ethier's. I believe this is due to cut card effect, which would not have played a role in Ethier's method of an exact combinatorial analysis.
Trente Et Quarante Definition
Written by:Michael Shackleford