“. A fairly simple game, Quarante et Trente offers you a chance to have an expected return of more than 98%!”

TRENTE ET QUARANTE

Everything sounds better in French. In case you don’t know, Trente et Quarante is a famous game of cards, also known as Rouge et Noir, or Red and Black. It’s a game the French developed, that requires a deck of cards and a special table. Trente et Quarante is one of the two most famous games played in the grand gambling rooms of Monte Carlo. Roulette is the other one that you have surely seen, in the movies. What those movies didn’t reveal, is that there is one hell of an advantage to playing Trente et Quarante. The odds. While Trente et Quarante may be French for Red and Black, it’s also another way to say, Great Deal in a Casino.

Maybe that’s why this game is so popular in continental European casinos. A fairly simple game, Quarante et Trente offers you a chance to have an expected return of more than 98%!

What? You don’t speak French? You don’t plan a trip to Europe any time soon? No problem. Now you can play this fabulous game online, at my favorite Internet casino. Here’s how I got into it.


How the game is played

As I said earlier, Trente et Quarante is basically French for "thirty and forty." It’s an old European casino game still found in Monte Carlo and other major French casinos. When I went to Monte Carlo, as a young man, I didn't know what I was looking at, the first time I saw this game played. What I do remember, is the man playing the game, at the table. He was one of the coolest looking guys I have ever seen. The man was British, and possessed all the elegance some Brits still managed, in those days. He was wearing a black tuxedo. His hair was gray. There have been very few men that can pull off smoking a cigarette with a fancy holder. FDR, guys that that. This guy was one of those guys. He puffed on it as he squinted at his cards.

He won a lot of money that night.

I’ve never been back to Monte Carlo. And I never did learn French. But I do play Trente et Quarante, all the time. It surely adds a little romance to my life. Trente et Quarante is often compared to baccarat. In this game, there are two hands, and you bet on which one you think will have the better score. In this case, however, the lower the score, the better.


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The basics

1. Six 52-card decks are used.

2. Aces are valued as one point, 2s to 10s according to pip value, and face cards as 10 points.

3. There are four wagers available: Black, Red, Color, and Inverse. In addition, an Insurance wager is available on each of these four bets.

4. 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.

5. Next, the dealer will do the same thing but for the "red" hand.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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

This table shows you the probability for 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


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This table shows you the probability for 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 you the return table for the Black, Red, Color, and Inverse wagers. The lower right cell shows a house edge of 1.10%.

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

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The next table shows you the return table for Insurance, assuming you choose 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 proves that Insurance is indeed a wise wager. 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.

More math….

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

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Strategy

Like the odds? Now I understand what the cool guy I saw in Monte Carlo was doing that night. He was a smart Trente et Quarante player. And he was raking in the dough. After scouting the Internet, I developed a strategy that has worked well for me, too. Here are three very important factors to consider:

  • 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.

Methodology

According to my research sources, this analysis was based on a random simulation from more than 26 billion hands. A cut card was used in each simulation, placed after 271 cards.


Back to the table

At a typical Quarante et Trente table, there may be anywhere from one to eight players. When you sit at this table, you are expected to conduct yourself like a gentleman. No cursing or spitting, please. A little French goes a long way.


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The Aim of the game

Each player bets on the color of the row of cards which will have a total lower than the second row, and knows that this total must always be between 30 and 40. In Monte Carol, four casino employees take places around the Trente et Quarante table. Two croupiers handle the cards and the wagers. The “bout de table ” (“table-end”) ;and “chef de partie” (“game supervisor”) are there to ensure that the games proceed smoothly. Before the game can begin, the croupier shuffles six packs of 52 cards and asks one of the players to cut the deck. He takes the last five cards in the deck, including a red card, and places them in the shoe. When the red card appears, that’s the end of that cut, and the croupier has to re-shuffle the cards. The game begins when the croupier says “Faites vos jeux” (“Place your bets”).

Each player must then place his bets from four possibilities. All are paid at even money : Red, Black, Color and Inverse.

You can only make two wagers at a time. Such as Red and Inverse OR Black and Inverse OR Red and Color OR Black and Color.

When the croupier declares “Rien ne va plus” (“No more bets)”, players stop betting and the croupier deals two rows of cards in front of him. The first row determines the point value for Black and the second row for Red.

The cards are counted at their face value – this includes the ace, which counts as 1, and picture cards which count as 10. The croupier deals as many cards as necessary for each row until he goes over 30. The winning row is the one with the total nearest to 30.

The croupier never announces the total, only the final digit (eg.. : if the total is 36, he announces “6”). Traditionally, the croupier only announces the result of the Red row. If it has the lowest score, the croupier says “Red wins” : if it is the Black row which scores nearest to 30, he announces “Red loses”.

Color and Inverse are determined by the first card in the first row. If it is the same color as that of the winning row, Color wins and Inverse loses. If the first card is a different color, Inverse wins and Color loses .

When the two rows score the same total of points, the game is null and void unless both rows score 31. The croupier then announces “1 after”. In this case, stakes are “locked in” – ie. blocked – and lose half of their value. The player then has two options for playing :

  • He can ask to share his stake.
  • He can wait until the next round and, if his wager wins, his bet is unblocked. He can then recover it or put it back into play.

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Advanced Players

The cool guy I saw in Monte Carlo must have known some solid strategy. These are the kind of moves you can make to play smart:

At the start of the game, take out insurance worth 1% of your wager to protect from the case of “1 after”. This insurance – which takes the form of a small, white rectangular chip called a “bone” – prevents you from losing half the value of your wager, as insured wagers are not locked in. In the next round, the wager is played as usual.


No tricks

Unlike many other card games, Trente et Quarante seems to be immune to most advantage playing strategies. While blackjack can be beaten with complicated strategies like card counting and shuffle tracking, these do not really help you in Trente et Quarante. Nor is there any counting system or betting system that can improve your odds in color betting. You can refer to the calculations I provided here, but as you see, it’s pretty straightforward. Edward Thorp, author of Beat the Dealer, The Mathematics of Gambling and other books, even proved through computer analysis that there is no real way to use advantage playing in Trente et Quarante.

This is another reason I like it. And possibly one of the reasons that elegant gentleman was winning so much money. As you can see, Trente et Quarante has a lot of great things going for it, from a gambler’s point of view. The low house edge, the simple rules and the insurance all make it a very fair game to play. If you ever encounter this game when you are in a European casino, I urge you to try it out. You might like it as much as I do.


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Where to play

Well, I don’t see any big trips to Europe on the horizon for myself. No more nights in Monte Carol for me. The good news, is that Trente et Quarante is available on the Internet. I play at the casino run by my favorite online sportsbook, youwager.eu. Their casino features all of the standard games, plus I’ve been doing business with them for years. This top-rated book is a First Fidelity-owned company, and I personally recommend them. As their slogan says, they “pay like a bank.” When you are competitive enough to win as often as I do, that part is very important. Play like you intend to win, and the right casino will make it worth your while.

Show me the money!

That’s what youwager.eu does. They show me the money I won, right away. They also offer some great bonuses I have yet to find anywhere else. Their Gambler Insurance program even reimburses players a portion of their losses, if they qualify.

The man I saw playing Trente et Quarante that night? Well, years later, I came across pictures of him in LIFE magazine. Turns out that fellow was Ian Fleming, an English author, journalist and former naval intelligence officer. Recognize the name? He’s best known for his James Bond novels. With his hero, Mr. Fleming has taught several generations of boys how to be cool. Or, how cool would look if we were all as handsome as Sean Connery, and strong and brave as James Bond, agent 007. Fleming was an avid gambler. The first book in the Bond series was Casino Royale.

Mr. Fleming also taught me some important lessons about gambling

Play a game that’s fair.
Try to have a little class.

So maybe you will never, in your wildest imagination, be able to live like James Bond, or even Ian Fleming. But you can play Trente et Quarante. Online. The next time the croupier announces a total, and says “Red wins,” it could be you sitting there at the table, raking in the dough. You could even try out a fancy cigarette holder, in the privacy of your own home. I won’t tell. No one will. That’s the beauty of the Internet.



Let’s review what we have learned.

Trente et Quarante dates back to at least the 17th century, and was one of the most popular games in Monte Carlo. The game is also known as Rouge et Noir, or Red and Black. Trente et Quarante offers you a chance to gamble against a small house edge of less than 2%.

Trente et Quarante is somewhat similar to baccarat, as two hands are dealt and one wins or they both tie.


The rules, one more time:

    Six standard decks of 52 cards are used, with no jokers or wild cards. Aces count as one point, all other cards are counted as their numerical value, 2 through 10, and face cards also count as 10. The dealer shuffles the cards, has the player cut the cards, and they are placed in a shoe.
    There are four possible wagers to choose:
    Black: a wager on the Black hand winning with total points closest to 31
    Red: a wager on the Red hand winning with total points closest to 31
    Color: a wager on the hand that is signified by the first card dealt to the Black hand
    Inverse: a wager on the hand that is signified by the opposite color of the first hand dealt to the Black hand
    To play Trente et Quarante, each player chooses one or more of the four wagers, and the dealer begins by dealing cards to the Black hand and stops when the point total is 31 or more. Then, the dealer begins dealing cards to the Red hand, stopping when the point total is 31 or more. The hand closest to 31 wins, and all wagers on that color wins even-money, or a payoff of 1 to 1. If there is a tie on any point total between 32 and 40, the hand is a push, and no money is exchanged.
    But if there is a tie, when both the Black and Red hands total 31, the house will take the wagers and place them En Prison. This money is held until the next hand is played-out. If the same hand originally wagered on wins, the bet is returned. If the hand loses, the bet is lost. This works out to the player losing half of all wagers when a 31-tie is dealt.

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Insurance

To guard against losing on a 31-tie, the house offers insurance in the form of a bet 1% of the hand wager. When there is no tie, the insurance wager is lost. If there is a tie of 32 to 40 points, the insurance bet is also a tie, and the bet remains. However, if there is a 31-tie, the house pays 49 to 1, or the anticipated size of the loss on a En Prison hand, which is half a bet.

In essence, an insurance wager covers the standard wagers from loss on any 31-tie. Since a 31-tie occurs about once every 38 hands, but pays 49-1, the bet is in the player’s favor at all times! That means you should always take insurance – you have an edge of about 18%.

When combined with the house edge on the hand wagers, the overall house edge is only about 1%.

This is a very fair game for the player.

Here, I have offered free and voluntarily, all I know about my favorite game. Why? Maybe it will become a favorite game for you, too. I think that any game that promotes elegance and provides fair odds is good for everyone. It’s even good for the entire Internet, the way I see it.

Above all else, why not try to have a little class in your life. And why not win some money, while you are at it?



Are you game?


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