Trente et quarante

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Trente et quarante (German: "30 and 40") is a game of chance with six packets of French playing cards , which is now mainly played in casinos in France and in Monte Carlo . This game was developed from the older Rouge et noir by adding two additional betting fields, sometimes marked with C and I , for the opportunities Couleur and Inverse .

In the 19th century, Trente et quarante was, alongside roulette, the main attraction in the casinos of German seaside resorts. After Alexej Ivanovich, the main character in Dostoyevsky's famous novel The Gambler, broke the bank at two roulette tables, he continued his game at Trente et quarante in order to win and lose his love here too:

“The Trente-et-quarante has an aristocratic audience. This is not a roulette, but a card game. Here the bank has to pay for profits of up to one hundred thousand thalers. The largest stake is also four thousand guilders. I didn't understand anything about the game and hardly knew any of the possible types of bets, namely only red and black, which were also available here. So I stuck to these colors. The entire audience of players crowded around me. I don't remember if I thought of Polina even once in the whole time. At that time it gave me an immense pleasure to hold more and more banknotes and to pull them towards myself; they grew in a sizable heap in front of me. "

The game

The sequence of the game corresponds to that of Rouge et noir (sd) with the following difference: The first row laid out by Tailleur - that's the name of the croupier in Trente et quarante - does not apply to Rouge , but to Noir .

In addition, with Trente et quarante, the very first card withdrawn is of particular importance, it is decisive for the two additional opportunities:

Couleur (German color ) wins,

  • if Rouge wins and the first card displayed is red, i.e. a heart or a diamond card, or
  • if Noir wins and the first card displayed is black, i.e. a pique or club card.

Inverse (German opposite color ) wins,

  • if Rouge wins and the first card displayed is black, or
  • if Noir wins and the first card displayed is red.

The Couleur and Inverse odds, like the Rouge and Noir odds, are simple odds; H. you win in a ratio of 1: 1.

When the tailleur announces the result of a coup, he always only mentions the chances of rouge and color and never noir or inverse : So if noir and inverse win, he announces “ rouge perd et color. "; if, for example, Rouge and Inverse win, the announcement is " Rouge gagne et couleur perd. " etc.

The bank advantage with Trente and Quarante is 1.28% as with Rouge et noir (see analysis there ). From a certain minimum stake, a pointeur can be insured against the refait against payment of an insurance premium of 1% of his rate , so the bank advantage is only 1/101 = 0.99%, and so the Trente et quarante is one of the for cheapest casino games for the player.

Card counting

Card sled

If the card slide still contains an above-average number of low cards after a few spins, the probability of a refait increases , but if there are still predominantly high cards in the talon , this will decrease.

The chances of rouge and noir , however, are always the same regardless of the composition of the talon. However, this does not apply to the chances Couleur and Inverse , as one can easily see from the following extreme example.

Suppose the talon contains only eight cards, a red ace and seven black tens. Depending on where the ace comes to rest, Inverse wins in five cases - namely exactly when the ace comes to the first, fifth, sixth, seventh or eighth position - e.g. B. if

Noir Poker-sm-221-Ah.png Poker-sm-213-Qs.png Poker-sm-245-Tc.png Poker-sm-214-Js.png 31 points
rouge Poker-sm-212-Ks.png Poker-sm-243-Qc.png Poker-sm-215-Ts.png Poker-sm-242-Kc.png 40 points
Rouge perd et couleur.

or about if

Noir Poker-sm-215-Ts.png Poker-sm-213-Qs.png Poker-sm-245-Tc.png Poker-sm-214-Js.png 40 points
rouge Poker-sm-212-Ks.png Poker-sm-243-Qc.png Poker-sm-221-Ah.png Poker-sm-242-Kc.png 31 points
Rouge gagne et couleur perd.

and only in three cases of color - namely exactly when the ace is in the second, third or fourth position, such as:

Noir Poker-sm-245-Tc.png Poker-sm-213-Qs.png Poker-sm-221-Ah.png Poker-sm-214-Js.png 31 points
rouge Poker-sm-212-Ks.png Poker-sm-243-Qc.png Poker-sm-215-Ts.png Poker-sm-242-Kc.png 40 points
Rouge perd et couleur gagne.

If the waist still predominantly contains high black and low red cards, but a few low black and a few high red cards (in the example above, the pile does not contain a single card of this type), the balance shifts in favor of Inverse .

If you divide the playing cards into two categories as follows:

  • Category I contains the high black and low red cards,
  • Category II therefore contains the low black and high red cards,

(Sevens - as "middle" cards - are not assigned to any category and are not counted), if cards in the first category are overweight, the chances of inverses improve and vice versa: If the talon still mainly contains cards from the second category, so the balance shifts in favor of couleur .

Deviations of this kind cannot be used for winning strategies, however, by counting the cards played, the player cannot overcome the bank advantage ( Edward O. Thorp and William E. Walden, The fundamental theorem of card counting with applications to trente-et-quarante and baccarat , Int. J. Game Theory 2 109-119, 1973)

As you can see from the above example, depending on the position of the ace, rouge wins in four cases and noir in four cases , these chances are always symmetrical - contrary to the widespread opinion that a preponderance of high or low cards means the appearance of rouge or Noir (in the example given there is obviously an extreme preponderance of high cards).

literature

  • Victor Bethell: Monte Carlo - Anecdotes and Systems of Play [1] , London, 1910
  • Claus Grupp: Games of chance with balls, dice and cards , Falken Verlag, Wiesbaden, 1976
  • Siméon Denis Poisson Mémoire sur l'avantage du banquier au jeu de trente et quarante . Annales de Mathématiques Pures et Appliquées 16 173–208, 1825. ( PDF )
  • Alexander B. Szanto: Roulette, Trente-et-Quarante, Baccara, Black Jack , Perlen Reihe , Volume 645, Vienna, 1977

Individual evidence

  1. http://www.archive.org/details/montecarloanecdo00bethiala Victor Bethell: Monte Carlo - Anecdotes and Systems of Play , London, 1910, p 56 ff