Trente et Quarante: probability, EV & shoe analysis

Refait at 31, house advantage and Noir, Rouge, Couleur and Inverse EV from the remaining shoe composition.

Composition-dependent shoe analysis

The standard game uses six decks. Enter the remaining cards by value and color to calculate Refait at 31, house advantage, the EV of all four wagers, Couleur/Inverse sensitivity and the effect of removing one card.

Shoe

Starting composition

Cards remaining312

Decks End of shoe

Value	Black	Red	Total
Total	156	156	312

Set the shoe and press Calculate.

House advantage

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—%

Per coup, including 32–40 ties

Refait at 31—

Excluding 32–40 ties—

Expected value of wagers

per unit wagered

Noir and Rouge have the same expected value. Couleur and Inverse also depend on the color distribution by value.

Coup outcomes

Refait at 31both rows finish at 31—

Tie 32–40same point from 32 to 40; the coup is void—

Noir winsthe first row is closer to 30—

Rouge winsthe second row is closer to 30—

Couleur winsthe first card of the Noir row has the same color as the winning row—

Inverse winsthe first card of the Noir row has the opposite color to the winning row—

Effect of removal on the house edge

Change in house advantage after removing one card of the indicated value. Negative values reduce the edge; positive values increase it.

not calculated

Couleur / Inverse sensitivity

Value-specific coefficient measuring the effect of black/red imbalance. Results are in percentage points.

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Cards used to finish exactly at 31

Exact distribution of the length of one row conditional on finishing at 31.

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Essential rules for reading the results

Noir is the first row and Rouge the second; the total closest to 31 wins. A tie from 32 to 40 voids the coup; a Refait at 31 is modeled by its half-stake loss equivalent. Couleur and Inverse depend on the color of Noir’s first card relative to the winning row. To connect EV, variance and capital, also use the bankroll and risk-of-ruin calculators.