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Games, rules and the arithmetic behind them

Learning the Games

Why baccarat scoring drops the tens digit

A baccarat hand is scored by adding the cards and keeping only the last digit. It is the single rule that makes the rest of the game intelligible.

Flat illustration of a baccarat scoring board showing two-card totals
Totals are read modulo ten, so a hand can never be worth more than nine.

Baccarat looks opaque from a distance because the scoring does something no other common card game does: it throws away part of the total. Add the cards, take the units digit, and that is the hand.

Card values are simple. Aces count one. Two through nine count their face value. Tens and the three court cards count zero. There is no ace-high convention and no suit ranking of any kind.

The scoring rule is what surprises people. A seven and an eight total fifteen, and the hand is worth five. A nine and a nine total eighteen, and the hand is worth eight. Because only the units digit survives, no hand can exceed nine, and there is no equivalent of going bust.

That ceiling explains the vocabulary. A two-card total of eight or nine is a natural, and the deal stops there. Everything else is resolved by a fixed table of drawing rules that neither the player nor the dealer chooses.

The player side draws a third card on a total of zero through five and stands on six or seven. The banker side's third-card rule is conditional: it depends on the banker's own total and, where the player has drawn, on the rank of the card the player drew. It is a lookup table, printed and followed exactly.

This is the part worth internalising. In the common form of the game, no decision belongs to anyone at the table once the wager is placed. The cards are turned, the table is consulted, and the outcome follows. The dealer is not exercising judgement and neither is the player.

The three propositions on the cloth are the player hand, the banker hand and a tie. The banker hand wins slightly more often than the player hand as a direct consequence of drawing last with more information, which is why a commission is charged on banker wins to restore the balance. That commission is a rule of the table and is printed with the rest.

Once the modulo ten rule is clear, the drawing table stops looking arbitrary and starts looking like what it is: a fixed procedure for finishing a hand that has no room left to grow.

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