Baccarat Math Specification

Card Valuation

Card	Value
2-9	Face value (2-9)
10, J, Q, K	0
A	1

Hand Score

The score of a hand is calculated by summing the values of all cards in the hand and taking the last digit (modulo 10).

Score = (Sum of card values) mod 10

Example	Calculation	Score
K♥ + 7♠	0 + 7 = 7	7
8♦ + 7♣	8 + 7 = 15	5
Q♣ + J♥ + 5♠	0 + 0 + 5 = 5	5

Initial Deal

Four cards are drawn from the deck after the provably fair cut:

Position	Recipient
1	Player
2	Banker
3	Player
4	Banker

Player receives cards at positions 1 & 3. Banker receives cards at positions 2 & 4.

Natural Detection

After the initial two-card deal, if either hand has a score of 8 or 9, a natural is declared. No further cards are drawn. The game ends immediately and the winner is determined.

IF player_score >= 8 OR banker_score >= 8:
    -> Natural -> Skip third cards -> Determine winner

Third-Card Drawing Rules

If neither hand is a natural, the third-card drawing rules are applied in this strict order.

Step 1: Player Decision

Player Score	Action
0, 1, 2, 3, 4, 5	Draw third card (position 5)
6, 7	Stand

The player has no choice, this is a fixed rule.

Step 2: Banker Decision (Player Stands on 6 or 7)

When the player does not draw a third card:

Banker Score	Banker Action	Card Position
0, 1, 2, 3, 4, 5	Draw	5
6, 7	Stand	N/A

Step 3: Banker Decision (Player Drew)

When the player has drawn a third card, the banker's decision depends on two variables: the banker's own score and the value of the player's third card.

Banker Score	Banker Draws?	Condition
0, 1, 2	Always	Unconditionally
3	Yes	Player's third card value ≠ 8
3	No	Player's third card value = 8
4	Yes	Player's third card ∈
4	No	Player's third card = 0, 1, 8, 9
5	Yes	Player's third card ∈
5	No	Player's third card = 0, 1, 2, 3, 8, 9
6	Yes	Player's third card ∈
6	No	Player's third card = 0, 1, 2, 3, 4, 5, 8, 9
7	No	Always stands

When the banker draws, the card is taken from position 6 (after the player's third card at position 5).

Winner Determination

IF player_final_score > banker_final_score -> PLAYER wins
IF banker_final_score > player_final_score -> BANKER wins
IF player_final_score == banker_final_score -> TIE

The winner is determined after all cards are drawn and final scores computed.

Payout Multipliers

Bet Type	Multiplier	Formula	Example ($100 bet)
Player	2.0×	win = bet × 2.0	$200
Banker	1.95×	win = bet × 1.95	$195
Tie	9.0×	win = bet × 9.0	$900

Tie Push Logic

When the result is a Tie, the settlement is:

IF winner == TIE:
    Tie bet    -> win = bet * 9.0     (pays 8:1)
    Player bet -> win = bet * 1.0     (push, bet returned)
    Banker bet -> win = bet * 1.0     (push, bet returned)

Player and Banker bets are not lost on a Tie, they are returned to the player. Only the Tie bet pays the 9.0× multiplier. This is a critical difference from games where non-winning bets are forfeited.

Configurable Parameters

Parameter	Default	Range
player_multiplier	2.0	≥ 1.0
banker_multiplier	1.95	≥ 1.0
tie_multiplier	9.0	≥ 1.0

All multipliers are configurable per-game-instance by the operator.