Rules, Card Values, and the Third Card

Level 1 · Lesson 3 of 4 · Foundations

Rules, Card Values, and the Third Card: The Tableau Explained

Why the tableau exists at all

In Chemin de Fer, the older form of the game, the player acting as Banker decides whether to draw a third card. Punto Banco was created to remove that decision. By the late 1950s the major Nevada casinos wanted a baccarat variant that ran on volume, didn't require an experienced Banker at the table, and presented a fixed house edge for accounting purposes. The result was the punto banco tableau, where the third-card decision is made entirely by the rules.

The tableau wasn't designed at random. It was reverse-engineered to give Banker a small edge while keeping Player competitive. The Banker side wins about 45.86% of hands, Player wins 44.62%, and 9.52% are ties. After the 5% commission that Banker pays on wins, the house edge settles at 1.06% on Banker and 1.24% on Player. Both are extraordinarily low by casino-game standards. They're also stable, because no human decision changes them.

Card values, in detail

Every card has a fixed point value:

CardPoints
Ace1
2 to 9Face value
100
Jack0
Queen0
King0

Suit is irrelevant. Colour is irrelevant. A heart and a spade of the same rank score identically. The only thing the table reads is the point value.

Hand totals are read modulo 10. Practically that means you add the two cards and take only the last digit of the sum. A 9 and a 7 makes sixteen, scores six. A king and a 5 is five (the king counts zero, so the total is five). A 4 and a 6 is ten, scores zero. The minimum hand total is zero. The maximum is nine. There is no concept of "going bust" the way there is in blackjack, because the modulo arithmetic clips any total back into the 0-to-9 range.

This is the rule that confuses new players more than any other. A face card looks like it should be high. In baccarat it's zero. A 10 and a 10 is still zero. A 9 and a 9 sums to eighteen and scores eight, because only the last digit counts. Do the addition, drop the leading digit, and that's your total.

The Player rule, in full

The Player rule is short enough to memorise in five seconds:

  • Player's two-card total is 0, 1, 2, 3, 4, or 5: Player draws a third card.
  • Player's two-card total is 6 or 7: Player stands.
  • Player's two-card total is 8 or 9: it's a natural, the hand ends, no draws on either side.

That's the entire Player rule. There is nothing else to know.

The Banker rule, in full

The Banker rule depends on what Player did. If Player stood on 6 or 7, Banker draws on totals of 0 to 5, and stands on 6 or 7. If Player drew a third card, Banker's draw depends on both Banker's two-card total and the value of Player's third card.

The full Banker tableau is:

Banker's two-card totalBanker's action
0, 1, 2Always draws
3Draws, unless Player's third card was 8
4Draws if Player's third card was 2, 3, 4, 5, 6, or 7
5Draws if Player's third card was 4, 5, 6, or 7
6Draws if Player's third card was 6 or 7
7Always stands

If neither side is dealt a natural, and Player stands on 6 or 7, Banker plays as if Player had stood and uses the simpler "draw on 0 to 5, stand on 6 or 7" rule.

The reason Banker's rule is longer is that Banker acts second. By the time Banker decides, Player's third card is already known. The tableau is built to give Banker slightly better information, which is the source of Banker's 1.06% edge over Player's 1.24%. That extra fraction of a percentage point, multiplied across thousands of hands, is the entire reason Banker is the better main bet.

What this looks like at the table

You will never have to apply any of this. The dealer reads the tableau, calls the draw, and resolves the hand. The reason I've laid it out is so that the next time you see a Banker stand on 6 when Player drew a 1, you'll know why. Or the next time someone at the table says "Banker has to draw on a three", you can see whether that's correct given what Player's third card was. (It isn't, if Player's third card was 8.)

Watching the tableau play out is one of the more satisfying things about being at a baccarat table. The rules are visible, the maths is honest, and once you understand the structure, you can call the dealer's actions a beat before they call them. I've done exactly this at the Hippodrome's Heliot Salon Privé, reading the draw a second before the croupier moves. The dealer smiled. They know someone's been paying attention.

A worked example

Player is dealt a 4 and a 2. Total is 6. Player stands. Banker is dealt a 5 and an Ace. Total is 6.

Both sides are on 6. Player has stood. Banker also stands. The hand resolves as a tie.

Second hand: Player is dealt a 3 and a 2. Total is 5. Player draws a third card. The third card is a King, which scores zero. Player's final total is still 5. Banker is dealt an 8 and a 7. Total is 5. Player's third card was a King (zero). Banker draws on 5 if Player's third card was 4, 5, 6, or 7. A zero isn't in that range, so Banker stands.

Player 5, Banker 5. Tie.

Third hand: Player is dealt a King and a Queen. Total is 0. Player draws. Third card is a 7. Player's final total is 7. Banker is dealt a 3 and a Jack. Total is 3. Player's third card was a 7. Banker draws on 3 unless Player's third card was 8. The 7 isn't an 8, so Banker draws. Banker's third card is a 6. Banker's final total is 9.

Player 7, Banker 9. Banker wins.

You don't need to work these through at the table. The dealer does. But if you can read them on paper, the tableau stops being mystifying.

Key numbers

RuleDetails
Player draws on0 to 5
Player stands on6 to 7
Natural8 to 9
Banker draws on0 to 2 always; conditional on 3 to 6
Banker stands on7 always
Modulo arithmeticHand total = last digit of sum
Banker win rate45.86%
Player win rate44.62%
Tie rate9.52%
Banker edge1.06%
Player edge1.24%

Sources: Hippodrome Casino baccarat page, Les Ambassadeurs Club, UKGC industry statistics.