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:
| Card | Points |
|---|---|
| Ace | 1 |
| 2 to 9 | Face value |
| 10 | 0 |
| Jack | 0 |
| Queen | 0 |
| King | 0 |
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 total | Banker's action |
|---|---|
| 0, 1, 2 | Always draws |
| 3 | Draws, unless Player's third card was 8 |
| 4 | Draws if Player's third card was 2, 3, 4, 5, 6, or 7 |
| 5 | Draws if Player's third card was 4, 5, 6, or 7 |
| 6 | Draws if Player's third card was 6 or 7 |
| 7 | Always 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
| Rule | Details |
|---|---|
| Player draws on | 0 to 5 |
| Player stands on | 6 to 7 |
| Natural | 8 to 9 |
| Banker draws on | 0 to 2 always; conditional on 3 to 6 |
| Banker stands on | 7 always |
| Modulo arithmetic | Hand total = last digit of sum |
| Banker win rate | 45.86% |
| Player win rate | 44.62% |
| Tie rate | 9.52% |
| Banker edge | 1.06% |
| Player edge | 1.24% |
Sources: Hippodrome Casino baccarat page, Les Ambassadeurs Club, UKGC industry statistics.
Welcome to the lesson on rules, card values, and the third-card tableau.
I'm Annabel, and this is the lesson that most baccarat guides quietly skip over. The third-card rule has a reputation for being complicated, and it is, slightly, but only when you read it on a chart. At the table you'll never apply it. The dealer does. The reason I'm going to walk you through it anyway is that once you understand the structure of the tableau, the entire game stops feeling mysterious.
Let's start with card values, because everything flows from them.
Cards two through nine score face value. Picture cards and tens count zero. Aces count one. Suit doesn't matter. Colour doesn't matter. The only thing the table reads is the point value of the card.
Hand totals are read modulo ten, which means you add the two cards and take only the last digit. A nine and a seven makes sixteen, scores six. A king and a five is five, because the king counts zero. A four and a six is ten, scores zero. The minimum hand total is zero. The maximum is nine. There's no concept of going bust the way there is in blackjack, because the modulo arithmetic clips any total back into the zero-to-nine 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 ten and a ten is also zero. Do the addition, drop the leading digit, and that's your total.
Now the Player rule, which is genuinely simple.
Player draws a third card if the two-card total is zero through five. Player stands on six or seven. Player has a natural on eight or nine, and the hand ends immediately. That's the entire Player rule. Five seconds to memorise.
The Banker rule is the longer one. It exists because Banker acts second, after Player's third card is already known. The tableau gives Banker slightly better information, which is the source of Banker's edge.
Here's the Banker rule. Banker always draws on a two-card total of zero, one, or two. Banker always stands on seven. The rows in between depend on what Player's third card was.
On a Banker total of three, Banker draws unless Player's third card was an eight.
On a Banker total of four, Banker draws if Player's third card was two through seven.
On a Banker total of five, Banker draws if Player's third card was four through seven.
On a Banker total of six, Banker draws only if Player's third card was a six or a seven.
And if neither side gets a natural, and Player stood on six or seven without drawing, Banker uses the simpler rule: draw on zero through five, stand on six or seven.
Here's the thing I most want you to take from this. You will never apply this rule. The dealer reads it for you, every hand, without error. The reason I've laid it out is so that the next time you see a Banker stand on six when Player drew a low card, you'll know why. Or the next time someone at the table says "Banker has to draw on a three", you can check whether that's correct given what Player's third card actually was.
A quick worked example, because this lands faster as a scene than a rule.
Player is dealt a four and a two. Total is six. Player stands. Banker is dealt a five and an ace. Total is six. Player stood, so Banker uses the simple rule and stands on six. Both sides are on six. The hand resolves as a tie.
Now a more complicated one. Player is dealt a king and a queen. Total is zero. Player draws. The third card is a seven. Player's final total is seven. Banker is dealt a three and a jack. Total is three. Player's third card was a seven. Banker draws on a total of three unless Player's third card was an eight. The seven isn't an eight, so Banker draws. Banker's third card is a six. Banker's final total is nine.
Player seven. Banker nine. 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. I've watched the Hippodrome's croupiers read this tableau hundreds of times a night without hesitation. It becomes automatic. Your version of automatic is knowing why each draw happens, not how to execute it yourself.
This is the most important thing about the tableau. It's been unchanged since the late nineteen fifties, when the Nevada casinos fixed it to give Banker a small, stable edge. The rules are in the open, written down, and never modified. You're not being outsmarted. You're playing a known shoe with a known edge, and the only variable in the hand is which side you backed before the deal.
Read the tableau once. Understand why Banker's rule is longer than Player's. Then forget it again. The dealer remembers it for you.