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The Banker's turn, part 2: the table

Lesson 5 of 24 · The third-card rule · 8 min

When the Player drew, the Banker reads the Player's third card.

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This is the last piece. When the Player drew a third card, the Banker looks at its own two-card total and at the Player's third card (not the Player's total):

Banker has Banker draws if the Player's third card is Banker stands if it is
0, 1, 2 anything —
3 anything except 8 8
4 2 to 7 0, 1, 8, 9
5 4 to 7 0–3, 8, 9
6 6 or 7 0–5, 8, 9
7 — always stands

A ten or a picture card drawn by the Player counts as 0.

That looks like a lot, but there's a pattern. Read down the "draws if" column from Banker 4 to 6: 2–7, 4–7, 6–7. The top end is always 7, and the bottom end climbs by two each row. Banker 3 is the generous row: it draws on everything except an 8. Rows 0–2 always draw, and 7 always stands.

Why does the Banker draw more against a 2–7? A Player third card of 2–7 usually means the Player improved to a middle total, so a Banker sitting on 3–6 needs help. A Player's 8, 9, 0 or 1 is a sign the Player may have stayed low or gone backwards, so the Banker can afford to stand. The table was tuned long ago so the Banker makes roughly the best play in each spot. That one advantage, acting last with more information, is why the Banker wins more often (lesson 9).

What the Banker does, by the Banker's two-card total (rows) and the Player's third card (columns). Banker 8 or 9 is a natural and always stands.
Banker totalPlayer stood0123456789
Banker 0DrawDrawDrawDrawDrawDrawDrawDrawDrawDrawDraw
Banker 1DrawDrawDrawDrawDrawDrawDrawDrawDrawDrawDraw
Banker 2DrawDrawDrawDrawDrawDrawDrawDrawDrawDrawDraw
Banker 3DrawDrawDrawDrawDrawDrawDrawDrawDrawStandDraw
Banker 4DrawStandStandDrawDrawDrawDrawDrawDrawStandStand
Banker 5DrawStandStandStandStandDrawDrawDrawDrawStandStand
Banker 6StandStandStandStandStandStandStandDrawDrawStandStand
Banker 7StandStandStandStandStandStandStandStandStandStandStand
  • When the Player stood: Banker 0–5 draws, Banker 6, 7 stands.
  • Banker 0 always draws.
  • Banker 1 always draws.
  • Banker 2 always draws.
  • Banker 3 draws on anything except a Player third card of 8.
  • Banker 4 draws when the Player's third card is 2–7.
  • Banker 5 draws when the Player's third card is 4–7.
  • Banker 6 draws when the Player's third card is 6, 7.
  • Banker 7 always stands.
Show the math: How the table plays out

Because the Banker sometimes stands on 3–6 and sometimes draws, it draws a little less often than the Player: 43.5% of all hands, against the Player's 50.3%. A ten-value card is the most common third card (16 of every 52 cards), and it counts as 0. That's why Banker 4 and 5 stand on a Player's 0: a 0 leaves the Player's total unchanged.

Quiz

The Player drew a 9. The Banker has 3. What does the Banker do?

  1. Draws
  2. Stands
Show the answer

A: Draws. Banker 3 draws on everything except an 8.

Quiz

The Player drew a 1. The Banker has 4. What does the Banker do?

  1. Draws
  2. Stands
Show the answer

B: Stands. Banker 4 draws only on 2 to 7.

Quiz

The Player drew a 6. The Banker has 6. What does the Banker do?

  1. Draws
  2. Stands
Show the answer

A: Draws. Banker 6 draws on a Player third card of 6 or 7.

Quiz

The Player drew a queen. The Banker has 5. What does the Banker do?

  1. Draws
  2. Stands
Show the answer

B: Stands. A queen counts 0. Banker 5 draws only on 4 to 7.

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