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Why the Banker wins more often

Lesson 9 of 24 · EV basics · 6 min

Acting last is worth 1.24%, and the commission takes it back and a bit more.

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The two hands aren't treated equally. The Player follows a blind rule (0–5 draws). The Banker acts after seeing what the Player did, and in lesson 5 you saw how its table reacts to the Player's third card. That small information edge means the Banker wins a bit more often:

Result How often (8 decks)
Banker wins 45.86%
Player wins 44.62%
Tie 9.52%

Leave out the ties, and the Banker wins 50.68% of the hands that are decided.

If Banker paid even money, it would be a winning bet for you: +1.24%, exactly the mirror of the Player bet's −1.24%. Casinos fix that with the 5% commission. A Banker win then pays 95¢, and the bet goes from +1.24% to −1.06%.

So both bets lose in the long run, but the Banker bet loses less: about 1.06¢ per dollar against 1.24¢. Paying the commission feels like a cost, and it is, but it's smaller than the price of betting on the hand that wins less often.

Show the math: Where the commission sits

With the commission c, EV(Banker) = (1 − c) × P(Banker) − P(Player). At c = 0: +241149546272/19524993263685 ≈ +1.2351% (exactly minus EV(Player)). At c = 5%: −1.0579%. The bet breaks even at c = 1 − P(Player)/P(Banker) = 7535923321/279815987114 ≈ 2.69%. Some casinos charge 4%, which gives an edge of 2925372930848/488124831592125 ≈ 0.5993% (lesson 12).

Quiz

Why does the Banker win more often than the Player?

  1. The dealer favours it
  2. It acts last, with a rule that reacts to the Player's third card
  3. It gets an extra card
  4. It doesn't: they win equally
Show the answer

B: It acts last, with a rule that reacts to the Player's third card. The Banker's rule uses the information from the Player's draw.

Quiz

Without commission, what would the Banker bet's edge be?

  1. The house would still have 1.06%
  2. Zero
  3. About 1.24% in your favour
  4. About 5% in your favour
Show the answer

C: About 1.24% in your favour. Banker at even money would be the exact mirror of Player: +1.24% for you.

Quiz

After commission, which bet costs less?

  1. Player
  2. Banker
  3. They're equal
Show the answer

B: Banker. Banker 1.06% vs Player 1.24%.

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