EV and the house edge, in plain English
What a bet is worth on average, and how the EV sheet shows it.
Open this lesson in baccaratton — free, play money
No single hand of baccarat is predictable, but a thousand hands are. Expected value is what a bet returns on average if you could repeat the same bet forever. You get it by weighing each result by how often it happens.
Take $10 on Player. In an 8-deck shoe, the Player wins 44.62% of hands, the Banker wins 45.86%, and 9.52% are ties:
- win $10 × 44.62% = +$4.46
- lose $10 × 45.86% = −$4.59
- push $0 × 9.52% = $0
Total: −$0.12. On average, a $10 Player bet costs about 12 cents. That −1.24% is the house edge: the share of each bet the casino keeps on average.
The house edge doesn't mean you lose 12 cents every hand. You win $10 or lose $10 (or push), and over a few hands you can be well up or well down. What it means is that the average drifts toward −12 cents a hand, and over thousands of hands the drift is all that's left.
The EV sheet. Tap and hold any bet spot, or tap the EV button under the table, before you bet. The sheet shows:
- the bet's EV in dollars for the chips you're about to place, and its house edge;
- its rating: Good bet, Fair, Costly or Sucker bet, always written out, never shown by colour alone;
- what it costs per hour at 72 hands an hour;
- a better choice, if there is one on this table.
From now on the EV sheet is switched on in every lesson.
Show the math: The three EVs, exactly (8 decks, per $1)
P(Player wins) = 8712962041376/19524993263685 ≈ 0.446247 P(Banker wins) = 8954111587648/19524993263685 ≈ 0.458597 P(Tie) = 619306544887/6508331087895 ≈ 0.095156
EV(Player) = P(Player) − P(Banker) = −241149546272/19524993263685 ≈ −1.2351% EV(Banker) = 0.95 × P(Banker) − P(Player) = −114753351728/10847218479825 ≈ −1.0579% EV(Tie) = 8 × P(Tie) − (1 − P(Tie)) = −103841353768/723147898655 ≈ −14.3596%
They come from every possible order of cards in a full 8-deck shoe (4,998,398,275,503,360 ordered deals of up to six cards), dealt by the exact tableau.
Quiz
What does a house edge of 1.06% mean?
- You lose 1.06% of hands
- On average you lose about 1.06¢ per $1 bet
- The casino wins 1.06% more hands
- You'll lose exactly $1.06 per $100 tonight
Show the answer
B: On average you lose about 1.06¢ per $1 bet. It's an average cost per dollar bet, not a promise about any one session.
Quiz
Roughly what is the EV of a $10 Player bet?
- −$1.24
- −$0.12
- +$0.12
- $0
Show the answer
B: −$0.12. 1.24% of $10 is about 12 cents.
Quiz
Which bet does the EV sheet rate cheapest on a standard table?
- Player
- Banker
- Tie
- They're all the same
Show the answer
B: Banker. Banker: 1.06%. Player: 1.24%. Tie: 14.36%.