Swings, sessions and bankroll
In an hour, luck is ten times bigger than the edge.
Open this lesson in baccaratton — free, play money
In the short run, baccarat is all luck. A $10 Banker bet loses about 11 cents on average, but each hand actually moves you about $9.27 up or down (one standard deviation). Over an hour (72 hands):
| $10 Banker, flat | Expected | Typical swing (±1 SD) | Chance to be ahead (≈) |
|---|---|---|---|
| 1 hour | −$7.62 | ±$79 | 46% |
| 10 hours | −$76 | ±$249 | 38% |
| 100 hours | −$762 | ±$787 | 17% |
Luck grows with the square root of the number of hands, and the edge grows in a straight line. So luck dominates a night out, and the edge dominates a lifetime.
Some bets swing much harder than others (SD per $1 bet, per hand): Banker 0.93, Player 0.95, Dragon Bonus on Player 2.47, Tie 2.64, Pair 3.15, Dragon 7 6.08. Hard swingers give you more big wins and more busted sessions, at a much higher average cost.
How much to bring. Here's the chance that flat $10 Banker bets run a bankroll down until you can't place the next bet:
| Bankroll | Within 1 hour | Within 3 hours | Within 10 hours |
|---|---|---|---|
| $100 (10 bets) | 26% | 54% | 78% |
| $200 (20 bets) | 1.8% | 19% | 54% |
| $300 (30 bets) | 0.02% | 4.4% | 33% |
| $500 (50 bets) | 0.00% | 0.05% | 8.3% |
A practical rule: bring at least 20 to 30 bets for each hour you plan to play, and treat it as money you've already spent on entertainment. The expected cost is the price, and the bankroll is how much rope the swings get.
Show the math: Where these numbers come from
SD per $1, Banker: √(E[X²] − EV²) with X ∈ {+0.95, −1, 0}: ≈ 0.9274. Player: 0.9512. Tie 8:1: 2.6409. After n hands, the SD is 0.9274 × √n bets. For n = 72 that's 7.87 bets, or $78.69 at $10. "Chance to be ahead" uses the normal approximation Φ(−edge·√n / SD). The bankroll table is an exact dynamic program over the bankroll in 5¢ steps, with hands treated as independent (the shoe's memory is far too small to matter here, lesson 17).
Quiz
Over one hour of $10 Banker bets, which is bigger?
- The expected loss
- The typical swing
- They're equal
Show the answer
B: The typical swing. Expected −$7.62; typical swing about ±$79.
Quiz
Which bet swings the most per dollar?
- Banker
- Player
- Tie
- Dragon 7
Show the answer
D: Dragon 7. Dragon 7 pays 40 to 1 and rarely hits: SD ≈ 6.08 per $1.
Quiz
You'll play $10 Banker for 2 hours. Which bankroll is a sensible minimum?
- $20
- $100
- $400 to $600
- $10,000
Show the answer
C: $400 to $600. 20 to 30 bets per hour you plan to play: 40 to 60 bets, so $400 to $600.