理解撲克 Variance：SD、CI 與 Sample Size
2026年4月17日
Tracker 18,000 hand +4.2 bb/100——skill 還是 noise？SD、95% CI、sample size formula 與 Monte Carlo simulation。Measurement science，非 tilt advice。
- variance
- standard deviation
- confidence interval
- sample size
- win rate
- bb/100
- Monte Carlo simulation
- poker statistics
- cash game
- expected value
Tracker 顯示 +4.2 bb/100，18,000 hand $1/$2。18k hand 對 poker statistics 是 short sample。Screen 數字是 measurement，非 skill proof。Variance 是 measurement 與 true long-run win rate 的 gap。
Core Terms
| Term | Poker meaning |
|---|---|
| True win rate (μ) | long-run bb/100 |
| Observed WR | tracker bb/100 over sample |
| SD (σ) | swing width per 100 hands |
| Sample size (N) | hands logged |
| CI | range likely containing μ |
Typical SD
| Format | σ (bb/100) |
|---|---|
| 6-max | 85–110 |
| LAG 6-max | 100–120 |
Total SD (bb) = σ × √(N/100)
95% CI
$\text{95% CI} = \text{WR} \pm 1.96 \times \frac{\sigma}{\sqrt{N/100}}$
WR = +5，σ = 90，N = 50,000 → CI −2.9 to +12.9。Halve error bar 需 4× hands。
Sample Size
σ=90，±5 bb/100 → ~125,000 hands。2 bb/100 grinder 需 ~780,000 hands 才使 95% CI lower bound 轉正。
P(Losing) While Winning
WR = +5，σ = 90，N = 50,000 → P(loss) ≈ 11%。
Worked Audit
N=35,000，WR=+3.8，σ=95 → 95% CI −6.2 to +13.8 bb/100。Compatible with breakeven or strong winner。
總結
Variance 是 win-rate measurement 的 error bar width。「Enough data」常為 100k–500k hands。