Dice
2 dices, take the sum
Item | 概率 pp | Decimal odds | EV计算 | 是否正EV |
2 or 3 | 1/12 | 9.8 | 0.0833×9.8 ≈ 0.817 < 1 | ❌ 负EV |
4 | 1/12 | 9.8 | 0.817 < 1 | ❌ |
10 | 1/12 | 12.0 | 1.000 ≈ 1 | ⚖️ 公平（零EV） |
6,7 or 8 | 4/9 | 2.5 | 0.4444×2.5 ≈ 1.111 > 1 | ✅ 正EV |
11 or 12 | 1/12 | 13.1 | 0.0833×13.1 ≈ 1.092 > 1 | ✅ 正EV |
Even | 1/2 | 1.9 | 0.5×1.9 = 0.95 < 1 | ❌ 负EV |
Odd | 1/2 | 2.1 | 1.05 > 1 | ✅ 正EV |
For the above even and odd:
It’s possible for a risk-free arbitrage.
Coin
3 coins, head H and tail T.
Item | Odds | Probability | EV | 正/负EV |
All three identical | 3.3:1 (4.3) | 0.25 | 0.25×4.3 - 1 = 0.075 | ✅ 正EV |
More heads than tails | 0.8:1 (1.8) | 0.50 | 0.5×1.8 - 1 = -0.10 | ❌ 负EV |
More tails than heads | 0.9:1 (1.9) | 0.50 | 0.5×1.9 - 1 = -0.05 | ❌ 负EV |
Alternating (HTH/THT) | 3.3:1 (4.3) | 0.25 | 0.25×4.3 - 1 = 0.075 | ✅ 正EV |
Card
sum of 3 card to trade a market.