ꯔꯨꯂꯦꯠ ꯁꯤꯛꯁ ꯂꯥꯏꯟ ꯕꯦꯠ
ꯔꯨꯂꯦꯠꯀꯤ ꯁꯤꯛꯁ ꯂꯥꯏꯟ ꯕꯦꯠꯅ ꯆꯤꯞ ꯑꯃꯈꯛ ꯌꯨꯝꯂꯣꯟꯅꯕ ꯔꯣ ꯑꯅꯤꯗ ꯊꯝꯃꯤ: ꯃꯁꯤꯡ ꯇꯔꯨꯛ꯫

ꯃꯁꯤꯡ ꯇꯔꯨꯛ, ꯄꯦꯑꯥꯎꯠ 5:1꯫ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 16.22%꯫
ꯔꯨꯂꯦꯠꯇ ꯁꯤꯛꯁ ꯂꯥꯏꯟ ꯍꯥꯌꯕꯁꯤ ꯀꯔꯤꯅꯣ?
ꯆꯤꯞꯁꯦꯜꯆꯤꯞꯂꯦꯞꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯃꯜ ꯇꯥꯛꯄ ꯇꯣꯀꯟ, ꯕꯦꯠ ꯊꯝꯅꯕ ꯂꯦꯑꯥꯎꯠꯇ ꯊꯝꯃꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯆꯦꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨ ꯒ꯭ꯔꯤꯗꯀꯤ ꯃꯄꯥꯟꯊꯣꯡꯒꯤ ꯃꯊꯛꯇ, ꯔꯣ ꯑꯅꯤꯒꯤ ꯃꯔꯛꯀꯤ ꯂꯥꯏꯟꯗ ꯊꯝꯃꯤ, ꯑꯃꯁꯨꯡ ꯃꯁꯤꯅ ꯑꯅꯤꯃꯛ ꯀꯨꯞꯏ: ꯈꯨꯗꯝꯅ 16-17-18 ꯑꯃꯁꯨꯡ 19-20-21꯫ ꯁꯤꯛꯁ ꯂꯥꯏꯟ ꯇꯔꯥꯅꯤꯊꯣꯏ ꯂꯩ (1–6 ꯗꯒꯤ 31–36 ꯐꯥꯑꯣꯕ)꯫ ꯁꯤꯛꯁ ꯂꯥꯏꯟ ꯑꯃꯠꯇꯅ ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯌꯥꯎꯗꯦ꯫ ꯆꯤꯞ ꯑꯗꯨ ꯔꯣꯒꯤ ꯂꯥꯏꯟ ꯑꯃꯁꯨꯡ ꯒ꯭ꯔꯤꯗꯀꯤ ꯃꯊꯛ ꯊꯦꯡꯅꯕ ꯃꯐꯃꯗ ꯂꯩꯒꯗꯕꯅꯤ; ꯔꯣꯒꯤ ꯂꯥꯏꯟꯗ ꯈꯛꯇ ꯂꯩꯔꯕꯗꯤ ꯃꯁꯤ ꯁ꯭ꯇ꯭ꯔꯤꯠꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯤꯠꯂꯦꯑꯥꯎꯠꯀꯤ ꯂꯥꯏꯟ ꯑꯃꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯑꯍꯨꯝ, 11:1 ꯄꯦꯑꯥꯎꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯇ꯭ꯔꯥꯟꯁꯚꯔꯁꯥꯜ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯅꯤ꯫
ꯄꯦꯑꯥꯎꯠ ꯑꯃꯁꯨꯡ ꯐꯪꯒꯗꯕ ꯃꯃꯜ
ꯆꯨꯝꯃꯤꯟꯅꯕ ꯑꯣꯗꯁ 5.17 ꯗꯒꯤ 1 ꯅꯤ; ꯇꯦꯕꯜꯅ 5 ꯈꯛ ꯄꯤ꯫ ꯃꯥꯏꯄꯥꯛꯂꯕ $10 ꯒꯤ ꯁꯤꯛꯁ ꯂꯥꯏꯟ ꯑꯃꯅ $50 ꯍꯜꯂꯀꯏ꯫ ꯑꯦꯚꯔꯦꯖ ꯁ꯭ꯄꯤꯟ 37 ꯗ: ꯃꯥꯏꯄꯥꯛꯄ ꯇꯔꯨꯛ (+$300), ꯃꯥꯏꯊꯤꯕ 31 (−$310), ꯅꯦꯠ −$10꯫
ꯃꯑꯣꯡ ꯃꯇꯧ
ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯆꯥꯎꯕ ꯃꯅꯨꯡꯒꯤ ꯕꯦꯠꯕꯦꯠꯃꯅꯨꯡꯒꯤ ꯕꯦꯠꯒ꯭ꯔꯤꯗꯀꯤ ꯃꯁꯤꯡꯁꯤꯡꯒꯤ ꯃꯊꯛꯇ ꯅꯠꯔꯒ ꯃꯈꯣꯌꯒꯤ ꯃꯔꯛꯇ ꯊꯝꯕ ꯕꯦꯠ ꯀꯔꯤꯒꯨꯝꯕ: ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ, ꯁ꯭ꯞꯂꯤꯠ, ꯁ꯭ꯇ꯭ꯔꯤꯠ, ꯀꯣꯔꯅꯔ, ꯁꯤꯛꯁ ꯂꯥꯏꯟ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯁꯨꯡ ꯃꯄꯥꯟꯒꯤ ꯕꯦꯠꯁꯤꯡꯗ ꯆꯠꯅꯕ ꯊꯣꯡꯅꯤ: ꯀꯨꯞꯄꯗ ꯗꯖꯟꯒꯤ ꯁꯔꯨꯛ ꯑꯍꯦꯟꯕ, ꯃꯥꯟꯅꯕ ꯄꯦꯑꯥꯎꯠꯁꯦꯜꯄꯦꯑꯥꯎꯠꯃꯥꯏꯄꯥꯛꯄ ꯕꯦꯠ ꯑꯃꯅ ꯍꯜꯂꯛꯄ ꯁꯦꯜ, ꯍꯜꯂꯀꯄ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯊꯛꯇ “X ꯗꯒꯤ 1” ꯍꯥꯌꯅ ꯍꯥꯌꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯂꯩꯅꯕ꯫ ꯃꯥꯏꯄꯥꯛꯄ ꯃꯇꯝ ꯌꯥꯝꯅꯥ ꯁ꯭ꯄꯤꯟ ꯇꯔꯨꯛ ꯈꯨꯗꯤꯡꯗ ꯂꯥꯛꯏ, ꯑꯃꯁꯨꯡ ꯁ꯭ꯄꯤꯟ 100 ꯒꯤ ꯁꯦꯁꯟ ꯑꯃꯗ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯠꯇ ꯂꯩꯇꯕꯥ ꯌꯥꯝꯅꯥ ꯈꯟꯗꯦ꯫ ꯁꯤꯛꯁ ꯂꯥꯏꯟ ꯑꯁꯤ ꯖꯦꯃꯁ ꯕꯣꯟꯗꯀꯤ ꯊꯧꯔꯥꯡꯒꯤ ꯆꯤꯞ ꯃꯉꯥꯒꯤ ꯁꯔꯨꯀꯁꯨ ꯑꯣꯏ; ꯃꯗꯨꯅ 13–18 ꯗ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯉꯥ ꯊꯝꯃꯤ꯫
ꯁꯤꯛꯁ ꯂꯥꯏꯟ ꯑꯃꯁꯨꯡ ꯗꯖꯟ
ꯁꯤꯛꯁ ꯂꯥꯏꯟ ꯑꯅꯤꯅ ꯗꯖꯟꯕꯦꯠꯗꯖꯟ1–12, 13–24 ꯅꯠꯔꯒ 25–36, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯥ ꯑꯣꯏ (1–6 ꯑꯃꯁꯨꯡ 7–12 ꯅ 1–12 ꯀꯨꯞꯏ)꯫ ꯗꯖꯟ ꯑꯗꯨ ꯂꯥꯀꯄꯥ ꯃꯇꯃꯗ $10 ꯒꯤ ꯁꯤꯛꯁ ꯂꯥꯏꯟ ꯑꯅꯤꯅ $50 − $10 = $40 ꯄꯤ; $20 ꯒꯤ ꯗꯖꯟꯅꯁꯨ $40 ꯄꯤ꯫ ꯕꯦꯠ ꯑꯃꯈꯛꯇꯅꯤ, ꯃꯑꯣꯡ ꯑꯅꯤ꯫ ꯗꯖꯟ ꯑꯃꯒꯤ ꯁꯔꯨꯛ ꯑꯍꯦꯟꯕꯗ ꯑꯣꯖꯟ ꯍꯦꯟꯅꯥ ꯊꯝꯕ ꯄꯥꯝꯂꯕꯗ ꯅꯠꯔꯒ ꯗꯖꯟ ꯑꯅꯤꯒꯤ ꯃꯔꯛ ꯀꯨꯞꯄ ꯄꯥꯝꯂꯕꯗ, ꯈꯨꯗꯝꯅ 10–15, ꯁꯤꯛꯁ ꯂꯥꯏꯟꯅ ꯀꯥꯟꯅꯕ ꯄꯤ꯫
ꯔꯨꯂꯦꯠ ꯂꯥꯏꯟ ꯕꯦꯠ, ꯗꯕꯜ ꯁ꯭ꯇ꯭ꯔꯤꯠ ꯑꯃꯁꯨꯡ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡꯁꯤꯡ
ꯐ꯭ꯔꯦꯟꯆꯇ ꯁꯤꯖꯦꯟꯐ꯭ꯔꯦꯟꯆ · ꯁꯤꯛꯁ ꯂꯥꯏꯟꯁꯤꯖꯦꯟꯁꯤꯛꯁ ꯂꯥꯏꯅꯒꯤ ꯐ꯭ꯔꯦꯟꯆ ꯃꯃꯤꯡ: ꯂꯥꯏꯟ ꯑꯅꯤꯗ ꯃꯁꯤꯡ ꯇꯔꯨꯛ, 5:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯅꯠꯔꯒ ꯇ꯭ꯔꯥꯟꯁꯚꯔꯁꯥꯜꯐ꯭ꯔꯦꯟꯆ · ꯁ꯭ꯇ꯭ꯔꯤꯠꯇ꯭ꯔꯥꯟꯁꯚꯔꯁꯥꯜꯁ꯭ꯇ꯭ꯔꯤꯠ (ꯇ꯭ꯔꯥꯟꯁꯚꯔꯁꯥꯜ ꯄ꯭ꯂꯦꯟ, ꯃꯁꯤꯡ 3) ꯑꯃꯁꯨꯡ ꯁꯤꯛꯁ ꯂꯥꯏꯟ (ꯇ꯭ꯔꯥꯟꯁꯚꯔꯁꯥꯜ ꯁꯦꯝꯞꯜ, ꯃꯁꯤꯡ 6) ꯒꯤ ꯐ꯭ꯔꯦꯟꯆ ꯃꯃꯤꯡ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯁꯦꯝꯄ꯭ꯂꯦ; ꯏꯉ꯭ꯂꯤꯁꯇ “ꯂꯥꯏꯟ ꯕꯦꯠ”, “ꯗꯕꯜ ꯁ꯭ꯇ꯭ꯔꯤꯠ” ꯅꯠꯔꯒ “ꯁꯤꯛꯁ-ꯅꯝꯕꯔ ꯕꯦꯠ”; ꯂꯥꯏꯕ ꯏꯟꯇꯔꯐꯦꯁꯁꯤꯡꯗ ꯃꯇꯝ ꯈꯔꯗ ꯋꯥꯍꯩ ꯑꯃꯈꯛ ꯑꯣꯏꯅ “ꯁꯤꯛꯁꯂꯥꯏꯟ”꯫
ꯋꯥꯍꯪꯁꯤꯡ
ꯌꯥꯔꯣꯏ꯫ ꯖꯤꯔꯣ ꯑꯁꯤ ꯂꯦꯑꯥꯎꯠꯈꯨꯠꯂꯥꯏꯂꯦꯑꯥꯎꯠꯇꯦꯕꯜꯗ ꯏꯔꯕ ꯕꯦꯠ ꯊꯝꯕꯒꯤ ꯒ꯭ꯔꯤꯗ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯇꯦꯕꯜ, ꯐꯦꯜꯠ, ꯀ꯭ꯂꯣꯊ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯀꯤ ꯃꯊꯛꯇ ꯂꯩꯕ ꯕꯛꯁ ꯑꯃꯈꯛꯇꯅꯤ ꯑꯃꯁꯨꯡ ꯃꯁꯤꯅ ꯁ꯭ꯇ꯭ꯔꯤꯠꯁꯤꯡ (0-1-2, 0-2-3) ꯑꯃꯁꯨꯡ ꯕꯥꯁ꯭ꯀꯦꯠꯕꯦꯠꯕꯥꯁ꯭ꯀꯦꯠꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ ꯆꯛꯔꯗ: ꯆꯤꯞ ꯑꯃꯅ 0, 1, 2, 3, 8:1 ꯄꯦꯑꯥꯎꯠ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯑꯍꯥꯅꯕ ꯃꯔꯤ, ꯀꯥꯠꯔ ꯄ꯭ꯔꯦꯃꯤꯌꯦ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯁꯦꯝꯃꯤ, ꯁꯤꯛꯁ ꯂꯥꯏꯟ ꯅꯠꯇꯦ꯫
√(p·25 + (1−p) − EV²), p = 6/37 ꯑꯣꯏꯔꯒ꯫ ꯑꯇꯣꯞꯄ ꯃꯅꯨꯡꯒꯤ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗꯒꯤ ꯅꯦꯝꯃꯤ꯫
ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯆꯥꯎꯕ ꯃꯅꯨꯡꯒꯤ ꯕꯦꯠ, ꯃꯄꯥꯟꯒꯤ ꯕꯦꯠꯀꯤ ꯃꯃꯥꯡꯗ ꯂꯩꯕ ꯑꯔꯣꯏꯕ ꯑꯗꯨ꯫
ꯍꯧꯔꯛꯐꯃꯁꯤꯡ
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.