ꯔꯨꯂꯦꯠꯀꯤ ꯑꯣꯗꯁ ꯑꯃꯁꯨꯡ ꯈꯨꯗꯣꯡꯆꯥꯕꯒꯤ ꯇꯦꯕꯜ
ꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛ, ꯃꯗꯨꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, ꯄꯦꯑꯥꯎꯠ, ꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯦꯊꯃꯦꯇꯤꯛꯁꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯇꯝ ꯁꯥꯡꯅ ꯌꯦꯡꯂꯕꯗ ꯕꯦꯠ ꯑꯃꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩ꯫ ꯃꯔꯨꯑꯣꯏꯕ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯁꯨꯡ ꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯗꯤꯚꯤꯌꯦꯁꯟꯒꯥ ꯂꯣꯌꯅꯅ꯫
ꯕꯦꯠ ꯄꯨꯝꯅꯃꯛꯀꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯑꯗꯨꯃꯛ ꯑꯣꯏ, ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −2.70%꯫ ꯃꯈꯣꯌ ꯈꯥꯌꯗꯣꯛꯄ ꯑꯁꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯃꯁꯨꯡ ꯁ꯭ꯞꯔꯦꯗꯇ ꯈꯛꯇꯅꯤ꯫
ꯔꯨꯂꯦꯠꯀꯤ ꯑꯣꯗꯁ ꯆꯥꯔꯠ ꯑꯁꯤ ꯀꯔꯝꯅ ꯄꯥꯒꯗꯒꯦ
ꯈꯨꯗꯣꯡꯆꯥꯕꯅꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯅꯍꯥꯛꯅ ꯀꯌꯥ ꯌꯥꯝꯅꯥ ꯃꯥꯏꯄꯥꯛꯀꯅꯤ ꯍꯥꯌꯕ ꯇꯥꯀꯏ; ꯔꯨꯂꯦꯠꯀꯤ ꯑꯣꯗꯁ ꯑꯣꯏꯅ ꯍꯥꯌꯕ ꯄꯦꯑꯥꯎꯠꯅꯁꯦꯜꯄꯦꯑꯥꯎꯠꯃꯥꯏꯄꯥꯛꯄ ꯕꯦꯠ ꯑꯃꯅ ꯍꯜꯂꯛꯄ ꯁꯦꯜ, ꯍꯜꯂꯀꯄ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯊꯛꯇ “X ꯗꯒꯤ 1” ꯍꯥꯌꯅ ꯍꯥꯌꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯀꯌꯥ ꯐꯪꯒꯅꯤ ꯍꯥꯌꯕ ꯇꯥꯀꯏ; σ ꯅ ꯆꯠꯀꯗꯕ ꯂꯝꯕꯤ ꯑꯗꯨ ꯀꯌꯥ ꯌꯥꯝꯅꯥ ꯍꯣꯡꯂꯛ-ꯍꯣꯡꯊꯛ ꯂꯩꯒꯅꯤ ꯍꯥꯌꯕ ꯇꯥꯀꯏ꯫ EV ꯀꯂꯝ ꯑꯁꯤ ꯁꯦꯃꯈꯤꯕ ꯃꯑꯣꯡ ꯑꯗꯨꯅꯥ ꯃꯔꯝ ꯑꯣꯏꯗꯨꯅ ꯔꯣ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯑꯗꯨꯃꯛ ꯑꯣꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯇꯦꯕꯜ ꯑꯁꯤ ꯇꯁꯦꯡꯅ ꯃꯃꯜ ꯑꯃꯈꯛꯇꯗ ꯂꯩꯕ ꯚꯦꯌꯔꯤꯌꯦꯟꯁꯁꯤꯡꯒꯤꯃꯦꯊꯃꯦꯇꯤꯛꯁꯚꯦꯌꯔꯤꯌꯦꯟꯁꯃꯍꯩꯁꯤꯡ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯒꯤ ꯑꯀꯣꯌꯕꯗ ꯀꯌꯥ ꯁꯟꯗꯣꯛꯅ ꯂꯩꯕꯒꯦ ꯍꯥꯌꯕꯒꯤ ꯆꯥꯡ꯫ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯇ ꯋꯥꯡꯏ, ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡꯗ ꯅꯦꯝꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯦꯅꯨ ꯑꯃꯅꯤ꯫
ꯀꯣꯜ ꯕꯦꯠꯁꯤꯡ
ꯁꯦꯛꯇꯔꯆꯛꯔꯁꯦꯛꯇꯔꯆꯛꯔꯗ ꯃꯔꯛ ꯂꯩꯇꯅ ꯃꯈꯥ ꯆꯠꯅꯅ ꯂꯩꯕ ꯄꯣꯀꯦꯠꯁꯤꯡꯒꯤ ꯁꯔꯨꯛ, ꯂꯦꯑꯥꯎꯠꯇ ꯂꯩꯕ ꯀꯥꯡꯂꯨꯞ ꯑꯃꯗꯒꯤ ꯇꯣꯉꯥꯟꯅ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯕꯦꯠꯁꯤꯡ ꯑꯁꯤ ꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯕꯦꯠꯁꯤꯡꯒꯤ ꯄꯨꯟꯁꯤꯅꯕꯅꯤ ꯑꯃꯁꯨꯡ ꯃꯈꯣꯌꯒꯤ ꯍꯥꯎꯁ ꯑꯦꯖ ꯑꯗꯨꯃꯛ ꯂꯧꯏ꯫ ꯆꯤꯞꯁꯤꯡꯁꯦꯜꯆꯤꯞꯂꯦꯞꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯃꯜ ꯇꯥꯛꯄ ꯇꯣꯀꯟ, ꯕꯦꯠ ꯊꯝꯅꯕ ꯂꯦꯑꯥꯎꯠꯇ ꯊꯝꯃꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯆꯦꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨ ꯆꯞ ꯃꯥꯟꯅꯗꯅ ꯊꯝꯕꯅꯥ ꯃꯔꯝ ꯑꯣꯏꯗꯨꯅ ꯃꯈꯣꯌ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯃꯁꯥꯒꯤ ꯄꯦꯑꯥꯎꯠꯀꯤ ꯃꯑꯣꯡ ꯂꯩ꯫
ꯁ꯭ꯄꯤꯟ ꯀꯌꯥꯒꯤ ꯃꯅꯨꯡꯗ
ꯁ꯭ꯄꯤꯟ k ꯒꯤ ꯃꯅꯨꯡꯗ ꯌꯥꯃꯗ꯭ꯔꯕꯗ ꯑꯃꯨꯛ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯁꯤꯡ, ꯃꯤꯅꯝꯅ ꯍꯪꯂꯤꯕ ꯋꯥꯍꯪ ꯈꯔꯒꯤꯗꯃꯛ꯫
ꯁꯦꯁꯟꯒꯤ ꯁ꯭ꯞꯔꯦꯗꯁꯤꯡ
$10 ꯒꯤ ꯐ꯭ꯂꯦꯠ ꯕꯦꯇꯤꯡꯗ ꯁ꯭ꯄꯤꯟ 100 ꯒꯤ ꯁꯦꯁꯟ ꯑꯃꯒꯤ ꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯗꯤꯚꯤꯌꯦꯁꯟꯃꯦꯊꯃꯦꯇꯤꯛꯁꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯗꯤꯚꯤꯌꯦꯁꯟꯚꯦꯌꯔꯤꯌꯦꯟꯁꯀꯤ ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯔꯨꯠ; ꯃꯍꯩ ꯑꯃꯅ ꯐꯪꯒꯗꯕ ꯃꯃꯜꯗꯒꯤ ꯌꯥꯝꯅ ꯂꯥꯞꯄ ꯃꯑꯣꯡ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, ꯕꯦꯠ ꯈꯨꯗꯤꯡꯒꯤ ꯃꯇꯨꯡ ꯏꯟꯅ, ꯄꯨꯟꯅ ꯐꯪꯒꯗꯕ ꯃꯍꯩ −$27 ꯒꯥ ꯂꯣꯌꯅꯅ꯫
ꯋꯥꯍꯪꯁꯤꯡ
ꯃꯔꯃꯗꯤ ꯄꯦꯑꯥꯎꯠ ꯈꯨꯗꯤꯡꯃꯛ ꯆꯨꯝꯃꯤꯟꯅꯕ 37/n − 1 ꯒꯤ ꯃꯍꯨꯠꯇ 36/n − 1 ꯑꯣꯏ꯫ ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤꯃꯦꯊꯃꯦꯇꯤꯛꯁꯍꯥꯎꯁ ꯑꯦꯖꯊꯝꯂꯕ ꯁꯦꯜ ꯈꯨꯗꯤꯡꯗꯒꯤ ꯀꯦꯁꯤꯅꯣꯅ ꯑꯦꯚꯔꯦꯖꯗ ꯊꯃꯖꯤꯜꯂꯤꯕ ꯁꯔꯨꯛ: ꯌꯨꯔꯣꯄꯤꯌꯟ ꯔꯨꯂꯦꯠꯇ 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯂꯃꯥꯏ ꯌꯦꯡꯕꯤꯌꯨ꯫
ꯐ꯭ꯔꯦꯟꯆ ꯇꯦꯕꯜ ꯑꯃꯗ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡꯕꯦꯠꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯑꯉꯥꯡꯕ/ꯑꯃꯨꯕ, ꯕꯤꯖꯣꯔ/ꯖꯣꯔ, ꯑꯋꯥꯡꯕ/ꯑꯅꯦꯝꯕ꯫ ꯃꯁꯤꯡ 18, 1:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →: p ꯑꯃꯁꯨꯡ ꯄꯦꯑꯥꯎꯠ ꯍꯣꯡꯗꯦ, EV −1.35%, σ ≈ 0.99꯫
37 ꯒꯤ ꯃꯍꯨꯠꯇ 38 ꯅ ꯈꯥꯌꯕꯤꯌꯨ, ꯑꯗꯨꯒ EV ꯀꯂꯝ ꯑꯁꯤ ꯔꯣ ꯈꯨꯗꯤꯡꯃꯛꯇ −5.26% ꯑꯣꯏꯔꯛꯀꯅꯤ, ꯃꯁꯤꯡ ꯃꯉꯥꯒꯤ ꯕꯦꯠꯀꯤꯗꯃꯛ −7.89%꯫
ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ
ꯕꯦꯠ ꯃꯥꯄꯟ, ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯑꯃꯈꯛꯇ, ꯅꯤꯡꯁꯤꯡꯕ ꯑꯃꯠꯇ ꯂꯩꯇꯦ꯫
ꯍꯧꯔꯛꯐꯃꯁꯤꯡ
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.