ꯀꯦꯂꯤ ꯀ꯭ꯔꯥꯏꯇꯦꯔꯤꯌꯟ ꯑꯃꯁꯨꯡ ꯔꯨꯂꯦꯠ

Q: ꯀꯦꯂꯤꯅ ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯔꯨꯂꯦꯠꯇ ꯕꯦꯠ ꯊꯝꯕꯤꯌꯨ ꯍꯥꯌꯕꯔꯥ?

ꯕꯥꯏꯌꯥꯁ ꯂꯩꯕ ꯆꯛꯔ ꯑꯃꯗꯒꯤ ꯅꯠꯔꯒ ꯃꯇꯝ ꯊꯤꯕ ꯗꯤꯚꯥꯏꯁ ꯑꯃꯗꯒꯤ ꯆꯥꯡꯈꯤꯕ ꯑꯦꯖ ꯂꯩꯔꯕꯗ ꯈꯛꯇꯅꯤ꯫ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯛꯔ ꯑꯃꯗ ꯅꯠꯇꯦ꯫

ꯀꯦꯂꯤ ꯀ꯭ꯔꯥꯏꯇꯦꯔꯤꯌꯟꯅ ꯑꯦꯖ ꯂꯩꯕ ꯕꯦꯠ ꯊꯝꯕ ꯃꯤ ꯑꯃꯕꯨ ꯀꯌꯥ ꯊꯝꯒꯗꯒꯦ ꯍꯥꯌꯕ ꯇꯥꯀꯏ꯫ ꯔꯨꯂꯦꯠꯀꯤꯗꯃꯛ ꯃꯁꯤꯅ ꯃꯌꯦꯛ ꯁꯦꯡꯕ ꯄꯥꯎꯈꯨꯝ ꯑꯃꯥ ꯄꯤꯔꯤ: ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯠꯇ ꯊꯝꯒꯅꯨ꯫

ꯊꯨꯅ ꯄꯥꯎꯈꯨꯝ

ꯀꯦꯂꯤ ꯊꯝꯂꯕ ꯁꯦꯜ = ꯑꯦꯖ / ꯑꯣꯗꯁ꯫ ꯑꯦꯖ ꯑꯗꯨ ꯅꯦꯒꯦꯇꯤꯕ ꯑꯣꯏꯔꯕꯗꯤ ꯐꯣꯔꯃꯨꯂꯥ ꯑꯁꯤꯅ ꯅꯦꯒꯦꯇꯤꯕ ꯁꯔꯨꯛ ꯑꯃꯥ ꯄꯤꯔꯤ, ꯃꯁꯤꯒꯤ ꯑꯔꯊꯗꯤ ꯕꯦꯠ ꯊꯝꯒꯅꯨ꯫ ꯕꯥꯏꯌꯥꯁ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯃꯈꯣꯌꯒꯤ ꯕꯦꯠꯀꯤ ꯆꯥꯡ ꯀꯔꯤꯒꯤ ꯃꯇꯧ ꯑꯗꯨꯒꯨꯝꯅ ꯂꯦꯞꯈꯤꯕꯒꯦ, ꯑꯃꯁꯨꯡ ꯑꯇꯩ ꯄꯨꯝꯅꯃꯛꯅ ꯀꯔꯤꯒꯤ ꯕꯖꯦꯠꯀꯤ ꯃꯇꯨꯡ ꯏꯟꯅ ꯆꯥꯡ ꯂꯦꯞꯀꯗꯒꯦ ꯍꯥꯌꯕ ꯈꯉꯅꯕꯗ ꯀ꯭ꯔꯥꯏꯇꯦꯔꯤꯌꯟ ꯑꯁꯤ ꯍꯧꯖꯤꯀꯁꯨ ꯀꯥꯟꯅꯩ꯫

ꯀꯦꯂꯤ ꯁꯔꯨꯛ

f* = (bp − q) / b

ꯑꯉꯥꯡꯕꯒꯤꯗꯃꯛ

(1 × 18/37 − 19/37) / 1 = −1/37

ꯑꯔꯊ

ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯠꯇ ꯊꯝꯒꯅꯨ

1/30 ꯄꯣꯀꯦꯠ ꯑꯃꯒꯤꯗꯃꯛ

≈ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ +0.6%

ꯀ꯭ꯔꯥꯏꯇꯦꯔꯤꯌꯟ

ꯖꯣꯟ ꯀꯦꯂꯤ (John Kelly, 1956) ꯅ ꯈꯉꯂꯕ ꯑꯦꯖ ꯂꯩꯕ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯕꯦꯡꯀꯔꯣꯜꯁꯦꯜꯕꯦꯡꯀꯔꯣꯜꯁꯥꯟꯅꯅꯕ ꯇꯣꯉꯥꯟꯅ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ꯫ ꯕꯦꯡꯀꯔꯣꯜ ꯃꯦꯅꯦꯖꯃꯦꯟꯠ ꯍꯥꯌꯕꯁꯤ ꯃꯗꯨꯒꯤ ꯀꯌꯥ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯁꯨꯡ ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡꯗ ꯈꯨꯗꯣꯡꯊꯤꯕꯗ ꯊꯃꯒꯗꯒꯦ ꯍꯥꯌꯕ ꯋꯥꯔꯦꯞ ꯂꯧꯕꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯇꯝ ꯁꯥꯡꯅ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯍꯦꯟꯅ ꯍꯦꯅꯒꯠꯍꯟꯅꯕ ꯕꯦꯠꯀꯤ ꯆꯥꯡ ꯀꯔꯝꯅ ꯂꯦꯞꯀꯗꯒꯦ ꯍꯥꯌꯅ ꯍꯪꯈꯤ꯫ b ꯗꯒꯤ 1 ꯄꯤꯕ, ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → p ꯑꯃꯁꯨꯡ ꯃꯥꯏꯊꯤꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ q = 1 − p ꯂꯩꯕ ꯕꯦꯠ ꯑꯃꯒꯤꯗꯃꯛ ꯄꯥꯎꯈꯨꯝ ꯑꯗꯨꯗꯤ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ f* = (bp − q) / b ꯁꯔꯨꯛ ꯊꯝꯕꯅꯤ꯫ f* ꯄꯣꯖꯤꯇꯤꯕ ꯑꯣꯏꯔꯕꯗꯤ ꯁꯔꯨꯛ ꯑꯗꯨ ꯊꯝꯕꯤꯌꯨ; ꯖꯤꯔꯣ ꯅꯠꯔꯒ ꯅꯦꯒꯦꯇꯤꯕ ꯑꯣꯏꯔꯕꯗꯤ ꯕꯦꯠ ꯊꯝꯒꯅꯨ꯫ ꯀꯦꯂꯤꯅ ꯕꯦꯜ ꯂꯦꯕꯁꯇ ꯊꯕꯛ ꯇꯧꯈꯤ, ꯑꯃꯁꯨꯡ ꯃꯍꯥꯛꯀꯤ ꯄꯦꯄꯔ “A new interpretation of information rate” ꯅ ꯁꯃꯁ꯭ꯌꯥ ꯑꯁꯤ ꯀ꯭ꯂꯣꯗ ꯁꯦꯅꯟꯒꯤ ꯏꯅꯐꯣꯔꯃꯦꯁꯟ ꯊꯤꯑꯣꯔꯤꯗ ꯊꯃꯈꯤ: ꯅꯣꯏꯖ ꯂꯩꯕ ꯂꯥꯏꯟ ꯑꯃꯗꯒꯤ ꯇꯤꯞ ꯐꯪꯂꯤꯕ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ, ꯆꯨꯝꯃꯤꯟꯅꯕ ꯑꯣꯗꯁꯇ, ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯕꯗ ꯂꯥꯏꯟ ꯑꯗꯨꯅ ꯏꯅꯐꯣꯔꯃꯦꯁꯟ ꯄꯨꯕꯒꯤ ꯔꯦꯠ ꯑꯗꯨꯗ ꯕꯦꯡꯀꯔꯣꯜ ꯍꯦꯅꯒꯠꯍꯟꯕ ꯌꯥꯏ꯫ 1961 ꯗ ꯂꯤꯑꯣ ꯕ꯭ꯔꯦꯃꯦꯟꯅ ꯀꯦꯂꯤ ꯕꯦꯇꯤꯡꯅ ꯃꯇꯝ ꯁꯥꯡꯅ ꯃꯔꯨ ꯑꯣꯏꯅ ꯈꯦꯠꯅꯕ ꯀꯔꯤꯒꯨꯝꯕ ꯊꯧꯔꯥꯡ ꯑꯃꯗꯒꯤ ꯃꯃꯥꯡꯗ ꯂꯩꯒꯅꯤ ꯑꯃꯁꯨꯡ ꯂꯦꯞꯂꯕ ꯄꯥꯟꯗꯝ ꯑꯃꯗ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯊꯨꯕ ꯃꯇꯝ ꯃꯔꯥꯡ ꯀꯥꯏꯗ ꯌꯧꯒꯅꯤ ꯍꯥꯌꯕ ꯎꯠꯈꯤ꯫

ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯅꯣꯏꯖ ꯂꯩꯕ ꯂꯥꯏꯟ ꯑꯃꯗꯒꯤ ꯇꯤꯞ ꯇꯥꯔꯤ ꯑꯃꯁꯨꯡ ꯃꯍꯥꯛꯀꯤ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ ꯁꯔꯨꯛ ꯑꯃꯥ ꯊꯝꯂꯤ꯫

ꯔꯨꯂꯦꯠꯇ ꯀꯦꯂꯤ ꯕꯦꯇꯤꯡ

ꯑꯉꯥꯡꯕꯒꯤꯗꯃꯛꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →: b = 1, p = 18/37, q = 19/37; f* = (18/37 − 19/37)/1 = −1/37꯫ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯃꯁꯤꯡ ꯑꯃꯈꯛꯇ, 35:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯒꯤꯗꯃꯛ: b = 35, p = 1/37, q = 36/37; f* = (35/37 − 36/37)/35 = −1/1295꯫ ꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯅꯦꯒꯦꯇꯤꯕ ꯀꯦꯂꯤ ꯁꯔꯨꯛ ꯄꯤꯔꯤ, ꯃꯔꯃꯗꯤ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯅꯦꯒꯦꯇꯤꯕ ꯑꯦꯖ ꯂꯩ, ꯑꯃꯁꯨꯡ ꯍꯦꯅꯒꯠꯄꯒꯤꯗꯃꯛ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯕ ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯁꯤ ꯖꯤꯔꯣꯅꯤ꯫ ꯔꯨꯂꯦꯠꯇ ꯀꯦꯂꯤ ꯕꯦꯇꯤꯡ ꯍꯥꯌꯕꯁꯤ ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯂꯃꯥꯏꯅ ꯍꯥꯌꯔꯤꯕ ꯑꯗꯨꯃꯛ ꯐꯣꯔꯃꯦꯜ ꯑꯣꯏꯅ ꯍꯥꯌꯕꯅꯤ: ꯅꯦꯒꯦꯇꯤꯕ ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯂꯩꯕ ꯕꯦꯠ ꯑꯃꯅ ꯕꯦꯡꯀꯔꯣꯜ ꯍꯦꯅꯒꯠꯍꯟꯕ ꯉꯝꯕ ꯆꯥꯡ ꯑꯃꯠꯇ ꯂꯩꯇꯦ꯫

ꯕꯦꯠbpf* = (bp − q)/bꯑꯔꯊ

ꯑꯉꯥꯡꯕ, ꯌꯨꯔꯣꯄꯤꯌꯟ118/37−0.027ꯕꯦꯠ ꯊꯝꯒꯅꯨ

ꯑꯉꯥꯡꯕ, ꯂꯥ ꯄꯥꯔꯇꯥꯖ118/37 (ꯖꯤꯔꯣꯗ +½)−0.0135ꯕꯦꯠ ꯊꯝꯒꯅꯨ

ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ351/37−0.00077ꯕꯦꯠ ꯊꯝꯒꯅꯨ

1/30 ꯄꯣꯀꯦꯠ ꯑꯃꯗ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ (ꯕꯥꯏꯌꯥꯁ ꯂꯩꯕ)351/30+0.0057ꯕꯦꯡꯀꯔꯣꯜꯒꯤ 0.57% ꯊꯝꯕ

1/25 ꯄꯣꯀꯦꯠ ꯑꯃꯗ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ351/25+0.0126ꯕꯦꯡꯀꯔꯣꯜꯒꯤ 1.26% ꯊꯝꯕ

ꯀꯦꯂꯤ ꯀꯗꯥꯏꯗ ꯁꯤꯖꯤꯟꯅꯈꯤꯕꯒꯦ

ꯕꯥꯏꯌꯥꯁ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯗ ꯑꯦꯖ ꯂꯩꯈꯤ ꯑꯃꯁꯨꯡ ꯆꯥꯡ ꯂꯦꯞꯄꯒꯤ ꯁꯃꯁ꯭ꯌꯥ ꯑꯃꯁꯨ ꯂꯩꯈꯤ꯫ ꯖꯦꯒꯔ, ꯒꯥꯔꯁꯤꯌꯥ-ꯄꯦꯂꯥꯌꯣ ꯏꯃꯨꯡ ꯑꯃꯁꯨꯡ ꯌꯨꯗꯦꯃꯟꯁꯅ ꯃꯈꯣꯌꯅ ꯆꯥꯡꯈꯤꯕ ꯑꯦꯗꯚꯥꯟꯇꯦꯖꯗ ꯀꯌꯥ ꯕꯦꯠ ꯊꯝꯒꯗꯒꯦ ꯍꯥꯌꯕ ꯋꯥꯔꯦꯞ ꯂꯧꯒꯗꯕꯅꯤ, ꯑꯃꯁꯨꯡ ꯍꯟꯅ ꯊꯝꯂꯕꯗꯤ ꯑꯦꯖ ꯑꯗꯨ ꯃꯥꯡꯏ ꯑꯗꯨꯒ ꯍꯦꯟꯅ ꯊꯝꯂꯕꯗꯤ ꯑꯦꯖ ꯑꯗꯨ ꯎꯕ ꯐꯪꯗ꯭ꯔꯤꯉꯩꯗ ꯕꯦꯡꯀꯔꯣꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕ ꯂꯩ꯫ 30 ꯗ 1 ꯊꯣꯛꯂꯤꯕ ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯒꯤꯗꯃꯛ, ꯀꯦꯂꯤꯅ ꯃꯁꯤꯡ ꯑꯗꯨꯗ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ 0.57% ꯍꯥꯌꯔꯤ: $10,000 ꯂꯩꯔꯕꯗꯤ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ $57 ꯃꯔꯥꯡ ꯀꯥꯏꯅ, ꯃꯁꯤꯅ ꯑꯣꯏꯕ ꯃꯑꯣꯡꯗ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ 0.054% ꯃꯔꯥꯡ ꯀꯥꯏꯅ ꯍꯦꯅꯒꯠꯍꯜꯂꯤ, ꯅꯠꯔꯒ ꯁ꯭ꯄꯤꯟ 1,000 ꯗ ×1.7꯫ ꯑꯦꯚꯔꯦꯖ ꯀꯥꯟꯅꯕ ꯑꯗꯨ ꯃꯁꯤꯒꯤ ꯑꯃꯨꯛ ꯑꯅꯤ, ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ 0.11%, ꯑꯗꯨꯕꯨ ꯀꯦꯂꯤꯅ ꯄꯥꯟꯗꯝ ꯊꯝꯂꯤꯕꯗꯤ ꯑꯣꯏꯕ ꯃꯑꯣꯡꯒꯤ ꯕꯦꯡꯀꯔꯣꯜꯅꯤ, ꯂꯥꯛ ꯐꯕ ꯔꯟ ꯈꯔꯅ ꯆꯥꯎꯍꯟꯂꯤꯕ ꯑꯦꯚꯔꯦꯖ ꯕꯦꯡꯀꯔꯣꯜ ꯅꯠꯇꯦ꯫ ꯑꯦꯖꯀꯤ ꯆꯥꯡ ꯊꯤꯕ ꯑꯗꯨ ꯁꯣꯏꯗꯅ ꯈꯉꯕ ꯉꯃꯗꯕꯅꯥ ꯍꯥꯐ-ꯀꯦꯂꯤ ꯑꯁꯤ ꯌꯥꯝꯅꯥ ꯁꯤꯖꯤꯟꯅꯕ ꯈꯅꯕꯅꯤ꯫

ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ ꯑꯃꯗ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ % ꯑꯣꯏꯅ ꯀꯦꯂꯤ ꯊꯝꯂꯕ ꯁꯦꯜ, ꯄꯣꯀꯦꯠꯀꯤ ꯑꯁꯦꯡꯕ ꯔꯦꯠꯀꯤ ꯃꯇꯨꯡ ꯏꯟꯅ%

1/37 (ꯆꯨꯝꯃꯤꯟꯅꯕ)

0% · ꯕꯦꯠ ꯊꯝꯒꯅꯨ

1/35

0.08%

1/33

0.26%

1/30

0.57%

1/25

1.26%

1/20

2.0%

012.0%

ꯆꯥꯎꯕ ꯕꯥꯏꯌꯥꯁ ꯑꯃꯗꯁꯨ ꯑꯄꯤꯛꯄ ꯕꯦꯠ ꯈꯛꯇꯃꯛ ꯃꯊꯧ ꯇꯥꯏ: ꯄꯦꯑꯥꯎꯠ ꯑꯁꯤ ꯂꯣꯡ ꯑꯣꯏ ꯑꯃꯁꯨꯡ ꯚꯦꯌꯔꯤꯌꯦꯟꯁ ꯋꯥꯡꯏ꯫

ꯃꯃꯤꯡ ꯂꯩꯔꯕ ꯔꯨꯂꯦꯠ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡ ꯌꯨꯗꯦꯃꯣꯅꯁꯤꯡ

ꯑꯣꯏꯕ ꯃꯑꯣꯡ ꯑꯃꯁꯨꯡ ꯑꯦꯚꯔꯦꯖ

ꯑꯣꯏꯕ ꯃꯑꯣꯡꯒꯤ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯃꯁꯨꯡ ꯑꯦꯚꯔꯦꯖ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ ꯃꯔꯛ ꯑꯁꯤ ꯌꯥꯝꯅꯥ ꯆꯥꯎꯏ꯫ 25 ꯗ ꯑꯃꯨꯛ 1 ꯊꯣꯛꯂꯤꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯥ ꯂꯧꯁꯤ, 44% ꯒꯤ ꯑꯦꯖ, ꯊꯣꯔꯄꯅ ꯃꯍꯥꯛꯀꯤ ꯗꯤꯚꯥꯏꯁꯀꯤꯗꯃꯛ ꯄꯤꯈꯤꯕ ꯃꯁꯤꯡ꯫ ꯀꯦꯂꯤꯅ ꯃꯁꯤꯗ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ 1.26% ꯊꯝꯏ꯫ ꯁ꯭ꯄꯤꯟ 1,000 ꯃꯇꯨꯡꯗ ꯑꯣꯏꯕ ꯃꯑꯣꯡꯒꯤ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯁꯤ ꯑꯃꯨꯛ 11.5 ꯃꯔꯥꯡ ꯀꯥꯏꯅ ꯍꯦꯅꯒꯠꯂꯛꯏ, ꯑꯗꯨꯒ ꯂꯥꯛ ꯌꯥꯝꯅꯥ ꯐꯕ ꯔꯟ ꯈꯔꯅ ꯋꯥꯡꯍꯟꯂꯤꯕ ꯑꯦꯚꯔꯦꯖ ꯑꯗꯨꯗꯤ ꯑꯃꯨꯛ 249 ꯃꯔꯥꯡ ꯀꯥꯏꯅ ꯍꯦꯅꯒꯠꯂꯛꯏ꯫ ꯀꯦꯂꯤꯗꯒꯤ ꯍꯦꯟꯅ ꯊꯝꯂꯕꯗꯤ ꯑꯦꯚꯔꯦꯖ ꯑꯗꯨ ꯋꯥꯡꯂꯛꯏ ꯑꯗꯨꯒ ꯑꯣꯏꯕ ꯃꯑꯣꯡꯒꯤ ꯃꯍꯩ ꯑꯗꯨ ꯍꯟꯊꯔꯛꯏ: ꯀꯦꯂꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯑꯃꯨꯛ ꯑꯅꯤꯗ ꯑꯣꯏꯕ ꯃꯑꯣꯡꯒꯤ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯁꯤ ꯑꯅꯤ ꯊꯣꯛ ꯈꯛꯇꯃꯛ ꯑꯣꯏꯔꯛꯏ, ꯑꯃꯁꯨꯡ ꯀꯦꯂꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯑꯃꯨꯛ ꯑꯅꯤ ꯑꯃꯁꯨꯡ ꯇꯉꯥꯏꯗ ꯃꯁꯤ ꯍꯟꯊꯔꯛꯏ, ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯍꯧꯖꯤꯀꯁꯨ 44% ꯒꯤ ꯑꯦꯖ ꯂꯩꯔꯕꯁꯨ꯫ ꯍꯟꯅ ꯊꯝꯂꯕꯗꯤ ꯌꯥꯝꯅꯥ ꯃꯥꯡꯗꯦ: ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯇꯉꯥꯏꯅ ꯍꯦꯅꯒꯠꯄꯒꯤ ꯁꯔꯨꯛ ꯃꯔꯤꯒꯤ ꯑꯍꯨꯝ ꯃꯔꯥꯡ ꯀꯥꯏꯅ ꯉꯥꯛꯂꯤ꯫

ꯊꯝꯂꯕ ꯁꯦꯜ, ꯀꯦꯂꯤꯒꯤ ꯁꯔꯨꯛꯊꯝꯂꯕ ꯁꯦꯜ, ꯕꯦꯡꯀꯔꯣꯜꯒꯤ %ꯁ꯭ꯄꯤꯟ 1,000 ꯃꯇꯨꯡꯒꯤ ꯑꯣꯏꯕ ꯃꯑꯣꯡꯒꯤ ꯕꯦꯡꯀꯔꯣꯜ

½0.63%× 6.7

11.26%× 11.5

1½1.89%× 7.4

22.51%× 2.2

2½3.14%× 0.38

33.77%× 0.04

25 ꯗ 1 ꯊꯣꯛꯂꯤꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯥ, 35 ꯗꯒꯤ 1 ꯄꯤꯕ꯫ ꯑꯣꯏꯕ ꯃꯑꯣꯡ ꯍꯥꯌꯕꯁꯤ ꯃꯤꯗꯤꯌꯥꯟꯅꯤ, e ꯕꯨ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯒꯤ ꯍꯦꯅꯒꯠꯄꯒꯤ 1,000 ꯊꯣꯛꯀꯤ ꯄꯥꯋꯔ ꯄꯤꯕ꯫

ꯑꯦꯖ ꯑꯗꯨ ꯈꯟꯖꯤꯟꯕ ꯈꯛꯇꯅꯤ ꯑꯣꯏꯔꯕꯗꯤ

ꯀꯦꯂꯤꯅ ꯑꯦꯖ ꯑꯗꯨ ꯈꯉꯂꯦ ꯍꯥꯌꯅ ꯂꯧꯏ꯫ ꯇꯦꯕꯜꯗꯗꯤ ꯃꯁꯤ ꯊꯤꯖꯤꯟꯕ ꯈꯛꯇꯅꯤ, ꯑꯃꯁꯨꯡ ꯊꯤꯖꯤꯟꯕ ꯑꯗꯨ ꯌꯥꯝꯅꯥ ꯀꯌꯥꯗ ꯌꯥꯝꯅꯥ ꯋꯥꯡꯏ꯫ ꯊꯣꯔꯄꯀꯤ 44% ꯗ ꯌꯨꯝꯐꯝ ꯑꯣꯏꯕ ꯑꯦꯞꯁ꯭ꯇꯥꯏꯅꯒꯤ ꯈꯨꯗꯝ ꯑꯁꯤ ꯗꯕꯜ-ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯆꯛꯔ ꯑꯃꯒꯤ ꯁ꯭ꯄꯤꯟ 1,225 ꯗ ꯑꯃꯨꯛ 49 ꯊꯣꯀꯈꯤꯕ ꯃꯁꯤꯡ ꯑꯃꯅꯤ: 25 ꯗ ꯑꯃꯨꯛ 1, 44% ꯒꯤ ꯑꯦꯖ, 1.26% ꯒꯤ ꯀꯦꯂꯤ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯑꯗꯨꯕꯨ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯗꯕꯜ-ꯖꯤꯔꯣ ꯆꯛꯔ ꯑꯃꯗ ꯃꯁꯤꯡ 38 ꯂꯩ, ꯑꯃꯁꯨꯡ ꯃꯈꯣꯌꯒꯤ ꯃꯅꯨꯡꯗ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯌꯥꯝꯅꯥ ꯊꯣꯛꯂꯤꯕ ꯑꯗꯨꯅ ꯁ꯭ꯄꯤꯟ 1,225 ꯗ ꯑꯃꯨꯛ 49 ꯅꯠꯔꯒ ꯃꯁꯤꯗꯒꯤ ꯍꯦꯟꯅ ꯌꯧꯕ ꯑꯁꯤ ꯃꯥꯄꯟꯗ ꯑꯃꯨꯛ ꯑꯃꯥ ꯃꯔꯥꯡ ꯀꯥꯏꯅ ꯊꯣꯛꯏ꯫ ꯀꯔꯤꯒꯨꯝꯕ ꯔꯦꯀꯣꯔꯗ ꯑꯃꯗ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯌꯥꯝꯅꯥ ꯊꯣꯛꯂꯤꯕ ꯃꯁꯤꯡ ꯑꯗꯨ ꯂꯥꯛꯅ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯍꯦꯟꯅ ꯃꯇꯦꯡ ꯄꯥꯡꯈꯤꯕ ꯑꯗꯨꯁꯨ ꯑꯣꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯇꯁꯦꯡꯅ ꯕꯥꯏꯌꯥꯁ ꯂꯩꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯁꯨ ꯔꯦꯀꯣꯔꯗꯇ ꯃꯁꯤꯒꯤ ꯑꯁꯦꯡꯕꯗꯒꯤ ꯍꯦꯟꯅ ꯐꯅ ꯎꯏ: ꯃꯁꯤ ꯃꯥꯏꯄꯥꯛꯄ ꯃꯤꯒꯤ ꯁꯥꯞ (winner’s curse) ꯅꯤ꯫ ꯄꯣꯀꯦꯠ ꯑꯗꯨ ꯇꯁꯦꯡꯅ ꯕꯥꯏꯌꯥꯁ ꯂꯩꯇꯕꯗꯤ, ꯀꯦꯂꯤ ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯗꯨ ꯑꯦꯚꯔꯦꯖꯗ 5.26% ꯃꯥꯡꯂꯤꯕ ꯕꯦꯠ ꯑꯃꯈꯛꯇꯅꯤ꯫ ꯌꯥꯝꯅꯥ ꯁꯤꯖꯤꯟꯅꯕ ꯄꯥꯎꯈꯨꯃꯁꯤꯡꯗꯤ ꯀꯦꯂꯤꯒꯤ ꯁꯔꯨꯛ ꯑꯃꯈꯛꯇ ꯊꯝꯕ ꯑꯃꯁꯨꯡ ꯑꯅꯧꯕ ꯔꯦꯀꯣꯔꯗ ꯑꯃꯗꯁꯨ ꯑꯦꯖ ꯑꯗꯨ ꯂꯩꯔꯤꯐꯥꯑꯣꯕ ꯃꯁꯤꯡ ꯊꯤꯕ ꯃꯈꯥ ꯆꯠꯊꯕꯅꯤ (ꯔꯨꯂꯦꯠ ꯆꯛꯔꯒꯤ ꯕꯥꯏꯌꯥꯁ ꯀꯔꯝꯅ ꯊꯤꯗꯣꯛꯀꯅꯤ ꯌꯦꯡꯕꯤꯌꯨ)꯫

ꯑꯦꯖ ꯂꯩꯕ ꯃꯤꯑꯣꯏꯁꯤꯡ

ꯑꯦꯖ ꯈꯉꯕ ꯍꯥꯌꯕꯁꯤ ꯃꯗꯨ ꯐꯅ ꯁꯤꯖꯤꯟꯅꯕꯒꯥ ꯆꯞ ꯃꯥꯟꯅꯗꯦ꯫ ꯍꯥꯒꯥꯅꯤ ꯑꯃꯁꯨꯡ ꯗꯤꯎꯏ (2016) ꯅ ꯃꯤ 61 ꯗ ꯃꯤ ꯈꯨꯗꯤꯡꯗ $25 ꯄꯤꯗꯨꯅ ꯄꯨꯡ ꯁꯔꯨꯛ ꯑꯃꯒꯤ ꯃꯅꯨꯡꯗ ꯄꯥꯏꯁꯥ ꯑꯃꯗ ꯕꯦꯠ ꯊꯝꯍꯅꯈꯤ, ꯄꯥꯏꯁꯥ ꯑꯗꯨ ꯃꯇꯃꯒꯤ 60% ꯗ ꯍꯦꯗ ꯊꯣꯛꯏ ꯍꯥꯌꯅ ꯃꯈꯣꯌꯗ ꯍꯥꯌꯈꯤ, ꯑꯃꯁꯨꯡ ꯃꯥꯏꯄꯥꯛꯇꯨꯅ ꯐꯪꯂꯕ ꯁꯦꯜ $250 ꯗ ꯉꯝꯈꯩ ꯊꯃꯈꯤ (ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯉꯝꯈꯩ ꯑꯗꯨ ꯌꯧꯕꯥ ꯃꯇꯃꯗ ꯈꯛꯇ ꯈꯉꯈꯤ)꯫ ꯀꯦꯂꯤꯅ ꯃꯇꯝ ꯈꯨꯗꯤꯡꯗ ꯍꯦꯗꯇ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ 20% ꯊꯝꯕꯤꯌꯨ ꯍꯥꯌꯔꯤ, ꯑꯃꯁꯨꯡ ꯏꯕꯥ ꯃꯤꯁꯤꯡꯅ 10–20% ꯒꯤ ꯂꯦꯞꯄ ꯂꯩꯇꯅ ꯊꯝꯕ ꯕꯦꯠꯁꯤꯡꯅ ꯃꯇꯃꯒꯤ 95% ꯃꯔꯥꯡ ꯀꯥꯏꯗ ꯉꯝꯈꯩ ꯑꯗꯨ ꯌꯧꯒꯅꯤ ꯍꯥꯌꯅ ꯊꯤꯖꯤꯜꯂꯤ꯫ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯒꯤ 21% ꯈꯛꯇꯅ ꯃꯐꯝ ꯑꯗꯨꯗ ꯌꯧꯈꯤ꯫ 28% ꯅ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯈꯤ, 61 ꯒꯤ ꯃꯅꯨꯡꯗ 18 ꯅ ꯄꯥꯏꯁꯥ ꯊꯥꯗꯣꯛꯄ ꯑꯃꯈꯛꯇꯗ ꯄꯨꯝꯅꯃꯛ ꯊꯃꯈꯤ, ꯑꯍꯨꯃꯗ ꯑꯃꯥ ꯃꯔꯥꯡ ꯀꯥꯏꯅ ꯍꯧꯔꯀꯄꯥ $25 ꯗꯒꯤ ꯍꯟꯅ ꯂꯣꯏꯁꯤꯅꯈꯤ, ꯑꯃꯁꯨꯡ ꯑꯦꯚꯔꯦꯖ ꯄꯦꯑꯥꯎꯠꯁꯦꯜꯄꯦꯑꯥꯎꯠꯃꯥꯏꯄꯥꯛꯄ ꯕꯦꯠ ꯑꯃꯅ ꯍꯜꯂꯛꯄ ꯁꯦꯜ, ꯍꯜꯂꯀꯄ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯊꯛꯇ “X ꯗꯒꯤ 1” ꯍꯥꯌꯅ ꯍꯥꯌꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ $91 ꯑꯣꯏꯈꯤ꯫ 61 ꯒꯤ ꯃꯅꯨꯡꯗ ꯃꯉꯥ ꯈꯛꯇꯅ ꯀꯦꯂꯤ ꯀ꯭ꯔꯥꯏꯇꯦꯔꯤꯌꯅꯒꯤ ꯃꯔꯃꯗ ꯇꯥꯈꯤꯕꯅꯤ꯫ ꯑꯦꯖ ꯂꯩꯔꯕꯗꯤ ꯕꯦꯠꯀꯤ ꯆꯥꯡꯅ ꯃꯗꯨ ꯉꯥꯛꯀꯅꯤ ꯅꯠꯔꯒ ꯅꯠꯇꯦ ꯍꯥꯌꯕ ꯂꯦꯞꯊꯣꯀꯏ; ꯂꯩꯇꯕꯗꯤ, ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯛꯔ ꯑꯃꯗ ꯂꯩꯕꯒꯨꯝꯅ, ꯀꯔꯤꯒꯨꯝꯕ ꯆꯥꯡ ꯑꯃꯠꯇꯅ ꯃꯇꯦꯡ ꯄꯥꯡꯗꯦ꯫

ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯄꯥꯏꯁꯥ ꯊꯥꯗꯣꯛꯄ ꯑꯃꯗ ꯄꯨꯝꯅꯃꯛ ꯊꯝꯂꯤ ꯑꯗꯨꯒ ꯃꯍꯥꯛꯀꯤ ꯃꯅꯥꯛꯇ ꯂꯩꯕ ꯃꯤꯅ ꯑꯄꯤꯛꯄ ꯁꯔꯨꯛ ꯑꯃꯈꯛꯇ ꯊꯝꯂꯤ꯫

ꯃꯗꯨꯒꯤ ꯃꯍꯨꯠꯇ ꯀꯔꯤ ꯁꯤꯖꯤꯟꯅꯒꯗꯒꯦ

ꯑꯦꯖ ꯂꯩꯇꯕꯗꯤ ꯆꯥꯡ ꯂꯦꯞꯄ ꯑꯁꯤ ꯕꯖꯦꯠꯀꯤ ꯋꯥꯍꯪꯅꯤ, ꯍꯦꯅꯒꯠꯄꯒꯤ ꯋꯥꯍꯪ ꯅꯠꯇꯦ: ꯊꯝꯂꯕ ꯁꯦꯜ = ꯅꯍꯥꯛꯅ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯁꯤꯖꯤꯟꯅꯕ ꯄꯥꯝꯂꯤꯕ ꯁꯦꯜ, ꯄꯨꯡ ꯈꯨꯗꯤꯡꯒꯤ ꯕꯖꯦꯠ ꯑꯃꯁꯨꯡ ꯇꯦꯕꯜꯒꯤ ꯊꯨꯅꯕꯗꯒꯤ ꯂꯧꯊꯣꯀꯄ (ꯕꯦꯡꯀꯔꯣꯜ ꯃꯦꯅꯦꯖꯃꯦꯟꯇꯀꯤ ꯂꯃꯥꯏ)꯫ ꯃꯤꯅꯝ ꯁꯥꯟꯅꯔꯤꯕꯗ ꯀꯦꯂꯤꯅ ꯄꯤꯕ ꯈꯨꯗꯣꯜ ꯑꯗꯨꯗꯤ ꯃꯁꯤꯒꯤ ꯄꯥꯎꯈꯨꯃꯒꯤ ꯃꯌꯦꯛ ꯁꯦꯡꯕꯅꯤ: ꯖꯤꯔꯣ꯫ ꯅꯍꯥꯛꯅ ꯖꯤꯔꯣꯗꯒꯤ ꯍꯦꯟꯅ ꯊꯝꯂꯤꯕ ꯄꯨꯝꯅꯃꯛ ꯑꯁꯤ ꯁꯥꯟꯅꯕꯒꯤ ꯃꯃꯂꯅꯤ, ꯅꯍꯥꯛꯅ ꯈꯅꯕ, ꯀꯔꯤꯒꯨꯝꯕ ꯐꯣꯔꯃꯨꯂꯥ ꯑꯃꯅ ꯑꯣꯞꯇꯤꯃꯥꯏꯖ ꯇꯧꯕ ꯅꯠꯇꯦ꯫

ꯁꯔꯨꯛ ꯀꯦꯂꯤ ꯑꯃꯁꯨꯡ “ꯁꯦꯜ ꯃꯦꯅꯦꯖꯃꯦꯟꯠ” ꯒꯤ ꯃꯔꯃꯗ ꯋꯥꯐꯝ ꯑꯃꯥ

“ꯔꯨꯂꯦꯠꯀꯤꯗꯃꯛ ꯀꯦꯂꯤ” ꯍꯥꯌꯅ ꯌꯣꯟꯂꯤꯕ, ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ ꯂꯦꯞꯄ ꯄꯔꯁꯦꯟꯇ ꯑꯃꯥ ꯊꯝꯅꯕ ꯍꯥꯌꯔꯤꯕ ꯁꯤꯁ꯭ꯇꯦꯝꯁꯤꯡ ꯑꯁꯤ ꯊꯝꯂꯕ ꯁꯦꯜ ꯍꯟꯊꯔꯛꯂꯤꯕ ꯐ꯭ꯂꯦꯠ ꯕꯦꯇꯤꯡꯊꯧꯔꯥꯡꯐ꯭ꯂꯦꯠ ꯕꯦꯇꯤꯡꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯁꯦꯜ ꯃꯥꯟꯅꯕ ꯊꯝꯕ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ ꯈꯨꯗꯤꯡꯃꯛ ꯆꯥꯡꯗꯝꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯃꯈꯥꯌꯣꯜꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯈꯛꯇꯅꯤ꯫ ꯃꯈꯣꯌꯅ ꯇꯔꯅꯑꯣꯚꯔꯒꯤꯁꯦꯜꯇꯔꯅꯑꯣꯚꯔꯁꯦꯁꯟ ꯅꯠꯔꯒ ꯃꯇꯝ ꯑꯃꯒꯤ ꯃꯅꯨꯡꯗ ꯕꯦꯠ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ, ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯝꯂꯕ ꯃꯥꯏꯄꯥꯛꯇꯨꯅ ꯐꯪꯂꯕ ꯁꯦꯜꯁꯨ ꯌꯥꯎꯅ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯍꯦꯟꯗꯜ, ꯑꯦꯛꯁꯟ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 2.70% ꯃꯥꯡꯏ, ꯑꯃꯁꯨꯡ ꯃꯥꯏꯊꯤꯕꯒꯥ ꯂꯣꯌꯅꯅ ꯊꯝꯂꯕ ꯁꯦꯜ ꯍꯟꯊꯔꯛꯄꯅꯥ ꯃꯔꯝ ꯑꯣꯏꯗꯨꯅ, ꯃꯈꯣꯌꯅ ꯕꯦꯡꯀꯔꯣꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕ ꯑꯗꯨ ꯊꯣꯛꯂꯣꯏꯗꯕ ꯑꯣꯏꯍꯟꯗꯦ, ꯇꯞꯅ ꯊꯣꯀꯍꯟꯏ ꯈꯛꯇꯅꯤ꯫ ꯃꯁꯤ ꯕꯖꯦꯠ ꯑꯃꯥ ꯁꯥꯡꯅ ꯆꯠꯍꯟꯅꯕ ꯃꯑꯣꯡ ꯑꯐꯕ ꯑꯃꯅꯤ; ꯃꯁꯤ ꯀꯦꯂꯤ ꯅꯠꯇꯦ, ꯀꯦꯂꯤꯅꯗꯤ ꯂꯦꯞꯄꯤꯌꯨ ꯍꯥꯌꯒꯅꯤ꯫

ꯐ꯭ꯂꯦꯠ ꯕꯦꯇꯤꯡ ꯔꯨꯂꯦꯠ ꯊꯧꯔꯥꯡ

ꯐꯣꯔꯃꯨꯂꯥ

f* = (b·p − q) / b

ꯑꯉꯥꯡꯕ: f* = −1/37 · ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ: f* = −1/1295

r ꯔꯦꯠꯇ ꯕꯥꯏꯌꯥꯁ ꯂꯩꯕ ꯄꯣꯀꯦꯠ: f* = (35r − (1 − r)) / 35

ꯋꯥꯍꯪꯁꯤꯡ

ꯀꯦꯂꯤꯅ ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯔꯨꯂꯦꯠꯇ ꯕꯦꯠ ꯊꯝꯕꯤꯌꯨ ꯍꯥꯌꯕꯔꯥ?

ꯕꯥꯏꯌꯥꯁ ꯂꯩꯕ ꯆꯛꯔꯂꯦꯕꯕꯥꯏꯌꯥꯁ ꯂꯩꯕ ꯆꯛꯔꯁꯛꯇꯝꯒꯤ ꯑꯁꯣꯏꯕꯁꯤꯡꯅ ꯄꯣꯀꯦꯠ ꯈꯔꯕꯨ 1/37 ꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯊꯣꯛꯍꯟꯕ ꯆꯛꯔ꯫ ꯌꯥꯝꯅ ꯌꯥꯝꯗꯦ, ꯊꯝꯂꯕ ꯁ꯭ꯄꯤꯟ ꯂꯤꯁꯤꯡ ꯀꯌꯥꯅ ꯈꯛꯇꯃꯛ ꯈꯉꯕ ꯉꯝꯃꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗꯒꯤ ꯅꯠꯔꯒ ꯃꯇꯝ ꯊꯤꯕ ꯗꯤꯚꯥꯏꯁ ꯑꯃꯗꯒꯤ ꯆꯥꯡꯈꯤꯕ ꯑꯦꯖ ꯂꯩꯔꯕꯗ ꯈꯛꯇꯅꯤ꯫ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯛꯔ ꯑꯃꯗ ꯅꯠꯇꯦ꯫

ꯍꯥꯐ-ꯀꯦꯂꯤ ꯀꯔꯤꯒꯤꯅꯣ?

ꯃꯔꯃꯗꯤ ꯑꯦꯖꯀꯤ ꯊꯤꯖꯤꯟꯕꯗ ꯑꯔꯥꯟꯕ ꯂꯩ, ꯑꯃꯁꯨꯡ ꯍꯦꯟꯅ ꯊꯝꯕ ꯑꯁꯤ ꯍꯟꯅ ꯊꯝꯕꯗꯒꯤ ꯃꯃꯜ ꯍꯦꯟꯅ ꯆꯥꯡꯏ꯫ ꯍꯥꯐ-ꯀꯦꯂꯤꯅ ꯚꯦꯌꯔꯤꯌꯦꯟꯁꯀꯤꯃꯦꯊꯃꯦꯇꯤꯛꯁꯚꯦꯌꯔꯤꯌꯦꯟꯁꯃꯍꯩꯁꯤꯡ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯒꯤ ꯑꯀꯣꯌꯕꯗ ꯀꯌꯥ ꯁꯟꯗꯣꯛꯅ ꯂꯩꯕꯒꯦ ꯍꯥꯌꯕꯒꯤ ꯆꯥꯡ꯫ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯇ ꯋꯥꯡꯏ, ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡꯗ ꯅꯦꯝꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯔꯤꯒꯤ ꯑꯃꯗ ꯍꯦꯅꯒꯠꯄꯒꯤ ꯃꯔꯤꯒꯤ ꯑꯍꯨꯝ ꯄꯤꯔꯤ꯫

ꯀꯦꯂꯤ ꯑꯃꯁꯨꯡ ꯕꯦꯡꯀꯔꯣꯜ ꯃꯦꯅꯦꯖꯃꯦꯟꯠ ꯑꯁꯤ ꯑꯗꯨꯃꯛꯇꯔꯥ?

ꯅꯠꯇꯦ꯫ ꯀꯦꯂꯤꯅ ꯑꯦꯖ ꯂꯩꯔꯕꯗ ꯍꯦꯅꯒꯠꯄ ꯑꯣꯞꯇꯤꯃꯥꯏꯖ ꯇꯧꯏ꯫ ꯕꯦꯡꯀꯔꯣꯜ ꯃꯦꯅꯦꯖꯃꯦꯟꯇꯅ ꯑꯦꯖ ꯂꯩꯇꯕꯗ ꯁꯦꯜ ꯁꯤꯖꯤꯟꯅꯕ ꯀꯟꯠꯔꯣꯜ ꯇꯧꯏ꯫

ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯥ ꯁꯥꯟꯅꯕ

ꯃꯁꯤꯁꯤꯡ ꯑꯍꯥꯅꯕꯗ ꯅꯍꯥꯛ ꯃꯁꯥꯃꯛꯅ ꯍꯣꯠꯅꯕꯤꯌꯨ꯫ ꯄꯥꯎꯈꯨꯝ ꯈꯨꯗꯤꯡꯃꯛ ꯊꯨꯡꯗꯨꯅ ꯊꯝꯂꯤ; ꯁꯦꯝ ꯁꯥꯔꯕ ꯃꯇꯃꯗ ꯍꯥꯡꯗꯣꯛꯄꯤꯌꯨ꯫

ꯊꯣꯔꯞ ꯑꯃꯁꯨꯡ ꯁꯦꯅꯟꯒꯤ ꯄ꯭ꯔꯤꯗꯤꯛꯁꯟ ꯗꯤꯚꯥꯏꯁꯅ 44% ꯈꯔꯒꯤ ꯑꯦꯖ ꯄꯤꯈꯤ꯫ ꯄ꯭ꯔꯤꯗꯤꯛꯇ ꯇꯧꯈꯤꯕ ꯃꯁꯤꯡ ꯑꯃꯈꯛꯇ, ꯀꯦꯂꯤꯅ ꯕꯦꯡꯀꯔꯣꯜꯁꯦꯜꯕꯦꯡꯀꯔꯣꯜꯁꯥꯟꯅꯅꯕ ꯇꯣꯉꯥꯟꯅ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ꯫ ꯕꯦꯡꯀꯔꯣꯜ ꯃꯦꯅꯦꯖꯃꯦꯟꯠ ꯍꯥꯌꯕꯁꯤ ꯃꯗꯨꯒꯤ ꯀꯌꯥ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯁꯨꯡ ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡꯗ ꯈꯨꯗꯣꯡꯊꯤꯕꯗ ꯊꯃꯒꯗꯒꯦ ꯍꯥꯌꯕ ꯋꯥꯔꯦꯞ ꯂꯧꯕꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯒꯤ 1.26% ꯊꯝꯅꯕ ꯍꯥꯌꯔꯤ꯫ 44% ꯒꯤ ꯑꯦꯖ ꯑꯗꯨꯃꯛ ꯌꯨꯝꯂꯣꯟꯅꯕ ꯃꯁꯤꯡ ꯃꯉꯥꯗ ꯁꯟꯗꯣꯀꯈꯤꯕ ꯕꯦꯠ ꯑꯃꯗ ꯂꯥꯛꯂꯕꯗꯤ ꯀꯔꯤ ꯑꯣꯏꯒꯅꯤ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯃꯗꯨꯗꯤ ꯀꯦꯂꯤꯅ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ 7.1% ꯍꯥꯌꯔꯤ, ꯑꯃꯁꯨꯡ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯁꯤ ꯑꯃꯨꯛ ꯇꯔꯨꯛ ꯃꯅꯥꯛ ꯊꯨꯅ ꯍꯦꯅꯒꯠꯂꯀꯏ: ꯕꯦꯠ 1,000 ꯗ ꯑꯃꯨꯛ 1.25 ꯃꯤꯂꯤꯌꯟ ꯈꯔ, ꯑꯃꯨꯛ 11.5 ꯈꯔꯒꯥ ꯆꯥꯡꯗꯝꯂꯕꯗ꯫
44% ꯒꯤ ꯑꯦꯖ ꯂꯩꯕ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯃꯁꯤꯡ ꯑꯃꯈꯛꯇ, 35:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯅ 0.04 ꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯒꯥ ꯂꯣꯌꯅꯅ ꯃꯥꯏꯄꯥꯀꯏ, ꯃꯔꯃꯗꯤ 36 × 0.04 = 1.44꯫ ꯀꯦꯂꯤꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯁꯤ ꯑꯦꯖꯕꯨ ꯑꯣꯗꯁꯅ ꯌꯦꯟꯊꯣꯀꯄꯅꯤ: 0.44/35 = 1.26%꯫ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯒꯤ ꯃꯇꯝ ꯄꯨꯝꯕꯒꯤ ꯍꯦꯅꯒꯠꯄ ꯑꯁꯤ 0.04 × ln(1 + 35 × 0.0126) + 0.96 × ln(1 − 0.0126) ≈ 0.00244, ꯃꯔꯝ ꯑꯗꯨꯅ ꯕꯦꯠ 1,000 ꯅ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯗꯨ e^2.44 ≈ 11.5 ꯈꯔꯅ ꯃꯜꯇꯤꯞꯂꯥꯏ ꯇꯧꯏ꯫
ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯃꯥ ꯃꯁꯤꯡ ꯃꯉꯥꯗ ꯁꯟꯗꯣꯛꯂꯕꯗꯤ ꯕꯦꯠ ꯑꯗꯨ 0.20 ꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯒꯥ ꯂꯣꯌꯅꯅ ꯃꯥꯏꯄꯥꯀꯏ ꯑꯃꯁꯨꯡ 1 ꯒꯤꯗꯃꯛ 36/5 ꯍꯜꯂꯛꯏ, ꯍꯥꯌꯕꯗꯤ 6.2 ꯗꯒꯤ 1: ꯍꯧꯖꯤꯀꯁꯨ 44% ꯒꯤ ꯑꯦꯖ, ꯃꯔꯃꯗꯤ 0.2 × 7.2 = 1.44꯫ ꯀꯦꯂꯤꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯁꯤ 0.44/6.2 = 7.10% ꯑꯣꯏꯔꯀꯏ, ꯑꯃꯁꯨꯡ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯒꯤ ꯍꯦꯅꯒꯠꯄ 0.01404, ꯑꯃꯨꯛ 5.75 ꯈꯔ꯫ ꯕꯦꯠ 1,000 ꯗ ꯃꯁꯤ e^14.04, 1.25 ꯃꯤꯂꯤꯌꯟ ꯈꯔ꯫
ꯑꯦꯖ ꯑꯗꯨ ꯃꯥꯟꯅꯩ; ꯆꯥꯎꯊꯣꯀꯆꯕ ꯑꯗꯨ ꯍꯦꯟꯅ ꯑꯄꯤꯛꯏ꯫ ꯃꯉꯥꯗ ꯑꯃꯨꯛ ꯃꯥꯏꯄꯥꯛꯄ ꯕꯦꯠ ꯑꯃꯅ ꯕꯦꯡꯀꯔꯣꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕ ꯌꯥꯎꯗꯅ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ ꯍꯦꯟꯅ ꯆꯥꯎꯕ ꯁꯔꯨꯛ ꯄꯨꯕ ꯌꯥꯏ, ꯑꯃꯁꯨꯡ ꯀꯦꯂꯤꯒꯤ ꯍꯦꯅꯒꯠꯄꯅ ꯃꯗꯨꯒꯤ ꯃꯃꯜ ꯄꯤꯏ꯫ Thorp (1984) ꯅ ꯈꯨꯗꯝ ꯑꯁꯤ ꯁꯤꯖꯤꯟꯅꯗꯨꯅ ꯄ꯭ꯔꯤꯗꯤꯛꯁꯟ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯀꯔꯤꯒꯤ ꯁꯦꯛꯇꯔꯆꯛꯔꯁꯦꯛꯇꯔꯆꯛꯔꯗ ꯃꯔꯛ ꯂꯩꯇꯅ ꯃꯈꯥ ꯆꯠꯅꯅ ꯂꯩꯕ ꯄꯣꯀꯦꯠꯁꯤꯡꯒꯤ ꯁꯔꯨꯛ, ꯂꯦꯑꯥꯎꯠꯇ ꯂꯩꯕ ꯀꯥꯡꯂꯨꯞ ꯑꯃꯗꯒꯤ ꯇꯣꯉꯥꯟꯅ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯗ ꯊꯝꯕꯒꯦ ꯍꯥꯌꯕ ꯇꯥꯛꯂꯤ꯫ ꯑꯁꯦꯡꯕꯗ ꯌꯨꯝꯂꯣꯟꯅꯕꯕꯦꯠꯌꯨꯝꯂꯣꯟꯅꯕ ꯕꯦꯠꯆꯛꯔꯗ ꯃꯁꯤꯡ ꯑꯃꯥ ꯑꯃꯁꯨꯡ ꯃꯗꯨꯒꯤ ꯅꯥꯀꯜ ꯑꯅꯤꯃꯛꯇ ꯂꯩꯕ ꯄꯣꯀꯦꯠ ꯑꯅꯤ ꯑꯅꯤ, ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ ꯆꯤꯞ ꯃꯉꯥ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯉꯥꯒꯤ ꯑꯦꯖ ꯑꯁꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯕ ꯃꯁꯤꯡ ꯑꯃꯈꯛꯀꯤꯗꯒꯤ ꯈꯔꯥ ꯍꯟꯊꯩ (ꯑꯦꯗꯚꯥꯟꯇꯦꯖ ꯄ꯭ꯂꯦ ꯌꯦꯡꯕꯤꯌꯨ)꯫
ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ 37 ꯗ 1 ꯒꯤ ꯃꯍꯨꯠꯇ 25 ꯗ ꯑꯃꯨꯛ 1 ꯊꯣꯛꯂꯤꯕ ꯌꯨꯝꯂꯣꯟꯅꯕ ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯅꯤ ꯊꯤꯗꯣꯛꯂꯦ꯫ ꯃꯈꯣꯌꯒꯤ ꯃꯔꯛꯀꯤ ꯁ꯭ꯞꯂꯤꯠꯕꯦꯠꯁ꯭ꯞꯂꯤꯠꯌꯨꯝꯂꯣꯟꯅꯕ ꯃꯁꯤꯡ ꯑꯅꯤ, 17:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨ 17 ꯗꯒꯤ 1 ꯗ ꯊꯝꯒꯗ꯭ꯔꯥ, ꯅꯠꯔꯒꯥ ꯃꯁꯤꯡ ꯈꯨꯗꯤꯡ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ ꯊꯝꯒꯗ꯭ꯔꯥ? ꯀꯦꯂꯤꯅ ꯀꯌꯥ ꯍꯥꯌꯔꯤ, ꯑꯃꯁꯨꯡ ꯃꯁꯤꯒꯨꯝꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯀꯥ ꯆꯥꯡꯗꯝꯂꯕꯗ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯁꯤ ꯀꯌꯥ ꯊꯨꯅ ꯍꯦꯅꯒꯠꯂꯀꯏ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯈꯦꯟꯅꯕ ꯂꯩꯇꯦ: ꯁ꯭ꯞꯂꯤꯠꯇ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ 2.59%, ꯅꯠꯔꯒꯥ ꯃꯁꯤꯡ ꯈꯨꯗꯤꯡꯗ 1.29%꯫ ꯃꯇꯝ ꯄꯨꯝꯕꯒꯤ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯁꯤ ꯁ꯭ꯄꯤꯟ 1,000 ꯗ ꯑꯃꯨꯛ 155 ꯈꯔ ꯍꯦꯅꯒꯠꯂꯀꯏ, ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯀꯥ ꯂꯣꯌꯅꯅ ꯑꯃꯨꯛ 11.5 ꯒꯥ ꯆꯥꯡꯗꯝꯂꯕꯗ꯫
ꯁ꯭ꯞꯂꯤꯠ ꯑꯁꯤ 2/25 = 0.08 ꯒꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯒꯥ ꯂꯣꯌꯅꯅ ꯃꯥꯏꯄꯥꯀꯏ ꯑꯃꯁꯨꯡ 17 ꯗꯒꯤ 1 ꯄꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯊꯝꯂꯕ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯈꯨꯗꯤꯡꯗ 18 × 0.08 = 1.44 ꯍꯜꯂꯛꯏ: 44% ꯒꯤ ꯑꯦꯖ, ꯕꯥꯏꯌꯥꯁ ꯂꯩꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯒꯥ ꯃꯥꯟꯅꯅ꯫ ꯀꯦꯂꯤꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯁꯤ ꯑꯦꯖꯕꯨ ꯑꯣꯗꯁꯅ ꯌꯦꯟꯊꯣꯀꯄꯅꯤ: 0.44/17 = 2.59%꯫
1.29% ꯒꯤ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ ꯕꯦꯠ ꯑꯅꯤꯅ ꯆꯨꯝꯅ ꯃꯍꯩ ꯑꯗꯨꯃꯛ ꯄꯤ꯫ ꯃꯁꯤꯡ ꯑꯃꯃꯛ ꯊꯣꯛꯂꯕꯗꯤ, ꯆꯤꯞꯁꯦꯜꯆꯤꯞꯂꯦꯞꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯃꯜ ꯇꯥꯛꯄ ꯇꯣꯀꯟ, ꯕꯦꯠ ꯊꯝꯅꯕ ꯂꯦꯑꯥꯎꯠꯇ ꯊꯝꯃꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯆꯦꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯅ 35 ꯗꯒꯤ 1 ꯃꯥꯏꯄꯥꯀꯏ ꯑꯃꯁꯨꯡ ꯑꯇꯣꯞꯄ ꯑꯗꯨ ꯃꯥꯡꯏ, ꯅꯦꯠ 34 × 1.29% = ꯕꯦꯡꯀꯔꯣꯜꯒꯤ 44%, ꯁ꯭ꯞꯂꯤꯠꯅ ꯄꯤꯕꯒꯨꯝꯅ; ꯀꯅꯥꯃꯛ ꯊꯣꯛꯇꯔꯕꯗꯤ ꯑꯅꯤꯃꯛ ꯃꯥꯡꯏ꯫
ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯒꯤ ꯍꯦꯅꯒꯠꯄ ꯑꯁꯤ 0.00505, ꯄꯣꯀꯦꯠ ꯑꯃꯒꯤ 0.00244 ꯒꯥ ꯆꯥꯡꯗꯝꯂꯕꯗ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯁ꯭ꯄꯤꯟ 1,000 ꯗ ꯃꯇꯝ ꯄꯨꯝꯕꯒꯤ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯁꯤ e^2.44 ≈ 11.5 ꯒꯤ ꯃꯍꯨꯠꯇ e^5.046 ≈ 155 ꯍꯦꯅꯒꯠꯂꯀꯏ꯫ ꯐꯕ ꯃꯁꯤꯡ ꯑꯅꯤꯒꯤ ꯃꯃꯜ ꯑꯃꯒꯤ ꯑꯃꯨꯛ ꯑꯅꯤꯗꯒꯤ ꯌꯥꯝꯅꯥ ꯍꯦꯟꯅ ꯂꯩ, ꯃꯔꯝ ꯑꯁꯤꯅ ꯕꯥꯏꯌꯥꯁ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯃꯁꯤꯡꯒꯤ ꯀꯥꯡꯂꯨꯞꯁꯤꯡꯗ ꯊꯝꯏ꯫ Thorp (1984) ꯅ ꯆꯥꯡꯗꯝꯅꯕ ꯑꯗꯨꯃꯛ ꯇꯧꯔꯤ꯫

ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

$ꯔꯨꯂꯦꯠꯇ ꯍꯦꯅꯒꯠꯄꯒꯤꯗꯃꯛ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯕ ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯁꯤ ꯃꯤ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯈꯉꯂꯦꯕ ꯃꯁꯤꯡ ꯑꯃꯅꯤ꯫$

ꯔꯨꯂꯦꯠꯇ ꯍꯦꯅꯒꯠꯄꯒꯤꯗꯃꯛ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯕ ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯁꯤ ꯃꯤ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯈꯉꯂꯦꯕ ꯃꯁꯤꯡ ꯑꯃꯅꯤ꯫

ꯍꯧꯔꯛꯐꯃꯁꯤꯡ

Kelly, J. L. “A new interpretation of information rate.” Bell System Technical Journal 35(4), 1956.
Breiman, L. “Optimal gambling systems for favorable games.” Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, 1961.
Thorp, E. O. “Optimal gambling systems for favorable games.” Review of the International Statistical Institute 37(3), 1969.
Thorp, E. O. The Mathematics of Gambling. Gambling Times / Lyle Stuart, 1984.
Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, 2013.
Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010꯫ ꯆꯦꯞꯇꯔ 13, ꯔꯨꯂꯦꯠ꯫
Haghani, V. & Dewey, R. “Rational decision-making under uncertainty: observed betting patterns on a biased coin.” ꯋꯔꯀꯤꯡ ꯄꯦꯄꯔ, ꯑꯛꯇꯣꯕꯔ 2016; SSRN 2856963, arXiv:1701.01427꯫

ꯌꯦꯡꯁꯤꯅꯈꯤꯕ 2026-09-28ꯃꯣꯗꯦꯜ: ꯌꯨꯔꯣꯄꯤꯌꯟ, ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣꯃꯦꯊꯗꯣꯂꯣꯖꯤ ↗ꯍꯧꯔꯛꯐꯃꯁꯤꯡ ↗