ꯕꯦꯡꯀꯔꯣꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕ

Q: ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ ꯑꯃꯅ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕ ꯍꯟꯊꯍꯅꯕꯔꯥ?

ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯅ ꯃꯇꯝ ꯀꯨꯞꯄ ꯁꯦꯁꯟꯁꯤꯡꯗ ꯍꯟꯊꯍꯜꯂꯤ ꯑꯃꯁꯨꯡ ꯃꯇꯝ ꯁꯥꯡꯕ ꯁꯦꯁꯟꯁꯤꯡꯗ ꯌꯥꯝꯅꯥ ꯋꯥꯡꯍꯜꯂꯤ꯫ ꯍꯦꯟꯅꯥ ꯆꯥꯎꯕ ꯌꯨꯅꯤꯠ ꯑꯃꯒꯥ ꯐ꯭ꯂꯦꯠ ꯕꯦꯇꯤꯡ ꯑꯁꯤ ꯃꯁꯤ ꯍꯟꯊꯍꯅꯕꯒꯤ ꯑꯆꯨꯝꯕ ꯂꯝꯕꯤꯅꯤ꯫

ꯄꯥꯟꯗꯝ ꯌꯧꯗ꯭ꯔꯤꯉꯩꯗ ꯕꯦꯡꯀꯔꯣꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ꯫

ꯊꯨꯅ ꯄꯥꯎꯈꯨꯝ

ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡꯗ ꯕꯦꯡꯀꯔꯣꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕ ꯑꯁꯤ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯃꯥꯡꯍꯟ ꯇꯥꯀꯍꯟꯕꯒꯤ ꯐꯣꯔꯃꯨꯂꯥꯒꯤ ꯃꯇꯨꯡ ꯏꯟꯅꯩ꯫ $500 ꯒꯤ ꯕꯦꯡꯀꯔꯣꯜ, $10 ꯒꯤ ꯕꯦꯠꯁꯤꯡ ꯑꯃꯁꯨꯡ $600 ꯒꯤ ꯄꯥꯟꯗꯝ ꯂꯩꯔꯕꯗ ꯅꯍꯥꯛꯅ ꯃꯇꯃꯒꯤ 57% ꯃꯔꯛꯇ ꯄꯥꯟꯗꯝ ꯌꯧꯏ ꯑꯃꯁꯨꯡ ꯑꯇꯣꯞꯄꯗ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯏ꯫

ꯐꯣꯔꯃꯨꯂꯥ

ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯃꯥꯡꯍꯟ ꯇꯥꯀꯍꯟꯕ

p (ꯆꯞ ꯃꯥꯟꯅꯕ)

18/37

q/p

1.0556

ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯑꯔꯤꯕ ꯃꯍꯩ

ꯄꯥꯁ꯭ꯀꯦꯜ–ꯐꯔꯃꯥ, 1656

ꯋꯥꯍꯪ

ꯅꯍꯥꯛꯀꯤ ꯕꯦꯡꯀꯔꯣꯜꯁꯦꯜꯕꯦꯡꯀꯔꯣꯜꯁꯥꯟꯅꯅꯕ ꯇꯣꯉꯥꯟꯅ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ꯫ ꯕꯦꯡꯀꯔꯣꯜ ꯃꯦꯅꯦꯖꯃꯦꯟꯠ ꯍꯥꯌꯕꯁꯤ ꯃꯗꯨꯒꯤ ꯀꯌꯥ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯁꯨꯡ ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡꯗ ꯈꯨꯗꯣꯡꯊꯤꯕꯗ ꯊꯃꯒꯗꯒꯦ ꯍꯥꯌꯕ ꯋꯥꯔꯦꯞ ꯂꯧꯕꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → a ꯂꯩ ꯑꯃꯁꯨꯡ ꯌꯨꯅꯤꯠ a + b ꯌꯧꯕ ꯄꯥꯝꯃꯤ, ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → p = 18/37 ꯑꯃꯁꯨꯡ ꯃꯥꯏꯊꯤꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ q = 19/37 ꯂꯩꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯕꯦꯠꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯑꯉꯥꯡꯕ/ꯑꯃꯨꯕ, ꯕꯤꯖꯣꯔ/ꯖꯣꯔ, ꯑꯋꯥꯡꯕ/ꯑꯅꯦꯝꯕ꯫ ꯃꯁꯤꯡ 18, 1:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗ ꯑꯃꯨꯛꯇ ꯌꯨꯅꯤꯠ ꯑꯃꯥ ꯊꯝꯗꯨꯅ꯫ ꯖꯤꯔꯣꯗ ꯌꯧꯗ꯭ꯔꯤꯉꯩꯗ ꯄꯥꯟꯗꯝ ꯌꯧꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯀꯌꯥꯅꯣ? ꯄꯥꯎꯈꯨꯝ ꯑꯁꯤ 1650 ꯒꯤ ꯆꯍꯤꯁꯤꯡꯗ ꯄꯥꯁ꯭ꯀꯦꯜ, ꯐꯔꯃꯥ ꯑꯃꯁꯨꯡ ꯍꯣꯏꯒꯦꯟꯁꯅ ꯊꯤꯈꯤ ꯑꯃꯁꯨꯡ ꯃꯁꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯒꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯑꯔꯤꯕ ꯃꯍꯩꯁꯤꯡꯒꯤ ꯃꯅꯨꯡꯗꯒꯤ ꯑꯃꯅꯤ꯫

ꯕ꯭ꯂꯦꯖ ꯄꯥꯁ꯭ꯀꯦꯜ: ꯔꯨꯂꯦꯠ ꯆꯛꯔꯒꯤ ꯋꯥꯔꯤ

ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯃꯥꯡꯍꯟ ꯇꯥꯀꯍꯟꯕꯒꯤ ꯐꯣꯔꯃꯨꯂꯥ

P(ꯄꯥꯟꯗꯝ ꯌꯧꯕ) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ)꯫ ꯕꯦꯡꯀꯔꯣꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯕꯦꯡꯀꯔꯣꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕꯄꯥꯟꯗꯝ ꯅꯠꯔꯒ ꯁ꯭ꯄꯤꯟꯒꯤ ꯃꯁꯤꯡ ꯌꯧꯗ꯭ꯔꯤꯉꯩꯗ ꯕꯦꯡꯀꯔꯣꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯑꯃꯗꯒꯤ ꯃꯗꯨ ꯂꯧꯊꯣꯛꯂꯕꯅꯤ꯫ q/p = 19/18 ≈ 1.0556 ꯑꯣꯏꯔꯕꯗ ꯆꯥꯡ ꯑꯁꯤ ꯌꯨꯅꯤꯠ ꯀꯌꯥ ꯂꯩꯕꯒꯤ ꯃꯇꯨꯡ ꯏꯟꯅꯥ ꯑꯦꯛꯁꯄꯣꯅꯦꯟꯁꯤꯌꯦꯜ ꯑꯣꯏꯅ ꯍꯦꯅꯒꯠꯂꯀꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯐꯣꯔꯃꯨꯂꯥꯅ ꯑꯄꯤꯀꯄ ꯌꯨꯅꯤꯠꯁꯤꯡꯕꯨ ꯀꯟꯅꯅ ꯆꯩꯔꯥꯛ ꯄꯤ: ꯄꯥꯟꯗꯝ ꯌꯧꯅꯕ ꯕꯦꯠ ꯍꯦꯟꯅꯥ ꯃꯊꯧ ꯇꯥꯕꯥ ꯃꯇꯃꯗ ꯂꯝꯕꯤꯗ 2.70% ꯒꯤ ꯂꯧꯁꯦꯜ ꯑꯗꯨ ꯍꯦꯟꯅꯥ ꯀꯌꯥ ꯄꯤꯒꯗꯕꯅꯤ꯫

ꯕꯦꯡꯀꯔꯣꯜꯌꯨꯅꯤꯠꯄꯥꯟꯗꯝꯄꯥꯟꯗꯝ ꯐꯥꯑꯣꯕ ꯕꯦꯠꯁꯤꯡp(ꯄꯥꯟꯗꯝ ꯌꯧꯕ)ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕ

$500$10$60010≈ 57%≈ 43%

$500$50$6002≈ 79%≈ 21%

$500$10$1,00050≈ 6%≈ 94%

$500$100$1,0005≈ 43%≈ 57%

$500$500$1,000148.6%51.4%

$100$10$20010≈ 37%≈ 63%

ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡ, ꯍꯣꯡꯗꯕ ꯊꯝꯂꯕ ꯁꯦꯜ, ꯂꯥ ꯄꯥꯔꯇꯥꯖ ꯌꯥꯎꯗꯅ꯫ “ꯕꯦꯡꯀꯔꯣꯜ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕ ꯀꯦꯜꯀꯨꯂꯦꯇꯔ” ꯅ ꯀꯔꯤꯒꯨꯝꯕ ꯃꯁꯤꯡꯒꯤꯗꯃꯛ ꯊꯤꯖꯤꯟꯕ ꯑꯗꯨ ꯇꯧꯏ꯫

ꯄꯥꯕ

ꯑꯄꯤꯀꯄ ꯌꯨꯅꯤꯠꯁꯤꯡꯅ ꯑꯁꯣꯛ ꯑꯄꯟ ꯄꯤ꯫ $10 ꯒꯤ ꯕꯦꯠꯁꯤꯡꯅ $500 ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯟꯕ ꯍꯣꯠꯅꯕ ꯑꯁꯤ ꯃꯇꯃꯒꯤ 6% ꯗ ꯃꯥꯏꯄꯥꯛꯏ; $500 ꯒꯤ ꯕꯦꯠ ꯑꯃꯈꯛꯅ ꯃꯇꯃꯒꯤ 48.6% ꯗ ꯃꯥꯏꯄꯥꯛꯏ꯫ ꯊꯧꯅꯥ ꯂꯩꯕ ꯁꯥꯟꯅꯕ, ꯍꯦꯟꯅꯥ ꯌꯥꯝꯅꯥ ꯅꯠꯇꯕ ꯑꯗꯨꯕꯨ ꯍꯦꯟꯅꯥ ꯆꯥꯎꯕ ꯕꯦꯠꯁꯤꯡ, ꯑꯁꯤꯅ ꯅꯦꯒꯦꯇꯤꯕ ꯐꯪꯒꯗꯕ ꯂꯩꯕ ꯁꯥꯟꯅꯕ ꯑꯃꯗ ꯄꯥꯟꯗꯝ ꯌꯧꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯍꯜꯂꯤ, ꯃꯔꯃꯗꯤ ꯃꯁꯤꯅ ꯑꯦꯖ ꯆꯠꯂꯤꯕ ꯃꯇꯝ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯍꯟꯊꯍꯜꯂꯤ꯫ ꯃꯁꯤꯅ ꯅꯍꯥꯛꯇ ꯊꯣꯛꯀꯗꯕꯒꯤ ꯚꯦꯌꯔꯤꯌꯦꯟꯁꯃꯦꯊꯃꯦꯇꯤꯛꯁꯚꯦꯌꯔꯤꯌꯦꯟꯁꯃꯍꯩꯁꯤꯡ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯒꯤ ꯑꯀꯣꯌꯕꯗ ꯀꯌꯥ ꯁꯟꯗꯣꯛꯅ ꯂꯩꯕꯒꯦ ꯍꯥꯌꯕꯒꯤ ꯆꯥꯡ꯫ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯇ ꯋꯥꯡꯏ, ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡꯗ ꯅꯦꯝꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯁꯨ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯍꯜꯂꯤ, ꯑꯃꯁꯨꯡ ꯅꯨꯃꯤꯗꯥꯡ ꯑꯗꯨ ꯊꯨꯅ ꯂꯣꯏꯍꯜꯂꯤ꯫ ꯊꯤꯑꯣꯔꯦꯝ ꯑꯁꯤꯕꯨ “ꯊꯧꯅꯥ ꯂꯩꯕ ꯁꯥꯟꯅꯕ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯩ” ꯍꯥꯌꯅ ꯀꯧꯏ ꯑꯃꯁꯨꯡ ꯃꯁꯤ 1965 ꯗ ꯗꯨꯕꯤꯟꯁ ꯑꯃꯁꯨꯡ ꯁꯦꯚꯦꯖꯅ ꯄ꯭ꯔꯨꯐ ꯇꯧꯈꯤ꯫

ꯑꯉꯥꯡꯕꯗ $500 ꯕꯨ $1,000 ꯑꯣꯏꯍꯅꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ%

$500 ꯒꯤ ꯕꯦꯠ ꯑꯃꯈꯛ

48.6%

$100 ꯒꯤ ꯕꯦꯠꯁꯤꯡ

≈ 43%

$50 ꯒꯤ ꯕꯦꯠꯁꯤꯡ

≈ 37%

$20 ꯒꯤ ꯕꯦꯠꯁꯤꯡ

≈ 21%

$10 ꯒꯤ ꯕꯦꯠꯁꯤꯡ

≈ 6%

$5 ꯒꯤ ꯕꯦꯠꯁꯤꯡ

≈ 0.5%

024.3048.6%

ꯕꯦꯠ ꯍꯦꯟꯅꯥ ꯃꯊꯧ ꯇꯥꯕꯥ ꯃꯇꯃꯗ ꯑꯦꯖ ꯍꯦꯟꯅꯥ ꯀꯌꯥ ꯄꯤꯒꯗꯕꯅꯤ꯫ ꯀꯤꯅꯥ ꯁꯥꯟꯅꯕ ꯑꯁꯤ ꯃꯃꯜ ꯌꯥꯝꯅꯥ ꯋꯥꯡꯏ꯫

ꯁꯃꯁ꯭ꯌꯥ ꯑꯁꯤ ꯀꯗꯥꯏꯗꯒꯤ ꯍꯧꯈꯤꯕꯒꯦ

ꯋꯥꯍꯪ ꯑꯁꯤ ꯔꯨꯂꯦꯠꯇꯒꯤ ꯍꯦꯟꯅꯥ ꯑꯔꯤꯕꯅꯤ꯫ 1656 ꯗ ꯄꯥꯁ꯭ꯀꯦꯂꯅ ꯐꯔꯃꯥꯗ ꯄꯖꯜ ꯑꯃꯥ ꯄꯤꯈꯤ: ꯁꯥꯟꯅꯔꯤꯕ ꯑꯅꯤꯅ ꯗꯥꯏꯁ ꯑꯍꯨꯝ ꯊꯥꯗꯣꯀꯏ, ꯑꯃꯃꯃꯅ ꯀꯥꯎꯟꯇꯔ 12 ꯂꯧꯗꯨꯅ ꯍꯧꯏ; 11 ꯊꯥꯗꯣꯛꯂꯕꯗ ꯀꯥꯎꯟꯇꯔ ꯑꯃꯥ ꯃꯥꯏꯀꯩ ꯑꯃꯗ ꯆꯠꯂꯤ, 14 ꯊꯥꯗꯣꯛꯂꯕꯗ ꯑꯇꯣꯞꯄ ꯃꯥꯏꯀꯩꯗ꯫ ꯑꯅꯤꯃꯛꯅ ꯃꯁꯤ ꯊꯤꯖꯤꯅꯈꯤ, ꯑꯃꯁꯨꯡ ꯃꯦꯊꯃꯦꯇꯤꯁꯤꯌꯥꯟ ꯄꯤꯌꯦꯔ ꯗꯦ ꯀꯥꯔꯀꯥꯚꯤꯒꯤ ꯆꯤꯊꯤ ꯑꯃꯗꯒꯤ ꯃꯁꯤꯒꯤ ꯃꯇꯥꯡꯗ ꯇꯥꯈꯤꯕ ꯍꯣꯏꯒꯦꯟꯁꯅ 1657 ꯗ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯒꯤ ꯃꯇꯥꯡꯗ ꯑꯍꯥꯅꯕ ꯂꯥꯏꯔꯤꯛꯀꯤ ꯃꯉꯥꯁꯨꯕ ꯁꯃꯁ꯭ꯌꯥ ꯑꯣꯏꯅ ꯃꯁꯤ ꯄꯥꯎꯈꯨꯝꯒꯥ ꯂꯣꯌꯅꯅ, ꯄ꯭ꯔꯨꯐ ꯌꯥꯎꯗꯅ ꯐꯣꯡꯗꯣꯀꯈꯤ꯫ ꯇꯔꯥꯃꯥꯊꯣꯏ ꯑꯁꯤ ꯂꯝꯕꯤ 27 ꯗ ꯊꯥꯗꯣꯛꯄ ꯌꯥꯏ ꯑꯃꯁꯨꯡ ꯇꯔꯥꯃꯔꯤ 15 ꯈꯛꯇꯗ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯀꯥꯎꯟꯇꯔ ꯈꯨꯗꯤꯡꯃꯛ 14 ꯗꯒꯤ 9 ꯒꯤ ꯃꯇꯃꯗ ꯑꯍꯥꯅꯕ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯃꯥꯏꯀꯩꯗ ꯆꯠꯂꯤ, ꯑꯃꯁꯨꯡ ꯃꯊꯛꯇ ꯂꯩꯕ ꯐꯣꯔꯃꯨꯂꯥꯅ, ꯑꯃꯃꯃꯗ ꯀꯥꯎꯟꯇꯔ 12 ꯂꯩꯔꯕꯗ, ꯃꯍꯥꯛꯅ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯗꯒꯤ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯃꯨꯛ 1,157 ꯃꯔꯛ ꯍꯦꯟꯍꯜꯂꯤ꯫ 2.70% ꯒꯤ ꯑꯦꯖ ꯑꯃꯥ ꯌꯥꯝꯅꯥ ꯑꯄꯤꯀꯄꯅꯤ, ꯑꯗꯨꯕꯨ ꯐꯣꯔꯃꯨꯂꯥ ꯑꯗꯨꯃꯛꯅ ꯃꯁꯤꯅ ꯕꯦꯠ ꯀꯌꯥꯗ ꯀꯔꯤ ꯇꯧꯕꯒꯦ ꯍꯥꯌꯕ ꯎꯠꯂꯤ꯫

ꯄꯥꯁ꯭ꯀꯦꯂꯒꯤ ꯄꯖꯂꯗ ꯗꯥꯏꯁ ꯑꯍꯨꯝ ꯊꯥꯗꯣꯀꯄ ꯈꯨꯗꯤꯡꯅ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯒꯤ ꯃꯔꯛꯇ ꯀꯥꯎꯟꯇꯔ ꯑꯃꯥ ꯆꯠꯍꯜꯂꯤ꯫

ꯑꯁꯦꯡꯕ ꯊꯧꯅꯥ ꯂꯩꯕ ꯕꯦꯠ ꯑꯃꯥ

2004 ꯒꯤ ꯑꯦꯞꯔꯤꯂꯗ ꯅꯍꯥ ꯑꯣꯏꯔꯤꯕ ꯏꯉ꯭ꯂꯤꯁ ꯃꯤꯑꯣꯏ ꯑꯦꯁ꯭ꯂꯤ ꯔꯦꯚꯦꯜ (Ashley Revell) ꯅ ꯃꯍꯥꯛꯀꯤ ꯐꯤꯔꯣꯜ ꯌꯥꯎꯅ ꯂꯩꯔꯤꯕ ꯄꯨꯝꯅꯃꯛ ꯃꯔꯛ ꯌꯣꯟꯊꯣꯀꯈꯤ ꯑꯃꯁꯨꯡ $135,300 ꯂꯥꯁ ꯚꯦꯒꯥꯁꯀꯤ ꯄ꯭ꯂꯥꯖꯥꯗ ꯄꯨꯈꯤ꯫ ꯑꯄꯤꯀꯄ ꯕꯦꯠ ꯈꯔꯒꯤ ꯃꯇꯨꯡꯗ ꯃꯍꯥꯛꯅ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ ꯑꯉꯥꯡꯕꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯗ ꯑꯃꯨꯛ ꯊꯝꯈꯤ꯫ ꯕꯣꯜꯈꯨꯠꯂꯥꯏꯕꯣꯜꯔꯣꯇꯔꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯇ꯭ꯔꯦꯛꯇ ꯊꯥꯗꯣꯛꯄ ꯑꯄꯤꯛꯄ ꯕꯣꯜ꯫ ꯍꯧꯖꯤꯛꯀꯤ ꯕꯣꯜꯁꯤꯡ ꯑꯥꯏꯚꯣꯔꯤꯟ ꯅꯠꯔꯒ ꯇꯦꯐ꯭ꯂꯣꯅꯅ ꯁꯦꯝꯃꯤ, 18–21 mm꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨ ꯑꯉꯥꯡꯕ 7 ꯗ ꯂꯥꯀꯈꯤ ꯑꯃꯁꯨꯡ ꯃꯍꯥꯛ $270,600 ꯂꯧꯗꯨꯅ ꯊꯣꯔꯀꯈꯤ꯫ ꯗꯕꯜ-ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯆꯛꯔ ꯑꯃꯗ ꯁ꯭ꯄꯤꯟ ꯑꯗꯨ 47.37% ꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯅꯤ ꯑꯃꯁꯨꯡ ꯑꯦꯚꯔꯦꯖꯗ $7,121 ꯃꯥꯡꯍꯜꯂꯤ, ꯕꯦꯠ ꯑꯃꯒꯤ 5.26% ꯑꯦꯖ꯫ $10 ꯒꯤ ꯕꯦꯠꯁꯤꯡꯗ ꯁꯟꯗꯣꯛꯂꯕꯗꯤ ꯄꯥꯟꯗꯝ ꯑꯗꯨꯃꯛ ꯌꯥꯝꯅꯥ ꯑꯥꯁꯥ ꯂꯩꯇꯕꯒꯤ ꯃꯅꯥꯛꯇ ꯂꯩꯒꯅꯤ꯫ ꯊꯧꯅꯥ ꯂꯩꯕ ꯁꯥꯟꯅꯕꯅ ꯕꯦꯠ ꯑꯗꯨ ꯐꯕ ꯑꯣꯏꯍꯟꯗꯦ; ꯃꯁꯤꯅ ꯃꯗꯨ ꯌꯥꯕꯃꯛ ꯊꯨꯅ ꯂꯣꯏꯍꯜꯂꯤ꯫

ꯑꯦꯁ꯭ꯂꯤ ꯔꯦꯚꯦꯂꯒꯤ ꯕꯦꯡꯀꯔꯣꯜ ꯄꯨꯝꯅꯃꯛ ꯗꯕꯜ-ꯖꯤꯔꯣ ꯆꯛꯔꯒꯤ ꯁ꯭ꯄꯤꯟ ꯑꯃꯈꯛꯇ ꯂꯩꯔꯤ꯫

ꯄꯥꯟꯗꯝ ꯌꯥꯎꯗꯕ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕ

ꯅꯍꯥꯛꯅ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕ ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ ꯁ꯭ꯄꯤꯟ N ꯒꯤ ꯃꯇꯨꯡꯗ ꯂꯦꯞꯄ ꯐꯥꯑꯣꯕ ꯁꯥꯟꯅꯔꯕꯗ ꯋꯥꯍꯪ ꯑꯗꯨ “ꯁ꯭ꯄꯤꯟ N ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯩꯒꯤ ꯕꯦꯡꯀꯔꯣꯜ ꯖꯤꯔꯣꯗ ꯌꯧꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯀꯌꯥꯅꯣ?” ꯑꯣꯏꯔꯛꯏ꯫ ꯃꯍꯧꯁꯥꯒꯤ N ꯒꯤꯗꯃꯛ ꯂꯣꯏꯁꯤꯜꯂꯕ ꯐꯣꯔꯃꯨꯂꯥ ꯑꯃꯠꯇ ꯂꯩꯇꯦ ꯑꯗꯨꯕꯨ ꯋꯦꯕꯁꯥꯏꯠ ꯑꯁꯤꯒꯤ ꯁꯤꯃꯨꯂꯦꯇꯔꯁꯤꯡꯅ ꯃꯁꯤ ꯊꯤꯖꯤꯜꯂꯤ: ꯑꯉꯥꯡꯕꯗ $10 ꯊꯝꯕ $500 ꯒꯤ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯃꯥ ꯁ꯭ꯄꯤꯟ 100 ꯗ ꯌꯥꯝꯅꯥ ꯈꯔꯥ ꯈꯛꯇꯗ ꯃꯥꯡꯏ (1% ꯗꯒꯤ ꯅꯦꯝꯅ), ꯁ꯭ꯄꯤꯟ 500 ꯗ ꯃꯇꯃꯒꯤ 9% ꯃꯔꯛ ꯃꯥꯡꯏ, ꯑꯃꯁꯨꯡ 5,000 ꯗ 95% ꯃꯔꯛ꯫ ꯂꯦꯞꯄꯒꯤ ꯅꯤꯌꯝ ꯑꯃꯠꯇ ꯂꯩꯇꯔꯕꯗ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯁꯤ 100% ꯗ ꯅꯛꯂꯛꯏ, ꯃꯁꯤ ꯍꯥꯎꯁ ꯑꯦꯖꯃꯦꯊꯃꯦꯇꯤꯛꯁꯍꯥꯎꯁ ꯑꯦꯖꯊꯝꯂꯕ ꯁꯦꯜ ꯈꯨꯗꯤꯡꯗꯒꯤ ꯀꯦꯁꯤꯅꯣꯅ ꯑꯦꯚꯔꯦꯖꯗ ꯊꯃꯖꯤꯜꯂꯤꯕ ꯁꯔꯨꯛ: ꯌꯨꯔꯣꯄꯤꯌꯟ ꯔꯨꯂꯦꯠꯇ 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯀꯤ ꯃꯇꯝ ꯁꯥꯡꯕꯒꯤ ꯃꯈꯂꯅꯤ꯫

ꯁꯦꯁꯟ ꯇꯔꯥ, $500 ꯒꯤ ꯕꯦꯡꯀꯔꯣꯜ, ꯑꯉꯥꯡꯕꯗ $25, ꯁ꯭ꯄꯤꯟ 200ꯍꯧꯔꯛꯐꯃꯒꯥ ꯆꯥꯡꯗꯝꯅꯕ ꯃꯍꯩ

ꯁꯦꯁꯟ 1,000 × ꯁ꯭ꯄꯤꯟ 500 · ꯃꯆꯨ ꯑꯃꯨ-ꯂꯩꯃꯜ p10/p25/p75/p90, ꯑꯉꯧ-ꯑꯁꯪꯕ ꯃꯤꯗꯤꯌꯥꯟ, ꯃꯌꯥꯏꯕ ꯈꯨꯗꯝ 81 · ꯁ꯭ꯄꯤꯟ ꯑꯃꯗ ꯀ꯭ꯕꯥꯟꯇꯥꯏꯜ ꯎꯅꯕ ꯆꯥꯔꯠꯀꯤ ꯃꯊꯛꯇ ꯃꯧꯁ ꯆꯠꯍꯅꯕꯤꯌꯨ

p10 −$500
p25 −$500
ꯃꯤꯗꯤꯌꯥꯟ −$500
p75 +$0
p90 +$350

ꯁꯦꯁꯟ 1,000 × ꯁ꯭ꯄꯤꯟ 500 · y-ꯑꯦꯛꯁꯤꯁ 1ꯁꯨꯕ–99ꯁꯨꯕ ꯄꯔꯁꯦꯟꯇꯥꯏꯜ ꯐꯥꯑꯣꯕꯥ ꯀꯛꯊꯠꯂꯤ (ꯑꯔꯣꯏꯕ ꯃꯁꯤꯡ −$500ꯗꯒꯤ +$1,500ꯐꯥꯑꯣꯕꯥ) · ꯁ꯭ꯄꯤꯟ 500 · ꯍꯧꯔꯛꯐꯝ $25 · ꯆꯞ ꯃꯥꯟꯅꯕ

ꯃꯈꯥꯗ ꯁꯣꯛꯂꯕ ꯂꯥꯏꯅꯁꯤꯡꯅ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯈ꯭ꯔꯦ꯫ ꯑꯄꯤꯀꯄ ꯌꯨꯅꯤꯠ ꯑꯃꯒꯥ ꯂꯣꯌꯅꯅ ꯃꯈꯣꯌ ꯍꯦꯟꯅꯥ ꯁꯥꯡꯅ ꯂꯩꯒꯅꯤ ꯑꯃꯁꯨꯡ ꯃꯐꯝ ꯑꯗꯨꯃꯛꯇ ꯂꯣꯏꯒꯅꯤ꯫

ꯃꯇꯝ ꯁꯥꯡꯅ ꯅꯛꯅꯕ: ꯔꯨꯂꯦꯠꯇ ꯑꯆꯧꯕ ꯃꯁꯤꯡꯒꯤ ꯅꯤꯌꯝ

ꯀꯌꯥ ꯁꯥꯡꯅ, ꯑꯃꯁꯨꯡ ꯀꯌꯥ ꯃꯥꯡꯖꯩꯅ

ꯑꯔꯤꯕ ꯃꯍꯩ ꯑꯅꯤꯅ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯇꯁꯦꯡꯅ ꯍꯪꯂꯤꯕ ꯋꯥꯍꯪꯁꯤꯡꯒꯤ ꯄꯥꯎꯈꯨꯝ ꯄꯤ꯫ ꯄꯥꯟꯗꯝ ꯌꯥꯎꯗꯅ, ꯍꯣꯡꯗꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡꯅ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯆꯛꯔꯗ ꯕꯦꯡꯀꯔꯣꯜꯒꯤ ꯌꯨꯅꯤꯠ ꯈꯨꯗꯤꯡꯗ ꯑꯦꯚꯔꯦꯖꯗ ꯁ꯭ꯄꯤꯟ 37 ꯑꯃꯁꯨꯡ ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔꯗ 19 ꯂꯦꯡꯏ, ꯃꯔꯃꯗꯤ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯅ ꯑꯦꯚꯔꯦꯖꯗ ꯌꯨꯅꯤꯠꯀꯤ 1/37 ꯂꯧꯏ (ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔꯗ 1/19): ꯌꯨꯅꯤꯠ 100 ꯅ ꯑꯦꯚꯔꯦꯖꯗ ꯁ꯭ꯄꯤꯟ 3,700 ꯂꯦꯡꯏ, ꯑꯗꯨꯕꯨ ꯑꯁꯤꯒꯨꯝꯕ ꯁꯦꯁꯟꯁꯤꯡꯒꯤ ꯁꯔꯨꯛ ꯑꯍꯦꯟꯕ 3,134 ꯒꯤ ꯃꯅꯨꯡꯗ ꯂꯣꯏꯏ (“ꯁꯦꯁꯟꯒꯤ ꯃꯇꯝ ꯑꯃꯁꯨꯡ ꯃꯃꯜ” ꯌꯦꯡꯕꯤꯌꯨ)꯫ ꯑꯃꯁꯨꯡ ꯕꯦꯡꯀꯔꯣꯜ ꯀꯌꯥ ꯆꯥꯎꯔꯕꯁꯨ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯆꯛꯔꯗ ꯀꯩꯗꯧꯉꯩꯗꯃꯛ ꯌꯨꯅꯤꯠ k ꯃꯥꯡꯖꯩꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ (18/19)ᵏ ꯅꯤ꯫ ꯃꯁꯤ ꯌꯨꯅꯤꯠ ꯑꯃꯒꯤꯗꯃꯛ 95% ꯑꯃꯁꯨꯡ ꯇꯔꯥꯒꯤꯗꯃꯛ 58% ꯅꯤ, ꯑꯗꯨꯕꯨ ꯀꯌꯥ ꯂꯨꯔꯕꯁꯨ ꯀꯔꯤꯒꯨꯝꯕ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯃꯠꯇꯅ ꯌꯨꯅꯤꯠ 13 ꯃꯥꯡꯖꯩꯕꯒꯤ ꯆꯞ ꯃꯥꯟꯅꯕ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯄꯤꯗꯦ; ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔꯗ ꯈꯨꯗꯣꯡꯆꯥꯕ (9/10)ᵏ ꯅꯤ ꯑꯃꯁꯨꯡ ꯌꯨꯅꯤꯠ 7 ꯗ ꯁꯔꯨꯛ ꯑꯍꯦꯟꯕꯗꯒꯤ ꯅꯦꯝꯅ ꯍꯟꯊꯔꯛꯏ꯫

ꯀꯔꯤꯒꯨꯝꯕ ꯃꯇꯝ ꯑꯃꯗ ꯃꯥꯡꯖꯩꯕ ꯌꯨꯅꯤꯠꯌꯨꯔꯣꯄꯤꯌꯟꯑꯃꯦꯔꯤꯀꯟ

194.7%90.0%

576.3%59.0%

1058.2%34.9%

1349.5%25.4%

2033.9%12.2%

506.7%0.5%

1000.45%0.003%

ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡ, ꯍꯣꯡꯗꯕ ꯊꯝꯂꯕ ꯁꯦꯜ, ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯂꯣꯏꯗꯕ ꯆꯥꯎꯕ ꯕꯦꯡꯀꯔꯣꯜ꯫ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯁꯤ ꯁꯤꯡꯒꯜ-ꯖꯤꯔꯣ ꯆꯛꯔꯗ (18/19)ᵏ ꯑꯃꯁꯨꯡ ꯗꯕꯜ-ꯖꯤꯔꯣ ꯆꯛꯔꯗ (9/10)ᵏ ꯅꯤ꯫

ꯁꯦꯁꯟꯒꯤ ꯃꯇꯝ ꯑꯃꯁꯨꯡ ꯃꯃꯜ ꯑꯃꯦꯔꯤꯀꯟ ꯔꯨꯂꯦꯠ ꯆꯛꯔ ꯑꯃꯁꯨꯡ ꯅꯤꯌꯝꯁꯤꯡ

ꯆꯞ ꯃꯥꯟꯅꯕ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯃꯒꯤꯗꯃꯛ ꯕꯦꯡꯀꯔꯣꯜ

ꯋꯥꯍꯪ ꯑꯗꯨ ꯑꯣꯟꯊꯣꯛꯄꯤꯌꯨ: ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯗ꯭ꯔꯤꯉꯩꯗ ꯂꯦꯞꯂꯕ ꯁꯦꯜ ꯑꯃꯥ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯌꯥꯃꯗ꯭ꯔꯕꯗ ꯆꯞ ꯃꯥꯟꯅꯕ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯐꯪꯅꯕ ꯀꯌꯥ ꯄꯨꯔꯛꯀꯗꯒꯦ? ꯑꯄꯤꯀꯄ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯒꯤꯗꯃꯛ ꯌꯥꯝꯅꯥ ꯃꯊꯧ ꯇꯥꯗꯦ꯫ ꯍꯦꯟꯅꯥ ꯆꯥꯎꯕ ꯑꯃꯒꯤꯗꯃꯛ ꯃꯊꯧ ꯇꯥꯕ ꯕꯦꯡꯀꯔꯣꯜ ꯌꯥꯝꯅꯥ ꯊꯨꯅ ꯍꯦꯅꯒꯠꯂꯀꯏ, ꯑꯃꯁꯨꯡ ꯃꯐꯝ ꯑꯃꯗꯒꯤ ꯃꯇꯨꯡꯗ ꯀꯔꯤꯒꯨꯝꯕ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯃꯠꯇ ꯃꯇꯤꯛ ꯆꯥꯗꯦ, ꯃꯔꯃꯗꯤ ꯂꯣꯏꯕ ꯅꯥꯏꯗꯕ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯃꯅꯁꯨ ꯃꯐꯝ ꯑꯗꯨ ꯐꯥꯑꯣꯕ ꯃꯥꯡꯖꯩꯕꯒꯤ ꯆꯞ ꯃꯥꯟꯅꯕ ꯈꯨꯗꯣꯡꯆꯥꯕꯗꯒꯤ ꯅꯦꯝꯅ ꯄꯤ꯫ ꯇꯦꯂꯔ (2021) ꯅ ꯃꯁꯤ ꯑꯇꯣꯞꯄ ꯃꯑꯣꯡꯗ ꯍꯥꯌꯔꯤ: ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔꯗ ꯌꯨꯅꯤꯠ 100 ꯌꯧꯕꯒꯤ ꯆꯞ ꯃꯥꯟꯅꯕ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯐꯪꯅꯕ ꯅꯍꯥꯛꯅ 94 ꯗꯒꯤ ꯍꯧꯒꯗꯕꯅꯤ, 6 ꯃꯥꯏꯄꯥꯛꯅꯕ 94 ꯈꯨꯗꯣꯡꯊꯤꯕꯗ ꯊꯃꯗꯨꯅ꯫ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯆꯛꯔꯗ 88 ꯃꯊꯧ ꯇꯥꯒꯅꯤ꯫

ꯃꯥꯏꯄꯥꯛꯅꯕꯌꯨꯔꯣꯄꯤꯌꯟꯑꯃꯦꯔꯤꯀꯟ

ꯌꯨꯅꯤꯠ 122

ꯌꯨꯅꯤꯠ 233

ꯌꯨꯅꯤꯠ 345

ꯌꯨꯅꯤꯠ 468

ꯌꯨꯅꯤꯠ 5712

ꯌꯨꯅꯤꯠ 6921

ꯌꯨꯅꯤꯠ 712ꯀꯔꯤꯒꯨꯝꯕ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯃꯠꯇ ꯃꯇꯤꯛ ꯆꯥꯗꯦ

ꯌꯨꯅꯤꯠ 815ꯀꯔꯤꯒꯨꯝꯕ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯃꯠꯇ ꯃꯇꯤꯛ ꯆꯥꯗꯦ

ꯌꯨꯅꯤꯠ 1024ꯀꯔꯤꯒꯨꯝꯕ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯃꯠꯇ ꯃꯇꯤꯛ ꯆꯥꯗꯦ

ꯌꯨꯅꯤꯠ 1246ꯀꯔꯤꯒꯨꯝꯕ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯃꯠꯇ ꯃꯇꯤꯛ ꯆꯥꯗꯦ

ꯌꯨꯅꯤꯠ 13 ꯅꯠꯔꯒ ꯍꯦꯟꯅꯥꯀꯔꯤꯒꯨꯝꯕ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯃꯠꯇ ꯃꯇꯤꯛ ꯆꯥꯗꯦꯀꯔꯤꯒꯨꯝꯕ ꯕꯦꯡꯀꯔꯣꯜ ꯑꯃꯠꯇ ꯃꯇꯤꯛ ꯆꯥꯗꯦ

ꯍꯣꯡꯗꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡꯒꯥ ꯂꯣꯌꯅꯅ, ꯕꯦꯡꯀꯔꯣꯜ ꯃꯥꯡꯗ꯭ꯔꯤꯉꯩꯗ ꯁꯦꯜ ꯑꯗꯨ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯌꯥꯃꯗ꯭ꯔꯕꯗ ꯆꯞ ꯃꯥꯟꯅꯕ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯄꯤꯕ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯑꯄꯤꯀꯄ ꯕꯦꯡꯀꯔꯣꯜ, ꯌꯨꯅꯤꯠꯇ꯫ ꯃꯊꯛꯇ ꯂꯩꯕ ꯐꯣꯔꯃꯨꯂꯥꯗꯒꯤ ꯑꯩꯈꯣꯌꯅ ꯊꯤꯖꯤꯜꯂꯕꯅꯤ꯫

ꯊꯕꯛꯇ ꯁꯤꯖꯤꯟꯅꯕ ꯇꯃꯖꯕ

ꯅꯍꯥꯛꯅ ꯀꯔꯤ ꯇꯧꯕ ꯍꯣꯠꯅꯔꯤꯕꯒꯦ ꯂꯦꯞꯄꯤꯌꯨ꯫ ꯄꯥꯟꯗꯝ ꯑꯗꯨ ꯑꯀꯛꯅꯕ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯥ ꯑꯣꯏꯔꯕꯗ ꯆꯥꯎꯅ ꯑꯃꯁꯨꯡ ꯈꯔꯥ ꯈꯛꯇ ꯊꯝꯕꯤꯌꯨ꯫ ꯄꯥꯟꯗꯝ ꯑꯗꯨ ꯁꯥꯡꯕ ꯅꯨꯃꯤꯗꯥꯡ ꯑꯃꯥ ꯑꯣꯏꯔꯕꯗ ꯑꯄꯤꯀꯄ ꯊꯝꯕꯤꯌꯨ ꯑꯃꯁꯨꯡ ꯑꯦꯖꯅ ꯑꯆꯧꯕ ꯇꯔꯅꯑꯣꯚꯔꯁꯦꯜꯇꯔꯅꯑꯣꯚꯔꯁꯦꯁꯟ ꯅꯠꯔꯒ ꯃꯇꯝ ꯑꯃꯒꯤ ꯃꯅꯨꯡꯗ ꯕꯦꯠ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ, ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯝꯂꯕ ꯃꯥꯏꯄꯥꯛꯇꯨꯅ ꯐꯪꯂꯕ ꯁꯦꯜꯁꯨ ꯌꯥꯎꯅ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯍꯦꯟꯗꯜ, ꯑꯦꯛꯁꯟ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯒꯤ 2.70% ꯂꯧꯒꯅꯤ ꯍꯥꯌꯕ ꯌꯥꯕꯤꯌꯨ꯫ ꯄꯥꯟꯗꯝ ꯑꯗꯨ ꯑꯅꯤꯃꯛ ꯑꯣꯏꯔꯕꯗ ꯑꯃꯅ ꯊꯥꯗꯣꯛꯀꯗꯕꯅꯤ, ꯑꯃꯁꯨꯡ ꯌꯥꯝꯅꯥ ꯃꯇꯝꯗ ꯃꯗꯨ ꯄꯥꯟꯗꯝ ꯑꯗꯨꯅꯤ꯫

ꯐꯣꯔꯃꯨꯂꯥ

P(ꯄꯥꯟꯗꯝ) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ)

ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕ = 1 − P(ꯄꯥꯟꯗꯝ)

ꯆꯞ ꯃꯥꯟꯅꯕꯒꯤꯗꯃꯛ q/p = 19/18

ꯄꯥꯟꯗꯝ ꯌꯥꯎꯗꯅ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕ ꯐꯥꯑꯣꯕꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯁ꯭ꯄꯤꯟ = 37 × ꯌꯨꯅꯤꯠ

P(ꯀꯩꯗꯧꯉꯩꯗꯃꯛ ꯌꯨꯅꯤꯠ k ꯃꯥꯡꯖꯩꯕ) = (18/19)ᵏ

ꯋꯥꯍꯪꯁꯤꯡ

ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ ꯑꯃꯅ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯊꯤꯕ ꯍꯟꯊꯍꯅꯕꯔꯥ?

ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯅꯊꯧꯔꯥꯡꯃꯥꯔꯇꯤꯟꯒꯦꯜꯃꯥꯏꯊꯤꯕ ꯈꯨꯗꯤꯡꯒꯤ ꯃꯇꯨꯡꯗ ꯕꯦꯠ ꯑꯗꯨ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯟꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ꯫ ꯃꯁꯤꯅ ꯀꯔꯤ ꯇꯧꯕꯒꯦ ꯑꯃꯁꯨꯡ ꯀꯔꯤ ꯇꯧꯗꯕꯒꯦ ꯍꯥꯌꯕ ꯊꯧꯔꯥꯡꯒꯤ ꯁꯦꯛꯁꯅꯗ ꯌꯦꯡꯕꯤꯌꯨ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯇꯝ ꯀꯨꯞꯄ ꯁꯦꯁꯟꯁꯤꯡꯗ ꯍꯟꯊꯍꯜꯂꯤ ꯑꯃꯁꯨꯡ ꯃꯇꯝ ꯁꯥꯡꯕ ꯁꯦꯁꯟꯁꯤꯡꯗ ꯌꯥꯝꯅꯥ ꯋꯥꯡꯍꯜꯂꯤ꯫ ꯍꯦꯟꯅꯥ ꯆꯥꯎꯕ ꯌꯨꯅꯤꯠ ꯑꯃꯒꯥ ꯐ꯭ꯂꯦꯠ ꯕꯦꯇꯤꯡꯊꯧꯔꯥꯡꯐ꯭ꯂꯦꯠ ꯕꯦꯇꯤꯡꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯁꯦꯜ ꯃꯥꯟꯅꯕ ꯊꯝꯕ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ ꯈꯨꯗꯤꯡꯃꯛ ꯆꯥꯡꯗꯝꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯃꯈꯥꯌꯣꯜꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯃꯁꯤ ꯍꯟꯊꯍꯅꯕꯒꯤ ꯑꯆꯨꯝꯕ ꯂꯝꯕꯤꯅꯤ꯫

ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ ꯕꯦꯠꯁꯤꯡꯗꯤ ꯀꯔꯝꯅꯣ?

ꯃꯊꯛꯇ ꯂꯩꯕ ꯐꯣꯔꯃꯨꯂꯥ ꯑꯁꯤ ꯆꯞ ꯃꯥꯟꯅꯕꯒꯤꯗꯃꯛꯅꯤ꯫ ꯚꯦꯌꯔꯤꯌꯦꯟꯁ ꯋꯥꯡꯕ ꯕꯦꯠꯁꯤꯡꯗ ꯑꯄꯤꯀꯄ ꯁꯦꯜꯗ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕ ꯍꯦꯟꯅꯥ ꯊꯣꯛꯄ ꯌꯥꯏ ꯑꯃꯁꯨꯡ ꯄꯥꯟꯗꯝ ꯑꯗꯨ ꯍꯦꯟꯅꯥ ꯆꯣꯡꯊꯕ ꯃꯑꯣꯡꯗ ꯌꯧꯏ; ꯀꯦꯜꯀꯨꯂꯦꯇꯔ ꯁꯤꯖꯤꯟꯅꯕꯤꯌꯨ꯫

q/p ꯑꯁꯤ ꯀꯔꯤꯒꯤ ꯃꯔꯨꯑꯣꯏꯕ ꯃꯁꯤꯡꯅꯣ?

ꯄꯥꯟꯗꯃꯗ ꯆꯠꯄ ꯈꯣꯡꯊꯥꯡ ꯈꯨꯗꯤꯡꯃꯛ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯕꯗ ꯆꯠꯄ ꯈꯣꯡꯊꯥꯡ ꯈꯨꯗꯤꯡꯃꯛꯇꯒꯤ ꯈꯔꯥ ꯍꯟꯊꯅ ꯊꯣꯛꯄ ꯌꯥꯏ; ꯆꯥꯡ ꯑꯁꯤ ꯈꯣꯡꯊꯥꯡ ꯀꯌꯥ ꯂꯩꯕꯒꯤ ꯃꯇꯨꯡ ꯏꯟꯅꯥ ꯄꯨꯟꯁꯤꯟꯗꯨꯅ ꯍꯦꯅꯒꯠꯂꯀꯏ꯫

ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯥ ꯁꯥꯟꯅꯕ

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

ꯅꯍꯥꯛꯀꯤ $100 ꯂꯩ ꯑꯃꯁꯨꯡ $1,000 ꯄꯥꯝꯃꯤ, ꯑꯉꯥꯡꯕꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯗꯈꯛ ꯊꯝꯂꯒꯥ꯫ ꯊꯧꯔꯥꯡ ꯑꯃꯥ: ꯑꯃꯨꯛꯇ $1 ꯊꯝꯕ꯫ ꯊꯧꯔꯥꯡ ꯑꯅꯤ: $500 ꯃꯄꯥꯟꯗ ꯆꯠꯂꯛꯠꯔꯤꯐꯥꯑꯣꯕ ꯂꯩꯔꯤꯕ ꯄꯨꯝꯅꯃꯛ ꯊꯝꯕ, ꯃꯇꯨꯡꯗ $1,000 ꯊꯨꯡꯅꯕꯒꯤ ꯃꯇꯤꯛ ꯆꯥꯕꯈꯛ ꯊꯝꯕ꯫ ꯀꯅꯥꯅ ꯍꯦꯟꯅ ꯐꯩ, ꯑꯃꯁꯨꯡ ꯀꯌꯥ ꯍꯦꯟꯅ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯊꯧꯔꯥꯡ ꯑꯅꯤ, ꯌꯥꯝꯅꯥ ꯍꯦꯟꯅ꯫ ꯃꯁꯤꯅ ꯃꯇꯝ 9.0% ꯈꯔꯗ $1,000 ꯊꯨꯡꯏ, ꯆꯨꯝꯃꯤꯟꯅꯕ 10% ꯒꯤ ꯃꯅꯥꯛꯇ꯫ ꯊꯧꯔꯥꯡ ꯑꯃꯥ ꯑꯁꯤ 10²² ꯗ ꯑꯃꯨꯛ 7 ꯈꯔꯈꯛ ꯃꯥꯌ ꯄꯥꯀꯏ꯫
ꯆꯨꯝꯃꯤꯟꯅꯕ ꯁꯥꯟꯅꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯆꯨꯝꯃꯤꯟꯅꯕ ꯁꯥꯟꯅꯕꯀꯅꯥꯒꯨꯝꯕ ꯃꯥꯏꯀꯩ ꯑꯃꯠꯇꯗ ꯑꯦꯖ ꯂꯩꯇꯕ ꯁꯥꯟꯅꯕ: ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯖꯤꯔꯣꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗ ꯅꯍꯥꯛꯅ ꯀꯔꯤ ꯇꯧꯔꯕꯁꯨ $100 ꯗꯒꯤ $1,000 ꯑꯁꯤ ꯇꯔꯥꯗ ꯑꯃꯨꯛ ꯊꯨꯡꯒꯅꯤ, ꯃꯔꯃꯗꯤ ꯅꯍꯥꯛꯀꯤ ꯁꯦꯜꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯃꯜ ꯑꯗꯨ $100 ꯗꯃꯛ ꯂꯩ꯫
ꯑꯦꯖ ꯑꯁꯤꯅ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯒꯤ 2.70% ꯂꯧꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯄꯨꯝꯅꯃꯛ ꯍꯟꯊꯅ ꯊꯝꯂꯕꯗꯤ ꯇꯔꯥꯗ ꯑꯃꯒꯤ ꯃꯅꯥꯛꯇ ꯍꯦꯟꯅ ꯂꯩ꯫ ꯊꯧꯔꯥꯡ ꯑꯅꯤꯅ ꯋꯥꯐꯝ ꯑꯁꯤ ꯕꯦꯠ ꯈꯔꯗ ꯂꯣꯏꯁꯤꯅꯍꯜꯂꯤ: $100 ꯑꯁꯤ $200, $400, $800 ꯑꯣꯏꯔꯀꯏ, ꯃꯇꯨꯡꯗ $200 ꯃꯇꯤꯛ ꯆꯥꯏ꯫ ꯃꯁꯤꯅ ꯃꯇꯝ 9.0% ꯈꯔꯗ ꯃꯥꯌ ꯄꯥꯀꯏ꯫ ꯊꯧꯔꯥꯡ ꯑꯃꯥ ꯑꯁꯤ ꯂꯣꯏꯗ꯭ꯔꯤꯉꯩ ꯃꯃꯥꯡꯗ ꯕꯦꯠ ꯂꯤꯁꯤꯡ ꯀꯌꯥ ꯆꯪꯏ, ꯑꯃꯁꯨꯡ ꯃꯈꯣꯌ ꯈꯨꯗꯤꯡꯗ ꯑꯄꯤꯛꯄ ꯑꯦꯖ ꯑꯗꯨ ꯄꯨꯟꯁꯤꯜꯂꯀꯄꯗ ꯌꯥꯝꯅꯥ ꯁꯣꯏꯗꯅ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯍꯜꯂꯤ꯫
ꯃꯁꯤ ꯗꯨꯕꯤꯟꯁ–ꯁꯦꯚꯦꯖꯒꯤ ꯃꯍꯩ ꯑꯁꯤꯒꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯂꯥꯏꯕ ꯃꯑꯣꯡꯅꯤ (Epstein, 2013): ꯀꯦꯁꯤꯅꯣꯕꯨ ꯃꯇꯦꯡ ꯄꯥꯡꯕ ꯁꯥꯟꯅꯕ ꯑꯃꯗ, ꯃꯊꯧ ꯇꯥꯕ ꯃꯇꯤꯛ ꯊꯝꯕꯤꯌꯨ, ꯌꯥꯔꯤꯕ ꯈꯟꯊꯕ ꯑꯃꯨꯛꯇ꯫
ꯅꯍꯥꯛꯀꯤ $500 ꯂꯩ ꯑꯃꯁꯨꯡ $1,000 ꯄꯥꯝꯃꯤ, ꯐꯪꯂꯕꯃꯇꯃꯗ ꯂꯦꯞꯀꯅꯤ꯫ ꯅꯍꯥꯛꯅ ꯕꯦꯠꯀꯤ ꯃꯈꯜ ꯑꯃꯥ ꯈꯅꯗꯨꯅ ꯑꯃꯨꯛ ꯃꯥꯏꯄꯥꯛꯂꯛꯠꯔꯤꯐꯥꯑꯣꯕ ꯅꯠꯔꯒꯥ ꯁꯦꯜ ꯂꯣꯏꯔꯛꯠꯔꯤꯐꯥꯑꯣꯕ ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯝꯏ꯫ ꯀꯔꯝꯕ ꯃꯈꯂꯅ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯕ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯄꯤꯒꯅꯤ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯑꯉꯥꯡꯕꯗ $500 ꯒꯤ ꯕꯦꯠ ꯑꯃꯈꯛ: 48.6%꯫ ꯁꯦꯜ ꯑꯗꯨ ꯑꯄꯤꯛꯄ ꯕꯦꯠꯁꯤꯡꯗ ꯁꯟꯗꯣꯛꯄ ꯊꯧꯔꯥꯡ ꯈꯨꯗꯤꯡꯅ ꯍꯦꯟꯅ ꯐꯠꯏ꯫
ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯈꯛ ꯃꯇꯤꯛ ꯆꯥꯅꯕ ꯊꯝꯂꯕ ꯁꯦꯜ ꯈꯨꯗꯤꯡ ꯈꯅꯕꯤꯌꯨ: ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯃꯁꯤꯡ ꯑꯃꯈꯛꯇ, 35:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯗ $30 ꯅ $1,050 ꯃꯥꯏꯄꯥꯀꯏ, ꯁ꯭ꯞꯂꯤꯠꯕꯦꯠꯁ꯭ꯞꯂꯤꯠꯌꯨꯝꯂꯣꯟꯅꯕ ꯃꯁꯤꯡ ꯑꯅꯤ, 17:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯗ $60 ꯅ $1,020 ꯃꯥꯏꯄꯥꯀꯏ, ꯑꯁꯤꯅꯆꯤꯡꯕ꯫ ꯃꯇꯨꯡꯗ ꯁꯦꯜ ꯂꯣꯏꯗ꯭ꯔꯤꯉꯩ ꯃꯃꯥꯡꯗ ꯕꯦꯠ ꯑꯃꯥ ꯌꯥꯃꯗ꯭ꯔꯕꯗꯁꯨ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯊꯤꯕꯤꯌꯨ꯫ $30 ꯒꯤ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ ꯇꯔꯥꯅꯤꯇꯔꯨꯛ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯏꯊꯤꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ (36/37)¹⁶ = 64.5%, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌꯅ ꯃꯇꯝ 35.5% ꯗ $1,000 ꯊꯨꯡꯏ꯫
ꯇꯦꯕꯜ ꯑꯁꯤꯅ ꯕꯦꯠ ꯈꯨꯗꯤꯡ ꯇꯥꯛꯂꯤ꯫ ꯑꯉꯥꯡꯕꯅ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯩ ꯃꯔꯃꯗꯤ ꯃꯁꯤꯅ ꯕꯦꯠ ꯑꯃꯈꯛꯇ ꯊꯨꯡꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯑꯦꯖ ꯑꯗꯨ $500 ꯗ ꯑꯃꯨꯛꯈꯛ ꯄꯤꯏ꯫ ꯁꯤꯛꯁ ꯂꯥꯏꯟꯕꯦꯠꯁꯤꯛꯁ ꯂꯥꯏꯟꯌꯨꯝꯂꯣꯟꯅꯕ ꯂꯥꯏꯟ ꯑꯅꯤꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯇꯔꯨꯛ, 5:1 ꯄꯦꯑꯥꯎꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯁꯤꯖꯦꯟ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯅꯤꯁꯨꯕꯗ ꯂꯩ ꯃꯔꯃꯗꯤ ꯃꯁꯤꯅ ꯑꯍꯨꯃꯈꯛ ꯃꯊꯧ ꯇꯥꯏ꯫ ꯗꯖꯟꯕꯦꯠꯗꯖꯟ1–12, 13–24 ꯅꯠꯔꯒ 25–36, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯈꯛꯀꯤ ꯕꯦꯠ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯠꯏ, 12/37 ꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ; $1,000 ꯅꯠꯔꯒꯥ ꯍꯦꯟꯅ ꯐꯪꯂꯛꯠꯔꯤꯐꯥꯑꯣꯕ $250 ꯒꯤ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯗ ꯁꯥꯟꯅꯔꯕꯁꯨ, ꯗꯖꯟꯅ ꯃꯇꯝ 46.4% ꯗꯈꯛ ꯊꯨꯡꯏ꯫
Bollman (2024) ꯅ ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔꯒꯤꯗꯃꯛ ꯇꯦꯕꯜ ꯑꯗꯨꯃꯛ ꯁꯦꯝꯃꯤ꯫ ꯃꯍꯥꯛꯀꯤ ꯗꯖꯟꯒꯤ ꯔꯣ ꯑꯗꯨꯗ ꯑꯔꯥꯟꯕ ꯑꯃꯥ ꯂꯩ: ꯃꯁꯤ 12/38 = 31.6% ꯑꯣꯏꯒꯗꯕꯅꯤ꯫
ꯕꯦꯠꯊꯝꯂꯕ ꯁꯦꯜ × ꯕꯦꯠꯀꯤ ꯃꯁꯤꯡ$1,000 ꯊꯨꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ
ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ$30 × 1635.5%
ꯁ꯭ꯞꯂꯤꯠ$60 × 835.9%
ꯁ꯭ꯇ꯭ꯔꯤꯠ$90 × 534.5%
ꯀꯣꯔꯅꯔ$125 × 436.7%
ꯁꯤꯛꯁ ꯂꯥꯏꯟ$166, $166, $16841.2%
ꯗꯖꯟ$500 × 132.4%
ꯑꯉꯥꯡꯕ$500 × 148.6%
ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯂꯣꯏꯗꯕ ꯕꯦꯡꯀꯔꯣꯜꯁꯦꯜꯕꯦꯡꯀꯔꯣꯜꯁꯥꯟꯅꯅꯕ ꯇꯣꯉꯥꯟꯅ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ꯫ ꯕꯦꯡꯀꯔꯣꯜ ꯃꯦꯅꯦꯖꯃꯦꯟꯠ ꯍꯥꯌꯕꯁꯤ ꯃꯗꯨꯒꯤ ꯀꯌꯥ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯁꯨꯡ ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡꯗ ꯈꯨꯗꯣꯡꯊꯤꯕꯗ ꯊꯃꯒꯗꯒꯦ ꯍꯥꯌꯕ ꯋꯥꯔꯦꯞ ꯂꯧꯕꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯒꯥ ꯂꯣꯌꯅꯅ ꯅꯍꯥꯛꯅ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯑꯉꯥꯡꯕꯗ ꯌꯨꯅꯤꯠ ꯑꯃꯥ ꯊꯝꯏ꯫ ꯑꯍꯥꯅꯕ ꯁ꯭ꯄꯤꯟꯒꯤ ꯃꯇꯨꯡꯗ ꯅꯍꯥꯛ ꯌꯨꯅꯤꯠ ꯑꯃꯥ ꯀꯥꯟꯅꯕꯗ ꯅꯠꯔꯒꯥ ꯌꯨꯅꯤꯠ ꯑꯃꯥ ꯃꯥꯡꯈꯤꯕꯗ ꯂꯩ꯫ ꯅꯍꯥꯛ ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯆꯨꯝꯅ ꯆꯞ ꯃꯥꯟꯅꯕꯗ ꯂꯩꯒꯗꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯀꯌꯥ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ 37 ꯗ 36, 97.3%꯫ ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔꯗ 38 ꯗ 36, 94.7%꯫
ꯑꯍꯥꯅꯕ ꯁ꯭ꯄꯤꯟ ꯃꯥꯏꯄꯥꯛꯂꯕꯗꯤ (37 ꯗ ꯑꯃꯨꯛ 18), ꯅꯍꯥꯛ ꯌꯨꯅꯤꯠ ꯑꯃꯥ ꯀꯥꯟꯅꯕꯗ ꯂꯩ, ꯑꯃꯁꯨꯡ ꯑꯦꯖ ꯑꯁꯤꯅ ꯂꯣꯏꯕ ꯅꯥꯏꯗꯕ ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡ ꯃꯈꯥꯗ ꯆꯤꯡꯊꯥꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯇꯨꯡꯗ ꯅꯠꯔꯒꯥ ꯊꯨꯅ ꯅꯍꯥꯛ ꯆꯞ ꯃꯥꯟꯅꯕꯗ ꯍꯜꯂꯛꯀꯅꯤ: ꯃꯁꯤ ꯁꯣꯏꯗꯅꯕꯅꯤ꯫ ꯃꯥꯏꯊꯤꯕꯔꯕꯗꯤ (37 ꯗ ꯑꯃꯨꯛ 19), ꯅꯍꯥꯛꯅ ꯌꯨꯅꯤꯠ ꯑꯃꯥ ꯀꯥꯒꯗꯕꯅꯤ, ꯑꯃꯁꯨꯡ ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯌꯨꯅꯤꯠ ꯑꯃꯥ ꯀꯥꯟꯅꯕꯗ ꯂꯩꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ 18/19 (ꯃꯊꯛꯇ ꯂꯩꯕ ꯇꯦꯕꯜ ꯌꯦꯡꯕꯤꯌꯨ)꯫
ꯄꯨꯟꯅ: 18/37 + 19/37 × 18/19 = 18/37 + 18/37 = 36/37꯫
ꯃꯇꯝ ꯄꯨꯝꯕꯗ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯁꯤ 1 ꯗꯒꯤ ꯁ꯭ꯄꯤꯟ ꯑꯃꯥ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯁꯨꯡ ꯃꯥꯏꯊꯤꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯒꯤ ꯈꯦꯟꯅꯕ ꯑꯗꯨ ꯂꯧꯊꯣꯀꯄꯅꯤ: ꯌꯨꯔꯣꯄꯤꯌꯟ ꯆꯛꯔꯗ 1 − 1/37, ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔꯗ 1 − 2/38꯫ ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯂꯩꯇꯕ ꯁꯥꯟꯅꯕ ꯑꯃꯗ ꯈꯦꯟꯅꯕ ꯑꯗꯨ ꯀꯔꯤꯁꯨ ꯅꯠꯇꯦ ꯑꯃꯁꯨꯡ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯗꯨ 1: ꯁ꯭ꯀꯣꯔ ꯑꯗꯨ ꯃꯇꯝ ꯄꯨꯝꯅꯃꯛꯇ ꯆꯞ ꯃꯥꯟꯅꯕꯗ ꯍꯜꯂꯛꯏ꯫ Epstein (2013) ꯅ ꯃꯇꯝ ꯄꯨꯝꯕꯒꯤ ꯅꯤꯌꯝ ꯄꯤꯔꯤ꯫
1656 ꯒꯤ ꯄꯥꯁ꯭ꯀꯦꯂꯒꯤ ꯄꯖꯜ: ꯁꯥꯟꯅꯔꯤꯕ ꯑꯅꯤꯅ ꯗꯥꯏꯁ ꯑꯍꯨꯝ ꯊꯥꯗꯣꯛꯏ, ꯑꯃꯃꯛꯅ ꯀꯥꯎꯟꯇꯔ 12 ꯒꯥ ꯂꯣꯌꯅꯅ ꯍꯧꯏ꯫ 11 ꯈꯨꯗꯤꯡꯅ ꯀꯥꯎꯟꯇꯔ ꯑꯃꯥ ꯑꯍꯥꯅꯕ ꯁꯥꯟꯅꯔꯤꯕꯗ ꯄꯨꯊꯣꯛꯏ, 14 ꯈꯨꯗꯤꯡꯅ ꯑꯃꯥ ꯑꯅꯤꯁꯨꯕꯗ ꯄꯨꯊꯣꯛꯏ; ꯑꯇꯣꯞꯄ ꯊꯥꯗꯣꯛꯄꯁꯤꯡ ꯃꯁꯤꯡ ꯊꯤꯗꯦ꯫ ꯑꯍꯥꯅꯕ ꯁꯥꯟꯅꯔꯤꯕꯅ 24 ꯄꯨꯝꯅꯃꯛ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯀꯌꯥ? ꯑꯃꯁꯨꯡ ꯃꯗꯨꯒꯤ ꯃꯍꯨꯠꯇ ꯕꯦꯡꯛ ꯑꯣꯏꯔꯤꯕ ꯃꯔꯨꯞ ꯑꯃꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯑꯉꯥꯡꯕꯗ ꯌꯨꯅꯤꯠ 1 ꯊꯝꯂꯕꯗꯤ, ꯑꯃꯃꯛꯀꯤ ꯌꯨꯅꯤꯠ 12, ꯅꯍꯥꯛꯅ 24 ꯄꯨꯝꯅꯃꯛ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯀꯌꯥ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯑꯍꯥꯅꯕ ꯁꯥꯟꯅꯔꯤꯕꯅ 1,158 ꯗ ꯑꯃꯨꯛ 1,157 ꯈꯔ ꯃꯥꯏꯄꯥꯀꯏ꯫ ꯑꯉꯥꯡꯕꯗ ꯊꯝꯂꯤꯕ ꯅꯍꯥꯛꯅ ꯌꯨꯅꯤꯠ 24 ꯄꯨꯝꯅꯃꯛ ꯃꯇꯝ 34% ꯈꯔꯗꯈꯛ ꯃꯥꯏꯄꯥꯀꯏ꯫
ꯗꯥꯏꯁ ꯑꯍꯨꯃꯅ 11 ꯑꯁꯤ ꯃꯑꯣꯡ 27 ꯗ ꯑꯃꯁꯨꯡ 14 ꯑꯁꯤ ꯃꯑꯣꯡ 15 ꯗ ꯁꯦꯝꯃꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯆꯠꯂꯤꯕ ꯀꯥꯎꯟꯇꯔ ꯈꯨꯗꯤꯡ 42 ꯗ ꯑꯃꯨꯛ 27, 14 ꯗ ꯑꯃꯨꯛ 9 ꯑꯍꯥꯅꯕ ꯁꯥꯟꯅꯔꯤꯕꯗ ꯆꯠꯏ꯫ ꯃꯥꯏꯀꯩ ꯈꯨꯗꯤꯡꯅ 12 ꯗꯒꯤ ꯍꯧꯔꯕꯗ, ꯄꯨꯝꯅꯃꯛ ꯂꯧꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ 1/(1 + r¹²), ꯃꯐꯝ ꯑꯗꯨꯗ r ꯑꯁꯤ ꯑꯇꯣꯞꯄ ꯃꯥꯏꯀꯩꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯃꯁꯨꯡ ꯅꯍꯥꯛꯀꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯒꯤ ꯔꯦꯁꯤꯑꯣꯅꯤ꯫
ꯑꯍꯥꯅꯕ ꯁꯥꯟꯅꯔꯤꯕꯒꯤꯗꯃꯛ r = 5/9, ꯑꯃꯁꯨꯡ (5/9)¹² ≈ 0.00086, ꯃꯔꯝ ꯑꯗꯨꯅ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯗꯨ 0.99914 ꯈꯔ: ꯑꯣꯗꯁ 9¹² ꯗꯒꯤ 5¹², ꯅꯠꯔꯒꯥ 282,429,536,481 ꯗꯒꯤ 244,140,625, 1,157 ꯗꯒꯤ 1 ꯈꯔ꯫ ꯍꯣꯏꯒꯦꯟꯁꯅ 1657 ꯗ ꯃꯁꯤꯡ ꯑꯗꯨꯃꯛ ꯆꯨꯝꯅ ꯐꯣꯡꯗꯣꯀꯈꯤ꯫
ꯑꯉꯥꯡꯕꯗ, ꯖꯤꯔꯣꯅ ꯃꯔꯝ ꯑꯣꯏꯗꯨꯅ r = 19/18, ꯑꯃꯁꯨꯡ (19/18)¹² ≈ 1.913: ꯅꯍꯥꯛꯀꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ 1/2.913 ≈ 34.3%꯫ ꯀꯣꯏꯟ ꯑꯃꯅ 50% ꯄꯤꯒꯅꯤ꯫ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯂꯩꯕ 2.70% ꯒꯤ ꯑꯦꯖ ꯑꯁꯤꯅ ꯃꯊꯧ ꯇꯥꯕ ꯕꯦꯠ ꯀꯌꯥꯗ ꯄꯨꯟꯁꯤꯜꯂꯀꯄꯗ ꯄꯣꯏꯟꯠ 16 ꯒꯤ ꯈꯦꯟꯅꯕ ꯑꯃꯥ ꯑꯣꯏꯔꯀꯏ꯫

ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

$ꯊꯧꯅꯥ ꯂꯩꯕ ꯁꯥꯟꯅꯕ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯩ꯫ ꯃꯁꯤ ꯊꯨꯅ ꯂꯣꯏꯁꯤꯜꯂꯤ꯫$

ꯊꯧꯅꯥ ꯂꯩꯕ ꯁꯥꯟꯅꯕ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯩ꯫ ꯃꯁꯤ ꯊꯨꯅ ꯂꯣꯏꯁꯤꯜꯂꯤ꯫

ꯍꯧꯔꯛꯐꯃꯁꯤꯡ

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3 ꯁꯨꯕ ꯑꯦꯗꯤꯁꯟ, 1968꯫ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯃꯥꯡꯍꯟ ꯇꯥꯀꯍꯟꯕ (gambler’s ruin), ꯆꯦꯞꯇꯔ XIV꯫
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꯫
Carcavi, P. de. Letter to Huygens, 28 September 1656, on the problem Pascal posed to Fermat. Œuvres complètes de Christiaan Huygens, vol. 1, 1888, pp. 492–494.
Huygens, C. De Ratiociniis in Ludo Aleae. 1657꯫ ꯐꯪꯒꯗꯕ ꯃꯃꯜ (expectation) ꯒꯤ ꯃꯇꯥꯡꯗ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯑꯍꯥꯅꯕ ꯐꯣꯡꯗꯣꯀꯈꯤꯕ ꯏꯔꯤꯕ꯫
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010꯫ ꯆꯦꯞꯇꯔ 13, ꯔꯨꯂꯦꯠ꯫
Reuters. “Briton bets it all on roulette spin, and wins.” 2004 ꯒꯤ ꯑꯦꯞꯔꯤꯜ꯫
Las Vegas Sun. “Man wagers life’s worth.” 2004 ꯒꯤ ꯑꯦꯞꯔꯤꯜ 12꯫

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