ꯔꯨꯂꯦꯠꯄꯨ ꯃꯥꯏꯊꯤꯍꯟꯕ ꯉꯃꯒꯗ꯭ꯔꯥ? ꯔꯨꯂꯦꯠꯇ ꯀꯔꯝꯅ ꯃꯥꯏꯄꯥꯛꯀꯗꯒꯦ

ꯁꯤꯁ꯭ꯇꯦꯝꯁꯤꯡ ꯀꯔꯤꯒꯤ ꯃꯥꯏꯊꯤꯕꯅꯣ

ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ EV = ꯃꯁꯥꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37꯫ ꯃꯃꯥꯡꯒꯤ ꯃꯍꯩꯁꯤꯡꯗꯒꯤ ꯀꯔꯝꯅ ꯈꯅꯔꯕꯁꯨ, ꯕꯦꯠꯁꯤꯡꯒꯤ ꯀꯔꯤꯒꯨꯝꯕ ꯃꯊꯪ ꯃꯊꯪ ꯑꯃꯒꯤ EV = ꯊꯝꯂꯕ ꯄꯨꯝꯅꯃꯛꯀꯤ −1/37꯫ ꯃꯁꯤ ꯔꯦꯟꯗꯝ ꯚꯦꯔꯤꯑꯦꯕꯂꯁꯤꯡꯒꯤ ꯃꯄꯨꯡꯒꯤ ꯃꯔꯃꯗ ꯊꯤꯑꯣꯔꯦꯝ ꯑꯃꯅꯤ, ꯍꯦꯟꯅꯥ ꯐꯕ ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯃꯅ ꯂꯧꯊꯣꯀꯄ ꯉꯝꯒꯗꯕ ꯎꯕꯥ ꯑꯃꯥ ꯅꯠꯇꯦ꯫ ꯖꯣꯁꯦꯐ ꯗꯨꯕ (Joseph Doob) ꯑꯃꯁꯨꯡ ꯄꯣꯜ ꯍꯥꯜꯃꯣꯁ (Paul Halmos) ꯅ 1930 ꯒꯤ ꯆꯍꯤꯁꯤꯡꯗ ꯃꯁꯤ ꯄ꯭ꯔꯨꯐ ꯇꯧꯈꯤ, ꯑꯃꯁꯨꯡ ꯀꯥꯔꯗ ꯃꯁꯤꯡ ꯊꯤꯗꯨꯅ ꯕ꯭ꯂꯦꯛꯖꯦꯛꯄꯨ ꯇꯁꯦꯡꯅ ꯃꯥꯏꯊꯤꯍꯅꯈꯤꯕ ꯑꯦꯗꯋꯥꯔꯗ ꯊꯣꯔꯞ (Edward Thorp) ꯅ ꯃꯁꯤꯅ ꯃꯊꯧ ꯇꯥꯕ ꯐꯤꯚꯃꯁꯤꯡ ꯊꯃꯈꯤ: ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛ ꯅꯦꯒꯦꯇꯤꯕ, ꯃꯔꯤ ꯂꯩꯅꯗꯕ ꯁ꯭ꯄꯤꯟꯁꯤꯡꯃꯦꯊꯃꯦꯇꯤꯛꯁꯃꯔꯤ ꯂꯩꯅꯗꯕ ꯁ꯭ꯄꯤꯟꯁꯤꯡꯍꯥꯟꯅꯒꯤ ꯃꯍꯩ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯣꯏꯔꯕꯁꯨ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯃꯥꯟꯅꯩ꯫ ꯋꯦꯕꯁꯥꯏꯠ ꯑꯁꯤꯒꯤ ꯊꯤꯕ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯌꯨꯝꯐꯝꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, ꯇꯦꯕꯜꯒꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯕ ꯑꯃꯁꯨꯡ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯦꯝꯕ ꯉꯝꯈꯩ꯫ ꯃꯍꯥꯛꯀꯤ 1966 ꯒꯤ ꯇꯦꯛꯁ꯭ꯇꯕꯨꯛꯅ ꯂꯥꯏꯕ ꯄ꯭ꯔꯨꯐ ꯑꯃꯥ ꯄꯤ꯫

ꯔꯨꯂꯦꯠ ꯇꯦꯕꯜꯒꯤ ꯉꯝꯈꯩꯁꯤꯡꯃꯔꯤ ꯂꯩꯅꯗꯕ ꯔꯨꯂꯦꯠ ꯁ꯭ꯄꯤꯟꯁꯤꯡ

ꯀꯔꯤꯅ ꯊꯕꯛ ꯇꯧꯈꯤꯕꯒꯦ

ꯋꯥꯐꯝ ꯑꯍꯨꯝ, ꯄꯨꯝꯅꯃꯛ ꯍꯛꯆꯥꯡꯒꯤ ꯆꯛꯔꯒꯥ ꯃꯔꯤ ꯂꯩꯅꯩ꯫ ꯕꯥꯏꯌꯥꯁ: ꯄꯣꯀꯦꯠꯁꯤꯡꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯆꯞ ꯃꯥꯟꯅꯅ ꯊꯣꯀꯄ ꯉꯃꯗꯕ ꯆꯛꯔ ꯑꯃꯥ, ꯁ꯭ꯄꯤꯟ ꯂꯤꯁꯤꯡ ꯀꯌꯥ ꯏꯔꯝ ꯊꯃꯗꯨꯅ ꯊꯤꯗꯣꯀꯈꯤ꯫ ꯈꯟꯊꯣꯀꯄ: ꯇꯥꯕꯒꯤ ꯁꯦꯛꯇꯔꯆꯛꯔꯁꯦꯛꯇꯔꯆꯛꯔꯗ ꯃꯔꯛ ꯂꯩꯇꯅ ꯃꯈꯥ ꯆꯠꯅꯅ ꯂꯩꯕ ꯄꯣꯀꯦꯠꯁꯤꯡꯒꯤ ꯁꯔꯨꯛ, ꯂꯦꯑꯥꯎꯠꯇ ꯂꯩꯕ ꯀꯥꯡꯂꯨꯞ ꯑꯃꯗꯒꯤ ꯇꯣꯉꯥꯟꯅ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯈꯟꯊꯣꯛꯅꯕ ꯕꯣꯜꯈꯨꯠꯂꯥꯏꯕꯣꯜꯔꯣꯇꯔꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯇ꯭ꯔꯦꯛꯇ ꯊꯥꯗꯣꯛꯄ ꯑꯄꯤꯛꯄ ꯕꯣꯜ꯫ ꯍꯧꯖꯤꯛꯀꯤ ꯕꯣꯜꯁꯤꯡ ꯑꯥꯏꯚꯣꯔꯤꯟ ꯅꯠꯔꯒ ꯇꯦꯐ꯭ꯂꯣꯅꯅ ꯁꯦꯝꯃꯤ, 18–21 mm꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯁꯨꯡ ꯔꯣꯇꯔꯒꯤꯈꯨꯠꯂꯥꯏꯔꯣꯇꯔꯄꯣꯀꯦꯠꯁꯤꯡ ꯄꯨꯔꯛꯄ ꯆꯛꯔꯒꯤ ꯀꯣꯏꯕ ꯁꯔꯨꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯇꯝ ꯂꯦꯄꯄ, 1970 ꯒꯤ ꯆꯍꯤꯁꯤꯡꯗꯒꯤ ꯍꯧꯔꯒ ꯂꯣꯠꯂꯕ ꯀꯝꯄꯤꯎꯇꯔꯁꯤꯡꯅ ꯇꯧꯈꯤ꯫ ꯗꯤꯂꯔꯒꯤ ꯁꯥꯏꯅ: ꯗꯤꯂꯔ ꯑꯃꯅ ꯕꯣꯜ ꯊꯥꯗꯣꯛꯄ ꯑꯗꯨ ꯇꯥꯕ ꯈꯟꯊꯣꯛꯅꯕ ꯃꯇꯤꯛ ꯆꯥꯕ ꯃꯥꯟꯅꯩ ꯍꯥꯌꯕ ꯋꯥꯈꯜ, ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯊꯥꯖꯕ ꯌꯥꯅ ꯎꯠꯈꯤꯗꯦ꯫ ꯑꯍꯨꯃꯃꯛꯅ ꯍꯛꯆꯥꯡꯒꯤ ꯆꯛꯔ, ꯁꯥꯡꯂꯕ ꯌꯦꯡꯁꯤꯟꯕ ꯑꯃꯁꯨꯡ ꯈꯉꯗ꯭ꯔꯤꯕ ꯀꯦꯁꯤꯅꯣ ꯑꯃꯥ ꯃꯊꯧ ꯇꯥꯏ꯫

ꯔꯨꯂꯦꯠ ꯗꯤꯂꯔꯒꯤ ꯁꯥꯏꯅꯦꯆꯔꯁꯦꯝꯄꯜ ꯁꯥꯏꯖ

ꯀꯔꯤꯒꯤ ꯍꯧꯖꯤꯛ ꯊꯕꯛ ꯇꯧꯗ꯭ꯔꯕꯅꯣ

ꯀꯦꯁꯤꯅꯣꯁꯤꯡꯅ ꯍꯨꯏꯜ ꯍꯦꯗꯁꯤꯡꯈꯨꯠꯂꯥꯏꯍꯨꯏꯜ ꯍꯦꯗꯔꯣꯇꯔꯒꯤ ꯃꯃꯤꯡ ꯑꯃꯅꯤ: ꯃꯁꯤꯡꯁꯤꯡ ꯄꯨꯔꯛꯄ ꯀꯣꯏꯕ ꯁꯔꯨꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯕꯧꯜꯁꯤꯡꯒꯤꯈꯨꯠꯂꯥꯏꯕꯧꯜꯆꯛꯔꯒꯤ ꯂꯦꯞꯄ ꯃꯄꯥꯟꯒꯤ ꯁꯔꯨꯛ: ꯕꯣꯜ ꯇ꯭ꯔꯦꯛ ꯑꯃꯁꯨꯡ ꯑꯦꯞꯔꯟ ꯊꯝꯕ ꯎꯒꯤ ꯅꯠꯔꯒ ꯀꯝꯄꯣꯖꯤꯠꯀꯤ ꯃꯄꯥꯟꯒꯤ ꯂꯝꯕꯤ, ꯃꯁꯤꯒꯤ ꯃꯅꯨꯡꯗ ꯔꯣꯇꯔ ꯀꯣꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯔꯛꯇ ꯍꯣꯟꯊꯣꯀꯏ, ꯕꯧꯜꯁꯤꯡ ꯆꯨꯝꯅ ꯊꯝꯃꯤ, ꯄꯣꯀꯦꯠꯁꯤꯡ ꯆꯥꯡ ꯌꯦꯡꯏ ꯑꯃꯁꯨꯡ ꯂꯦꯞꯂꯕ ꯃꯇꯃꯗ ꯐ꯭ꯔꯦꯠꯁꯤꯡꯈꯨꯠꯂꯥꯏꯐ꯭ꯔꯦꯠꯆꯛꯔꯗ ꯄꯣꯀꯦꯠ ꯑꯅꯤꯒꯤ ꯃꯔꯛꯇ ꯂꯩꯕ ꯃꯦꯇꯦꯂꯒꯤ ꯈꯥꯌꯗꯣꯛꯄ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯍꯣꯡꯗꯣꯀꯏ, ꯃꯁꯤꯅ ꯕꯥꯏꯌꯥꯁ ꯃꯥꯏꯊꯤꯍꯜꯂꯤ꯫ ꯂꯥꯏꯕ ꯁ꯭ꯇꯨꯗꯤꯑꯣꯁꯤꯡꯅ ꯕꯣꯜ ꯇꯞꯂꯛꯇ꯭ꯔꯤꯉꯩꯗ ꯕꯦꯠ ꯊꯝꯕ ꯂꯣꯏꯍꯜꯂꯤ ꯑꯃꯁꯨꯡ ꯁ꯭ꯇ꯭ꯔꯤꯝꯒꯤ ꯊꯦꯡꯅꯕ ꯂꯦꯞꯄꯤ, ꯃꯁꯤꯅ ꯃꯇꯝ ꯂꯦꯄꯄ ꯃꯥꯏꯊꯤꯍꯜꯂꯤ꯫ ꯑꯥꯏꯟꯒꯤ ꯃꯐꯝ ꯌꯥꯝꯅꯥꯗ ꯈꯟꯊꯣꯀꯄꯒꯤ ꯈꯨꯠꯂꯥꯏꯁꯤꯡ ꯑꯔꯥꯟꯕ ꯊꯕꯛ ꯑꯣꯏꯍꯜꯂꯦ꯫ ꯗꯤꯂꯔꯁꯤꯡꯗ ꯕꯣꯜ ꯊꯥꯗꯣꯛꯄ ꯈꯦꯠꯅꯍꯟꯅꯕ ꯌꯥꯊꯪ ꯄꯤ꯫ ꯂꯥꯏꯁꯦꯟꯁ ꯂꯩꯕ ꯀꯦꯁꯤꯅꯣ ꯅꯠꯔꯒ ꯁ꯭ꯇꯨꯗꯤꯑꯣꯗ ꯌꯦꯡꯁꯤꯟꯕ ꯍꯧꯖꯤꯛꯀꯤ ꯆꯛꯔ ꯑꯃꯒꯤꯗꯃꯛ ꯑꯆꯨꯝꯕ ꯄꯥꯎꯈꯨꯝ ꯑꯗꯨꯗꯤ ꯉꯝꯗꯦ꯫

ꯂꯥꯏꯕ ꯔꯨꯂꯦꯠ ꯀꯔꯝꯅ ꯊꯕꯛ ꯇꯧꯕꯒꯦ

ꯔꯨꯂꯦꯠꯄꯨ ꯀꯔꯝꯅ ꯃꯥꯏꯊꯤꯍꯅꯒꯗꯒꯦ, ꯋꯥꯈꯂꯗ ꯈꯛꯇ: ꯃꯁꯤꯅ ꯀꯔꯤ ꯃꯊꯧ ꯇꯥꯒꯅꯤ

ꯄꯣꯀꯦꯠ ꯑꯃꯅ 37 ꯗ 1 ꯒꯤ ꯃꯍꯨꯠꯇ 33 ꯗ 1 ꯊꯣꯀꯏ ꯍꯥꯌꯔꯁꯤ꯫ ꯃꯗꯨꯗ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯃꯁꯤꯡ ꯑꯃꯈꯛꯇ, 35:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯒꯤ EV = 35/33 − 32/33 = +3/33 ≈ +9%꯫ ꯄꯣꯀꯦꯠ ꯑꯗꯨ ꯂꯥꯛ ꯐꯕꯅ ꯅꯠꯇꯅ ꯕꯥꯏꯌꯥꯁ ꯂꯩꯕꯅꯤ ꯍꯥꯌꯕ ꯈꯉꯅꯕ ꯆꯛꯔ ꯑꯗꯨꯃꯛꯇꯒꯤ ꯏꯔꯝ ꯊꯝꯂꯕ ꯁ꯭ꯄꯤꯟ 10,000 ꯔꯣꯝ ꯃꯊꯧ ꯇꯥꯏ; ꯃꯗꯨ ꯁꯤꯖꯤꯟꯅꯅꯕ ꯅꯍꯥꯛꯅ ꯕꯦꯠ ꯊꯝꯂꯤꯉꯩꯗ ꯆꯛꯔ ꯑꯗꯨ ꯍꯣꯡꯗꯅ ꯂꯩꯕ ꯃꯊꯧ ꯇꯥꯏ꯫ ꯂꯦꯕꯀꯤ ꯂꯃꯥꯏꯁꯤꯡꯅ ꯁ꯭ꯇꯦꯇꯤꯁ꯭ꯇꯤꯛꯁ ꯁꯟꯗꯣꯛꯅ ꯇꯥꯀꯏ; ꯄꯨꯋꯥꯔꯤꯒꯤ ꯂꯃꯥꯏꯁꯤꯡꯅ ꯃꯁꯤ ꯇꯧꯈꯤꯕ ꯃꯤꯁꯤꯡꯗ ꯀꯔꯤ ꯊꯣꯀꯈꯤꯕꯒꯦ ꯁꯟꯗꯣꯛꯅ ꯇꯥꯀꯏ꯫

ꯑꯆꯨꯝꯕ ꯄꯥꯎꯈꯨꯝ

ꯁꯤꯁ꯭ꯇꯦꯝ ꯂꯩꯕ ꯄꯥꯕ ꯃꯤꯒꯤꯗꯃꯛ: ꯃꯁꯤꯅ ꯊꯕꯛ ꯇꯧꯔꯣꯏ, ꯑꯃꯁꯨꯡ ꯅꯍꯥꯛꯅ ꯁꯥꯏꯠ ꯑꯁꯤꯒꯤ ꯁꯤꯃꯨꯂꯦꯇꯔꯁꯤꯡꯅ ꯅꯨꯃꯤꯗꯥꯡ ꯑꯃꯈꯛꯇ ꯃꯗꯨ ꯆꯦꯛꯁꯤꯟꯕ ꯉꯝꯃꯤ꯫ ꯅꯣꯠꯕꯨꯛ ꯑꯃꯁꯨꯡ ꯑꯁꯥꯑꯣꯕ ꯂꯩꯇꯕ ꯄꯥꯕ ꯃꯤꯒꯤꯗꯃꯛ: ꯕꯥꯏꯌꯥꯁ ꯑꯁꯤ ꯋꯥꯈꯂꯗ ꯂꯩ ꯑꯃꯁꯨꯡ ꯊꯕꯛꯇ ꯏꯟꯖꯤꯅꯤꯌꯔꯤꯡꯅ ꯂꯧꯊꯣꯀꯏ꯫ ꯃꯤ ꯈꯨꯗꯤꯡꯃꯛꯀꯤꯗꯃꯛ: ꯔꯨꯂꯦꯠ ꯑꯁꯤ ꯄꯣꯠ ꯂꯩꯕ ꯑꯃꯅꯤ꯫ ꯅꯍꯥꯛ ꯅꯨꯡꯉꯥꯏꯕ ꯃꯃꯜ ꯑꯃꯥ, ꯅꯍꯥꯛꯅ ꯈꯅꯕ ꯌꯥꯡꯅꯕꯗ, ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯈꯛ ꯂꯩꯕ ꯑꯃꯁꯨꯡ ꯐꯪꯕ ꯌꯥꯔꯕꯗ ꯂꯥ ꯄꯥꯔꯇꯥꯖꯅꯤꯌꯝꯂꯥ ꯄꯥꯔꯇꯥꯖꯐ꯭ꯔꯦꯟꯆ ꯅꯤꯌꯝ: ꯖꯤꯔꯣ ꯊꯣꯛꯂꯕꯗꯤ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯀꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯁꯔꯨꯛ ꯑꯍꯦꯟꯕ ꯍꯜꯂꯀꯏ꯫ ꯕꯦꯠ ꯑꯗꯨꯁꯤꯡꯒꯤ ꯍꯥꯎꯁ ꯑꯦꯖ 1.35% ꯐꯥꯑꯣꯕ ꯁꯔꯨꯛ ꯑꯅꯤꯗ ꯊꯥꯖꯤꯜꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯂꯩꯕ ꯆꯛꯔ ꯑꯃꯗ ꯄꯤꯕꯤꯌꯨ꯫

ꯂꯥ ꯄꯥꯔꯇꯥꯖ ꯔꯨꯂꯦꯠ ꯅꯤꯌꯝ

ꯋꯥꯍꯪꯁꯤꯡ