ꯃꯦꯊꯃꯦꯇꯤꯛꯁ · ꯃꯔꯨ ꯑꯣꯏꯕ ꯋꯥꯈꯜꯂꯣꯟ · ꯃꯤꯅꯤꯠ 7

ꯔꯨꯂꯦꯠꯀꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯜ

ꯔꯨꯂꯦꯠꯀꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯑꯁꯤ ꯕꯦꯠ ꯑꯃꯥ ꯂꯣꯏꯕ ꯅꯥꯏꯗꯅ ꯍꯟꯖꯤꯟ ꯍꯟꯖꯤꯟ ꯇꯧꯕ ꯌꯥꯔꯕꯗꯤ ꯐꯪꯒꯗꯕ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩꯅꯤ꯫ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯔꯨꯂꯦꯠꯇ ꯃꯁꯤ ꯑꯣꯏꯕ ꯌꯥꯕ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯃꯥꯟꯅꯩ: ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯑꯦꯚꯔꯦꯖꯗ ꯊꯝꯂꯕ ꯁꯦꯜ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ 1/37 ꯃꯥꯡꯏ꯫

ꯂꯥꯏꯅ ꯍꯥꯌꯔꯕꯗꯤ

ꯑꯉꯥꯡꯕꯗ $10 ꯒꯤ ꯕꯦꯠ ꯑꯗꯨꯃꯛ ꯑꯃꯨꯛ ꯂꯥꯈ ꯇꯔꯥ ꯊꯝꯂꯤ ꯍꯥꯌꯅ ꯈꯟꯊꯕꯤꯌꯨ꯫ ꯁ꯭ꯄꯤꯟ ꯈꯔꯗ $10 ꯃꯥꯏꯄꯥꯛꯏ, ꯈꯔꯗ $10 ꯃꯥꯏꯊꯤꯏ꯫ ꯃꯍꯩ ꯄꯨꯝꯅꯃꯛ ꯄꯨꯟꯁꯤꯟꯗꯨꯅ ꯂꯥꯈ ꯇꯔꯥ ꯅ ꯌꯦꯟꯊꯣꯀꯄꯤꯌꯨ: ꯃꯇꯧ ꯑꯁꯨꯝꯅ −$0.27 ꯐꯪꯒꯅꯤ꯫ ꯃꯁꯤꯡ ꯑꯗꯨ ꯔꯨꯂꯦꯠ ꯕꯦꯠ ꯑꯃꯒꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯅꯤ꯫ ꯃꯁꯤ ꯀꯔꯤꯒꯨꯝꯕ ꯁ꯭ꯄꯤꯟ ꯑꯃꯗ ꯊꯣꯀꯄ ꯅꯠꯇꯦ; ꯃꯁꯤ ꯃꯇꯝ ꯁꯥꯡꯅ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯂꯩꯕ ꯑꯦꯚꯔꯦꯖꯅꯤ꯫

ꯊꯨꯅ ꯄꯥꯎꯈꯨꯝEV = ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ × ꯃꯥꯏꯄꯥꯛꯂꯕ ꯁꯦꯜ − ꯃꯥꯏꯊꯤꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ × ꯃꯥꯡꯈꯤꯕ ꯁꯦꯜ꯫ ꯑꯣꯏꯕ ꯌꯥꯕ ꯔꯨꯂꯦꯠ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯃꯁꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −2.70% ꯑꯣꯏꯔꯤ꯫

ꯔꯨꯂꯦꯠ ꯕꯦꯠ ꯑꯃꯒꯤ EV ꯒꯤ ꯐꯣꯔꯃꯨꯂꯥ

EV = p · W − (1 − p) · S
p = n/37 · W = S·(36/n − 1) · n = ꯌꯥꯎꯕ ꯃꯁꯤꯡꯁꯤꯡ · S = ꯊꯝꯂꯕ ꯁꯦꯜ

ꯔꯨꯂꯦꯠꯀꯤ ꯄꯦꯑꯥꯎꯠ ꯅꯤꯌꯝ, 36/n − 1, ꯍꯣꯡꯗꯣꯀꯄꯤꯌꯨ, ꯑꯗꯨꯒ n ꯃꯥꯡꯈꯤꯒꯅꯤ꯫ ꯃꯁꯤꯅꯤ ꯂꯥꯏꯟ ꯑꯃꯗ ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯋꯥꯔꯤ ꯄꯨꯝꯅꯃꯛ:

EV = (n/37)·S·(36/n − 1) − ((37−n)/37)·S
   = S·(36 − n − 37 + n)/37
   = −S/37

ꯇꯧꯔꯒ ꯌꯦꯡꯕꯤꯌꯨ: ꯔꯨꯂꯦꯠꯀꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯒꯤ ꯀꯦꯜꯀꯨꯂꯦꯇꯔ

ꯕꯦꯠ ꯑꯁꯤꯅ ꯃꯁꯤꯡ ꯀꯌꯥ ꯌꯥꯎꯕꯒꯦ ꯈꯅꯕꯤꯌꯨ꯫ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯃꯁꯨꯡ ꯄꯦꯑꯥꯎꯠ ꯍꯣꯡꯏ; ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯍꯣꯡꯗꯦ꯫

ꯌꯥꯎꯕ ꯃꯁꯤꯡ 1 · ꯄꯦꯑꯥꯎꯠ 35:1ꯊꯝꯂꯕ ꯁꯦꯜ $10
p(ꯃꯥꯏꯄꯥꯛꯄ)1/37 = 2.70%
ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯄꯦꯑꯥꯎꯠ+$350
ꯃꯥꯏꯊꯤꯕꯒꯤ ꯃꯃꯜ−$10
EV = p·W − (1−p)·S0.0270·$350 − 0.9730·$10
ꯐꯪꯒꯗꯕ ꯃꯃꯜꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ −$0.27 · −2.70%

ꯃꯇꯝ ꯆꯠꯄꯒ ꯂꯣꯌꯅꯅ ꯃꯁꯤ ꯀꯔꯝꯅ ꯎꯕꯒꯦ

$10 ꯒꯤ ꯑꯉꯥꯡꯕ ꯕꯦꯠ ꯑꯃꯒꯤ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩ, ꯁ꯭ꯄꯤꯟꯁꯤꯡ ꯍꯦꯅꯒꯠꯂꯛꯄꯒ ꯂꯣꯌꯅꯅ꯫ ꯍꯧꯔꯀꯐꯃꯗ ꯂꯥꯛꯅ ꯁꯥꯁꯟ ꯇꯧꯏ; ꯁꯦꯝꯄꯜ ꯍꯦꯅꯒꯠꯂꯛꯄꯒ ꯂꯣꯌꯅꯅ ꯆꯠꯂꯤꯕ ꯑꯦꯚꯔꯦꯖ ꯑꯁꯤ −$0.27 ꯒꯤ ꯃꯥꯏꯀꯩꯗ ꯂꯦꯞꯂꯛꯂꯤ꯫ ꯃꯁꯤꯅꯤ ꯀꯦꯁꯤꯅꯣꯅ ꯊꯥꯖꯕ ꯊꯝꯂꯤꯕ ꯃꯇꯝ ꯁꯥꯡꯅ ꯅꯛꯅꯕ꯫

EV −$0.27ꯁ꯭ꯄꯤꯟ 1ꯁ꯭ꯄꯤꯟ 2,000
ꯁ꯭ꯄꯤꯟ ꯑꯃꯒꯤ ꯃꯇꯨꯡꯗ ꯁ꯭ꯄꯤꯟ ꯑꯃꯥ, ꯆꯠꯂꯤꯕ ꯑꯦꯚꯔꯦꯖ ꯑꯁꯤ ꯍꯣꯡꯂꯛꯄ ꯂꯦꯞꯇꯨꯅ ꯖꯤꯔꯣꯒꯤ ꯈꯔꯥ ꯃꯈꯥꯗ ꯂꯦꯞꯂꯛꯂꯤ꯫

ꯌꯥꯝꯅ ꯊꯣꯀꯄ ꯑꯔꯥꯟꯕ ꯋꯥꯈꯂꯁꯤꯡ

“EV ꯅꯦꯒꯦꯇꯤꯕ ꯑꯣꯏꯕ ꯍꯥꯌꯕꯁꯤ ꯑꯩꯅ ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯃꯥꯏꯊꯤꯒꯅꯤ ꯍꯥꯌꯕꯅꯤ꯫”
ꯅꯠꯇꯦ꯫ ꯃꯁꯤꯅ ꯍꯥꯌꯔꯤꯕꯗꯤ ꯁꯦꯁꯟ ꯀꯌꯥꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯑꯁꯤ ꯃꯥꯡꯕꯅꯤ꯫ ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡꯃꯛ ꯌꯥꯝꯅ ꯈꯦꯠꯅꯩ, ꯑꯃꯁꯨꯡ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯒꯨꯝꯕ ꯚꯦꯌꯔꯤꯌꯦꯟꯁ ꯋꯥꯡꯕ ꯕꯦꯠꯁꯤꯡꯗ ꯍꯦꯟꯅꯥ ꯈꯦꯠꯅꯩ꯫
“ꯀꯦꯁꯤꯅꯣꯅ ꯃꯥꯏꯄꯥꯛꯅꯕ ꯃꯇꯝ ꯁꯥꯡꯅ ꯃꯊꯧ ꯇꯥꯏ꯫”
ꯀꯦꯁꯤꯅꯣꯒꯤ ꯑꯦꯖ ꯑꯁꯤ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯆꯠꯂꯤ; ꯃꯇꯝ ꯁꯥꯡꯅ ꯆꯠꯄꯅ ꯇꯧꯕꯗꯤ ꯃꯍꯩ ꯑꯗꯨ ꯂꯥꯎꯊꯣꯀꯄ ꯌꯥꯕ ꯑꯣꯏꯍꯟꯕꯅꯤ꯫ ꯁꯦꯁꯟ ꯑꯃꯈꯛꯇꯗꯤ ꯂꯥꯛꯅ ꯍꯦꯟꯅꯥ ꯄꯥꯉ꯭ꯒꯜ ꯂꯩ꯫
“ꯕꯦꯠ ꯈꯔꯒꯤ EV ꯑꯇꯣꯞꯄꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯐꯩ꯫”
ꯌꯨꯔꯣꯄꯤꯌꯟ ꯔꯨꯂꯦꯠꯇ ꯅꯠꯇꯦ, ꯑꯈꯟꯅꯕ ꯑꯃꯈꯛ ꯂꯩ: ꯂꯥ ꯄꯥꯔꯇꯥꯖ ꯅꯠꯔꯒ ꯑꯣꯡ ꯄ꯭ꯔꯤꯖꯣꯡꯒꯤ ꯃꯈꯥꯗ, ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡꯒꯤ ꯍꯥꯎꯁ ꯑꯦꯖ ꯃꯍꯧꯁꯥꯒꯤ ꯑꯣꯏꯕꯒꯤ ꯁꯔꯨꯛ ꯑꯍꯦꯟꯕ ꯈꯛꯇꯅꯤ꯫

ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

ꯁ꯭ꯄꯤꯟ ꯑꯃꯗ ꯊꯣꯀꯄ ꯅꯠꯇꯦ꯫ ꯃꯈꯣꯌ ꯄꯨꯝꯅꯃꯛꯀꯤ ꯑꯦꯚꯔꯦꯖꯅꯤ꯫

ꯁ꯭ꯄꯤꯟ ꯑꯃꯗ ꯊꯣꯀꯄ ꯅꯠꯇꯦ꯫ ꯃꯈꯣꯌ ꯄꯨꯝꯅꯃꯛꯀꯤ ꯑꯦꯚꯔꯦꯖꯅꯤ꯫