ᱨᱩᱞᱮᱴ ᱜᱚᱱᱤᱛ · ᱵᱮᱵᱷᱟᱨ · 8 ᱢᱤᱱᱤᱴ

ᱠᱮᱞᱤ ᱠᱨᱟᱭᱴᱮᱨᱤᱭᱚᱱ ᱟᱨ ᱨᱩᱞᱮᱴ

ᱠᱮᱞᱤ ᱠᱨᱟᱭᱴᱮᱨᱤᱭᱚᱱ ᱫᱚ ᱵᱟᱲᱛᱤ ᱢᱮᱱᱟᱜ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣᱤᱡ ᱮ ᱢᱮᱱᱟᱜ-ᱟ ᱡᱮ ᱛᱤᱱᱟᱹᱜ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱞᱟᱜᱟᱣ ᱞᱟᱹᱠᱛᱤ᱾ ᱨᱩᱞᱮᱴ ᱞᱟᱹᱜᱤᱫ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱛᱮᱞᱟ ᱥᱟᱯᱷᱟ: ᱪᱮᱫ ᱦᱚᱸ ᱵᱟᱝ᱾

ᱠᱷᱟᱴᱚ ᱛᱮᱞᱟ

ᱠᱮᱞᱤ ᱵᱟᱡᱤ ᱴᱟᱠᱟ = ᱵᱟᱲᱛᱤ / ᱚᱰᱥ᱾ ᱱᱮᱜᱮᱴᱤᱵᱷ ᱵᱟᱲᱛᱤ ᱨᱮ ᱯᱷᱚᱨᱢᱩᱞᱟ ᱫᱚ ᱱᱮᱜᱮᱴᱤᱵᱷ ᱦᱟᱹᱴᱤᱧ ᱮᱢᱟ, ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱢᱟᱱᱮ: ᱵᱟᱡᱤ ᱟᱞᱚᱢ ᱞᱟᱜᱟᱣᱟ᱾ ᱱᱚᱶᱟ ᱠᱨᱟᱭᱴᱮᱨᱤᱭᱚᱱ ᱫᱚ ᱱᱤᱛ ᱦᱚᱸ ᱵᱩᱡᱷᱟᱹᱣ ᱞᱟᱹᱜᱤᱫ ᱠᱟᱹᱢᱤ ᱨᱮ ᱦᱟᱜᱩᱜ-ᱟ ᱡᱮ ᱵᱟᱭᱟᱥ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱫᱚ ᱪᱮᱫᱟᱜ ᱚᱱᱟ ᱞᱮᱠᱟ ᱵᱟᱡᱤ ᱢᱟᱯ ᱠᱚ ᱵᱟᱪᱷᱟᱣ ᱞᱮᱫᱟ, ᱟᱨ ᱮᱴᱟᱜ ᱡᱚᱛᱚ ᱦᱚᱲ ᱫᱚ ᱪᱮᱫᱟᱜ ᱵᱟᱡᱮᱴ ᱞᱮᱠᱷᱟ ᱛᱮ ᱵᱟᱡᱤ ᱢᱟᱯ ᱵᱟᱪᱷᱟᱣ ᱞᱟᱹᱠᱛᱤᱭᱟ᱾

ᱠᱮᱞᱤ ᱦᱟᱹᱴᱤᱧ
f* = (bp − q) / b
ᱟᱨᱟᱜ ᱞᱟᱹᱜᱤᱫ
(1 × 18/37 − 19/37) / 1 = −1/37
ᱢᱟᱱᱮ
ᱪᱮᱫ ᱦᱚᱸ ᱵᱟᱡᱤ ᱟᱞᱚᱢ
1/30 ᱠᱷᱟᱱᱟ ᱞᱟᱹᱜᱤᱫ
ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ ≈ +0.6%

ᱠᱨᱟᱭᱴᱮᱨᱤᱭᱚᱱ

ᱡᱚᱱ ᱠᱮᱞᱤ (John Kelly) (1956) ᱫᱚ ᱠᱩᱠᱞᱤ ᱞᱮᱫᱟᱭ: ᱡᱟᱦᱟᱸ ᱡᱩᱣᱟᱲᱤ ᱴᱷᱮᱱ ᱵᱟᱲᱟᱭ ᱟᱠᱟᱱ ᱵᱟᱲᱛᱤ ᱢᱮᱱᱟᱜ-ᱟ, ᱩᱱᱤ ᱫᱚ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤᱴᱟᱠᱟᱠᱷᱮᱞ ᱯᱩᱸᱡᱤᱠᱷᱮᱞ ᱞᱟᱹᱜᱤᱫ ᱟᱞᱟᱜ ᱫᱚᱦᱚ ᱟᱠᱟᱱ ᱡᱚᱛᱚ ᱴᱟᱠᱟ᱾ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱥᱟᱢᱵᱷᱟᱞ ᱫᱚ ᱢᱮᱱᱮᱛ ᱢᱤᱫ ᱵᱟᱡᱤ ᱟᱨ ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱨᱮ ᱚᱱᱟ ᱠᱷᱚᱱ ᱛᱤᱱᱟᱹᱜ ᱡᱚᱠᱷᱤᱢ ᱨᱮ ᱫᱚᱦᱚᱭ ᱚᱱᱟ ᱴᱷᱟᱹᱣᱠᱟᱹ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ ᱡᱮᱞᱮᱧ ᱚᱠᱛᱚ ᱵᱟᱹᱲᱛᱤ ᱵᱷᱟᱹᱜᱤ ᱞᱟᱹᱜᱤᱫ ᱪᱮᱫ ᱞᱮᱠᱟ ᱵᱟᱡᱤ ᱢᱟᱯ ᱵᱟᱪᱷᱟᱣ ᱞᱟᱹᱠᱛᱤᱭᱟ? b ᱨᱮ 1 ᱵᱷᱩᱜᱛᱟᱱ ᱮᱢᱚᱜ ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ, ᱡᱤᱛ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟᱜᱚᱱᱤᱛᱥᱚᱢᱵᱷᱟᱵᱱᱟᱢᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, 0 ᱠᱷᱚᱱ 1 ᱟᱨᱵᱟᱝ 0% ᱠᱷᱚᱱ 100%᱾ ᱢᱤᱫ ᱮᱞ: 1/37 = 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → p ᱟᱨ ᱦᱟᱹᱱᱤ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ q = 1 − p ᱥᱟᱶ, ᱛᱮᱞᱟ ᱫᱚ: ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ f* = (bp − q) / b ᱦᱟᱹᱴᱤᱧ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱯᱮ᱾ f* ᱯᱚᱡᱤᱴᱤᱵᱷ ᱠᱷᱟᱱ ᱚᱱᱟ ᱦᱟᱹᱴᱤᱧ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ; ᱡᱤᱨᱚ ᱥᱮ ᱱᱮᱜᱮᱴᱤᱵᱷ ᱠᱷᱟᱱ ᱵᱟᱡᱤ ᱟᱞᱚᱢ᱾ ᱠᱮᱞᱤ ᱫᱚ ᱵᱮᱞ ᱞᱮᱵᱥ (Bell Labs) ᱨᱮ ᱠᱟᱹᱢᱤ ᱮ ᱠᱟᱹᱢᱤ ᱞᱮᱫᱟ, ᱟᱨ ᱩᱱᱤᱭᱟᱜ ᱚᱱᱚᱞ “A new interpretation of information rate” ᱫᱚ ᱥᱚᱢᱥᱭᱟ ᱠᱞᱚᱰ ᱥᱮᱱᱚᱱ (Claude Shannon) ᱨᱮᱭᱟᱜ ᱠᱷᱚᱵᱚᱨ ᱛᱮᱣᱨᱤ ᱨᱮ ᱫᱚᱦᱚ ᱞᱮᱫᱟᱭ: ᱡᱟᱦᱟᱸ ᱡᱩᱣᱟᱲᱤ ᱦᱩᱞᱟᱹᱢ ᱟᱠᱟᱱ ᱞᱟᱭᱤᱱ ᱛᱮ ᱥᱩᱞᱟᱹᱦ ᱮ ᱧᱟᱢᱟ, ᱱᱤᱭᱟᱭ ᱚᱰᱥ ᱨᱮ, ᱩᱱᱤ ᱫᱚ ᱵᱮᱥ ᱥᱮ ᱵᱮᱥ ᱚᱱᱟ ᱦᱟᱨ ᱛᱮ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱵᱟᱹᱲᱛᱤ ᱫᱟᱲᱮᱭᱟᱜ-ᱟᱭ ᱡᱟᱦᱟᱸ ᱦᱟᱨ ᱛᱮ ᱞᱟᱭᱤᱱ ᱫᱚ ᱠᱷᱚᱵᱚᱨ ᱤᱫᱤᱭᱟ᱾ 1961 ᱨᱮ ᱞᱤᱭᱳ ᱵᱽᱨᱮᱭᱢᱟᱱ (Leo Breiman) ᱫᱚ ᱯᱨᱚᱢᱟᱱ ᱞᱮᱫᱟᱭ ᱡᱮ ᱠᱮᱞᱤ ᱵᱟᱡᱤ ᱫᱚ ᱡᱮᱞᱮᱧ ᱚᱠᱛᱚ ᱨᱮ ᱡᱟᱦᱟᱱᱟᱜ ᱵᱷᱮᱜᱟᱨ ᱥᱴᱨᱮᱴᱮᱡᱤ ᱠᱷᱚᱱ ᱢᱟᱲᱟᱝ ᱛᱟᱦᱮᱸᱱᱟ ᱟᱨ ᱥᱮᱴ ᱟᱠᱟᱱ ᱡᱚᱥ ᱫᱚ ᱠᱚᱢ ᱵᱮᱥᱤ ᱥᱟᱱᱟᱢ ᱠᱷᱚᱱ ᱦᱩᱰᱤᱧ ᱚᱠᱛᱚ ᱨᱮ ᱥᱮᱴᱮᱨᱟ᱾

ᱢᱤᱫ ᱡᱩᱣᱟᱲᱤ ᱦᱩᱞᱟᱹᱢ ᱟᱠᱟᱱ ᱞᱟᱭᱤᱱ ᱛᱮ ᱥᱩᱞᱟᱹᱦ ᱮ ᱟᱸᱡᱚᱢᱟ ᱟᱨ ᱟᱡᱟᱜ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ ᱦᱟᱹᱴᱤᱧ ᱵᱟᱡᱤ ᱮ ᱞᱟᱜᱟᱣᱟ᱾

ᱨᱩᱞᱮᱴ ᱨᱮ ᱠᱮᱞᱤ ᱵᱟᱡᱤ

ᱟᱨᱟᱜᱵᱟᱡᱤᱟᱨᱟᱜ18 ᱟᱨᱟᱜ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱨᱩᱡᱽ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱞᱟᱹᱜᱤᱫ: b = 1, p = 18/37, q = 19/37; f* = (18/37 − 19/37)/1 = −1/37᱾ ᱥᱴᱨᱮᱴ ᱚᱯᱵᱟᱡᱤᱥᱴᱨᱮᱴ ᱚᱯᱢᱤᱫ ᱮᱞ, ᱵᱷᱩᱜᱛᱟᱱ 35:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱞᱟᱹᱜᱤᱫ: b = 35, p = 1/37, q = 36/37; f* = (35/37 − 36/37)/35 = −1/1295᱾ ᱡᱚᱛᱚ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱵᱟᱡᱤ ᱨᱮ ᱠᱮᱞᱤ ᱦᱟᱹᱴᱤᱧ ᱫᱚ ᱱᱮᱜᱮᱴᱤᱵᱷ ᱦᱩᱭᱩᱜ-ᱟ, ᱪᱮᱫᱟᱜ ᱥᱮ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱵᱟᱲᱛᱤ ᱱᱮᱜᱮᱴᱤᱵᱷ, ᱟᱨ ᱵᱟᱹᱲᱛᱤ ᱞᱟᱹᱜᱤᱫ ᱥᱟᱱᱟᱢ ᱠᱷᱚᱱ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱡᱤᱨᱚ᱾ ᱨᱩᱞᱮᱴ ᱨᱮ ᱠᱮᱞᱤ ᱵᱟᱡᱤ ᱫᱚ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱥᱟᱦᱴᱟ ᱨᱮᱭᱟᱜ ᱠᱟᱛᱷᱟ ᱜᱮ ᱵᱤᱫᱷᱤ ᱞᱮᱠᱟᱛᱮ ᱢᱮᱱᱟᱜ-ᱟ: ᱱᱮᱜᱮᱴᱤᱵᱷ ᱟᱸᱫᱟᱡᱽ ᱢᱮᱱᱟᱜ ᱵᱟᱡᱤ ᱫᱚ ᱡᱟᱦᱟᱸ ᱢᱟᱯ ᱨᱮ ᱦᱚᱸ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱵᱟᱝ ᱵᱟᱹᱲᱛᱤᱭᱟ᱾

ᱵᱟᱡᱤbpf* = (bp − q)/bᱢᱟᱱᱮ
ᱟᱨᱟᱜ, ᱭᱩᱨᱚᱯᱤᱭᱟᱱ118/37−0.027ᱵᱟᱡᱤ ᱟᱞᱚᱢ
ᱟᱨᱟᱜ, ᱞᱟ ᱯᱟᱨᱛᱟᱡᱽ118/37 (ᱡᱤᱨᱚ ᱨᱮ +½)−0.0135ᱵᱟᱡᱤ ᱟᱞᱚᱢ
ᱥᱴᱨᱮᱴ ᱚᱯ351/37−0.00077ᱵᱟᱡᱤ ᱟᱞᱚᱢ
1/30 ᱠᱷᱟᱱᱟ ᱨᱮ ᱥᱴᱨᱮᱴ ᱚᱯ (ᱵᱟᱭᱟᱥ)351/30+0.0057ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ 0.57% ᱵᱟᱡᱤ
1/25 ᱠᱷᱟᱱᱟ ᱨᱮ ᱥᱴᱨᱮᱴ ᱚᱯ351/25+0.0126ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ 1.26% ᱵᱟᱡᱤ

ᱚᱠᱟ ᱨᱮ ᱠᱮᱞᱤ ᱫᱚ ᱠᱟᱹᱢᱤ ᱞᱮᱫᱟ

ᱵᱟᱭᱟᱥ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱴᱷᱮᱱ ᱵᱟᱲᱛᱤ ᱛᱟᱦᱮᱸᱫ ᱠᱟᱱᱟ ᱟᱨ ᱵᱟᱡᱤ ᱢᱟᱯ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱥᱭᱟ ᱦᱚᱸ᱾ ᱡᱮᱜᱟᱨ (Jagger), ᱜᱟᱨᱥᱤᱭᱟ-ᱯᱮᱞᱟᱭᱳ (García-Pelayo) ᱯᱟᱨᱤᱣᱟᱨ ᱟᱨ ᱭᱩᱰᱤᱢᱚᱱ (Eudaemons) ᱫᱚ ᱡᱚᱛᱚ ᱠᱚ ᱴᱷᱟᱹᱣᱠᱟᱹ ᱞᱟᱹᱠᱛᱤ ᱞᱮᱱᱟ ᱡᱮ ᱢᱟᱯ ᱟᱠᱟᱱ ᱵᱟᱲᱛᱤ ᱨᱮ ᱛᱤᱱᱟᱹᱜ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱦᱩᱭᱩᱜ-ᱟ; ᱠᱚᱢ ᱵᱟᱡᱤ ᱫᱚ ᱵᱟᱲᱛᱤ ᱮ ᱱᱟᱥᱴᱟᱣᱟ, ᱵᱮᱥᱤ ᱵᱟᱡᱤ ᱫᱚ ᱵᱟᱲᱛᱤ ᱧᱮᱞᱚᱜ ᱞᱟᱦᱟ ᱨᱮ ᱯᱩᱸᱡᱤ ᱢᱩᱪᱟᱹᱫ ᱨᱮᱭᱟᱜ ᱡᱚᱠᱷᱤᱢ ᱮ ᱟᱹᱜᱩᱭᱟ᱾ 30 ᱫᱷᱟᱣ ᱨᱮ 1 ᱫᱷᱟᱣ ᱦᱤᱴᱚᱜ ᱠᱷᱟᱱᱟᱥᱟᱡ ᱥᱟᱢᱟᱱᱠᱷᱟᱱᱟᱨᱚᱴᱚᱨ ᱨᱮᱭᱟᱜ 37 ᱮᱞ ᱚᱞ ᱠᱷᱟᱱᱟ ᱠᱷᱚᱱ ᱢᱤᱫ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱞᱚᱴ, ᱠᱟᱯ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱞᱟᱹᱜᱤᱫ, ᱠᱮᱞᱤ ᱫᱚ ᱢᱮᱱᱟᱜ-ᱟ ᱡᱮ ᱚᱱᱟ ᱮᱞ ᱨᱮ ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ 0.57%: $10,000 ᱥᱟᱶ ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱠᱚᱢ ᱵᱮᱥᱤ $57, ᱟᱨ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱵᱟᱹᱲᱛᱤ ᱫᱚ ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱠᱚᱢ ᱵᱮᱥᱤ 0.054%, ᱥᱮ 1,000 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ×1.7᱾ ᱟᱣᱥᱚᱛ ᱞᱟᱵᱷ ᱫᱚ ᱚᱱᱟ ᱠᱷᱚᱱ ᱵᱟᱨ ᱫᱷᱟᱣ, ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ 0.11%, ᱢᱮᱱᱠᱷᱟᱱ ᱠᱮᱞᱤ ᱫᱚ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱥᱮᱫ ᱧᱮᱞᱟ, ᱟᱣᱥᱚᱛ ᱥᱮᱫ ᱫᱚ ᱵᱟᱝ, ᱪᱮᱫᱟᱜ ᱥᱮ ᱟᱣᱥᱚᱛ ᱫᱚ ᱠᱚᱭᱢᱟ ᱵᱷᱟᱜᱚ ᱫᱟᱣ ᱠᱚ ᱦᱩᱯᱩᱞ ᱪᱟᱞᱟᱣ ᱠᱟᱱᱟ᱾ ᱟᱫᱷᱟ-ᱠᱮᱞᱤ ᱫᱚ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱵᱮᱵᱷᱟᱨ ᱵᱟᱪᱷᱟᱣ ᱠᱟᱱᱟ, ᱪᱮᱫᱟᱜ ᱥᱮ ᱵᱟᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱫᱚ ᱵᱟᱝ ᱥᱟᱹᱨᱤ ᱜᱮ᱾

ᱥᱴᱨᱮᱴ ᱚᱯ ᱨᱮ ᱠᱮᱞᱤ ᱵᱟᱡᱤ ᱴᱟᱠᱟ, ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ %, ᱠᱷᱟᱱᱟ ᱨᱮᱭᱟᱜ ᱥᱟᱹᱨᱤ ᱦᱟᱨ ᱞᱮᱠᱷᱟ ᱛᱮ%
1/37 (ᱱᱤᱭᱟᱭ)
0% · ᱵᱟᱡᱤ ᱟᱞᱚᱢ
1/35
0.08%
1/33
0.26%
1/30
0.57%
1/25
1.26%
1/20
2.0%
%
012.0%
ᱢᱟᱨᱟᱝ ᱵᱟᱭᱟᱥ ᱨᱮ ᱦᱚᱸ ᱦᱩᱰᱤᱧ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱞᱟᱹᱠᱛᱤᱭᱟ: ᱵᱷᱩᱜᱛᱟᱱ ᱫᱚ ᱡᱮᱞᱮᱧ ᱟᱨ ᱣᱮᱨᱤᱭᱮᱱᱥ ᱫᱚ ᱵᱮᱥᱤ᱾

ᱧᱩᱛᱩᱢ ᱨᱩᱞᱮᱴ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚᱭᱩᱰᱮᱢᱚᱱᱥ

ᱥᱟᱫᱷᱟᱨᱚᱬ ᱟᱨ ᱟᱣᱥᱚᱛ

ᱥᱟᱫᱷᱟᱨᱚᱬ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱟᱨ ᱟᱣᱥᱚᱛ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱛᱟᱞᱟ ᱨᱮᱭᱟᱜ ᱯᱷᱟᱨᱟᱠ ᱫᱚ ᱢᱟᱨᱟᱝ᱾ 25 ᱫᱷᱟᱣ ᱨᱮ 1 ᱫᱷᱟᱣ ᱦᱤᱴᱚᱜ ᱢᱤᱫ ᱠᱷᱟᱱᱟ ᱦᱟᱛᱟᱣ ᱯᱮ, 44% ᱵᱟᱲᱛᱤ, ᱡᱟᱦᱟᱸ ᱮᱞ ᱫᱚ ᱛᱷᱚᱨᱯ (Thorp) ᱟᱡᱟᱜ ᱥᱟᱡ ᱞᱟᱹᱜᱤᱫ ᱮ ᱮᱢ ᱞᱮᱫᱟ᱾ ᱠᱮᱞᱤ ᱫᱚ ᱚᱱᱟ ᱨᱮ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ 1.26% ᱵᱟᱡᱤ ᱮ ᱞᱟᱜᱟᱣᱟ᱾ 1,000 ᱜᱷᱩᱨᱟᱹᱣ ᱛᱟᱭᱚᱢ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱫᱚ ᱠᱚᱢ ᱵᱮᱥᱤ 11.5 ᱫᱷᱟᱣ ᱵᱟᱹᱲᱛᱤ ᱮᱱᱟ, ᱢᱮᱱᱠᱷᱟᱱ ᱟᱣᱥᱚᱛ ᱫᱚ, ᱠᱚᱭᱢᱟ ᱟᱹᱰᱤ ᱵᱷᱟᱜᱚ ᱫᱟᱣ ᱛᱮ ᱪᱮᱛᱟᱱ ᱟᱹᱜᱩ ᱟᱠᱟᱱ, ᱠᱚᱢ ᱵᱮᱥᱤ 249 ᱫᱷᱟᱣ ᱵᱟᱹᱲᱛᱤ ᱮᱱᱟ᱾ ᱠᱮᱞᱤ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱵᱟᱡᱤ ᱫᱚ ᱟᱣᱥᱚᱛ ᱵᱟᱹᱲᱛᱤᱭᱟ ᱟᱨ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱨᱮᱡᱟᱞᱴ ᱠᱚᱢᱟ: ᱠᱮᱞᱤ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱵᱟᱨ ᱫᱷᱟᱣ ᱨᱮ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱫᱚ ᱵᱟᱨ ᱫᱷᱟᱣ ᱜᱮ ᱦᱩᱭᱩᱜ-ᱟ, ᱟᱨ ᱠᱮᱞᱤ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱟᱹᱲᱟᱭ ᱫᱷᱟᱣ ᱨᱮ ᱫᱚ ᱚᱱᱟ ᱦᱩᱰᱤᱧᱚᱜ-ᱟ, ᱡᱩᱫᱤ ᱦᱚᱸ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱨᱮ ᱱᱤᱛ ᱦᱚᱸ 44% ᱵᱟᱲᱛᱤ ᱢᱮᱱᱟᱜ-ᱟ᱾ ᱠᱚᱢ ᱵᱟᱡᱤ ᱨᱮ ᱦᱟᱹᱱᱤ ᱫᱚ ᱦᱩᱰᱤᱧ: ᱟᱫᱷᱟ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱵᱟᱹᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱠᱚᱢ ᱵᱮᱥᱤ ᱯᱮ ᱦᱟᱹᱴᱤᱧ ᱨᱮᱭᱟᱜ ᱯᱩᱱ ᱦᱟᱹᱴᱤᱧ ᱫᱚᱦᱚᱭᱟ᱾

ᱵᱟᱡᱤ ᱴᱟᱠᱟ, ᱠᱮᱞᱤ ᱨᱮᱭᱟᱜ ᱦᱟᱹᱴᱤᱧᱵᱟᱡᱤ ᱴᱟᱠᱟ, ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ %1,000 ᱜᱷᱩᱨᱟᱹᱣ ᱛᱟᱭᱚᱢ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ
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 ᱫᱷᱟᱣ ᱨᱮ 1 ᱫᱷᱟᱣ ᱦᱤᱴᱚᱜ ᱢᱤᱫ ᱠᱷᱟᱱᱟ, 35 ᱨᱮ 1 ᱵᱷᱩᱜᱛᱟᱱ᱾ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱢᱟᱱᱮ ᱢᱤᱰᱤᱭᱟᱱ: e ᱨᱮᱭᱟᱜ ᱯᱟᱣᱟᱨ, ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮᱭᱟᱜ ᱵᱟᱹᱲᱛᱤ ᱨᱮᱭᱟᱜ 1,000 ᱫᱷᱟᱣ᱾

ᱵᱟᱲᱛᱤ ᱫᱚ ᱟᱸᱫᱟᱡᱽ ᱜᱮ ᱠᱷᱟᱱ

ᱠᱮᱞᱤ ᱫᱚ ᱢᱮᱱᱮ ᱫᱚᱦᱚᱭᱟ ᱡᱮ ᱵᱟᱲᱛᱤ ᱫᱚ ᱵᱟᱲᱟᱭ ᱟᱠᱟᱱᱟ᱾ ᱴᱮᱵᱩᱞ ᱨᱮ ᱫᱚ ᱚᱱᱟ ᱟᱸᱫᱟᱡᱽ ᱜᱮ ᱦᱩᱭᱩᱜ-ᱟ, ᱟᱨ ᱟᱸᱫᱟᱡᱽ ᱫᱚ ᱡᱟᱹᱥᱛᱤ ᱛᱮ ᱟᱹᱰᱤ ᱵᱮᱥᱤ ᱜᱮ ᱦᱩᱭᱩᱜ-ᱟ᱾ ᱮᱯᱥᱴᱟᱭᱤᱱ (Epstein) ᱨᱮᱭᱟᱜ ᱫᱟᱹᱭᱠᱟᱹ, ᱛᱷᱚᱨᱯ ᱨᱮᱭᱟᱜ 44% ᱪᱮᱛᱟᱱ ᱵᱮᱱᱟᱣ ᱟᱠᱟᱱ, ᱫᱚ ᱢᱤᱫ ᱮᱞ ᱠᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱫᱚ ᱰᱚᱵᱚᱞ ᱡᱤᱨᱚᱪᱟᱠᱟᱡᱤᱨᱚᱢᱤᱫᱜᱮ ᱦᱟᱹᱨᱭᱟᱹᱲ ᱠᱷᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ, ᱰᱚᱡᱮᱱ ᱟᱨᱵᱟᱝ ᱠᱚᱞᱚᱢ ᱵᱟᱡᱤ ᱵᱟᱭ ᱠᱚᱵᱷᱟᱨᱟ; ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱢᱩᱞ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱤᱝᱜᱚᱞ ᱡᱤᱨᱚ, 0᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱪᱟᱠᱟ ᱨᱮᱭᱟᱜ 1,225 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ 49 ᱫᱷᱟᱣ ᱦᱤᱴ ᱞᱮᱱᱟ: 25 ᱫᱷᱟᱣ ᱨᱮ 1 ᱫᱷᱟᱣ, 44% ᱵᱟᱲᱛᱤ, 1.26% ᱠᱮᱞᱤ ᱵᱟᱡᱤ ᱴᱟᱠᱟ᱾ ᱢᱮᱱᱠᱷᱟᱱ ᱴᱷᱤᱠ ᱰᱚᱵᱚᱞ ᱡᱤᱨᱚ ᱪᱟᱠᱟ ᱨᱮ 38 ᱮᱞ ᱢᱮᱱᱟᱜ-ᱟ, ᱟᱨ ᱩᱱᱠᱩ ᱛᱟᱞᱟ ᱠᱷᱚᱱ ᱥᱟᱱᱟᱢ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱦᱤᱴᱚᱜ ᱮᱞ ᱫᱚ 1,225 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ 49 ᱥᱮ ᱵᱮᱥᱤ ᱦᱤᱴ ᱫᱚ ᱟᱨᱮ ᱫᱷᱟᱣ ᱨᱮ ᱠᱚᱢ ᱵᱮᱥᱤ ᱢᱤᱫ ᱫᱷᱟᱣ ᱦᱩᱭᱩᱜ-ᱟ᱾ ᱡᱟᱦᱟᱸ ᱨᱮᱠᱚᱨᱰ ᱨᱮ ᱦᱚᱸ ᱥᱟᱱᱟᱢ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱦᱤᱴᱚᱜ ᱮᱞ ᱫᱚ ᱚᱱᱟ ᱜᱮ ᱠᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱫᱚ ᱵᱷᱟᱜᱚ ᱵᱮᱥᱤ ᱜᱚᱲᱚ ᱟᱠᱟᱫᱟ, ᱚᱱᱟᱛᱮ ᱥᱟᱹᱨᱤ ᱵᱟᱭᱟᱥ ᱠᱷᱟᱱᱟ ᱦᱚᱸ ᱨᱮᱠᱚᱨᱰ ᱨᱮ ᱟᱡᱟᱜ ᱥᱟᱹᱨᱤ ᱠᱷᱚᱱ ᱵᱮᱥ ᱧᱮᱞᱚᱜ-ᱟ: ᱱᱚᱶᱟ ᱫᱚ ᱡᱤᱛᱤᱡ ᱨᱮᱭᱟᱜ ᱥᱟᱯ (winner’s curse) ᱠᱟᱱᱟ᱾ ᱡᱩᱫᱤ ᱚᱱᱟ ᱠᱷᱟᱱᱟ ᱫᱚ ᱥᱟᱹᱨᱤ ᱛᱮ ᱵᱟᱭᱟᱥ ᱵᱟᱝ ᱠᱷᱟᱱ, ᱠᱮᱞᱤ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱟᱣᱥᱚᱛ ᱛᱮ 5.26% ᱦᱟᱹᱱᱤ ᱮᱢᱚᱜ ᱵᱟᱡᱤ ᱜᱮ ᱠᱟᱱᱟ᱾ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱛᱮᱞᱟ ᱫᱚ: ᱠᱮᱞᱤ ᱨᱮᱭᱟᱜ ᱦᱟᱹᱴᱤᱧ ᱜᱮ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱯᱮ, ᱟᱨ ᱱᱟᱣᱟ ᱨᱮᱠᱚᱨᱰ ᱨᱮ ᱦᱚᱸ ᱵᱟᱲᱛᱤ ᱛᱟᱦᱮᱸᱱ ᱦᱟᱹᱵᱤᱡ ᱞᱮᱠᱷᱟ ᱞᱟᱜᱟᱣ ᱯᱮ (ᱧᱮᱞ ᱯᱮ ᱨᱩᱞᱮᱴ ᱪᱟᱠᱟ ᱵᱟᱭᱟᱥ ᱪᱮᱫ ᱞᱮᱠᱟ ᱧᱟᱢ ᱦᱩᱭᱩᱜ-ᱟ)᱾

ᱵᱟᱲᱛᱤ ᱢᱮᱱᱟᱜ ᱦᱚᱲ

ᱵᱟᱲᱛᱤ ᱵᱟᱲᱟᱭ ᱟᱨ ᱚᱱᱟ ᱵᱮᱥ ᱞᱮᱠᱟᱛᱮ ᱵᱮᱵᱷᱟᱨ ᱫᱚ ᱢᱤᱫ ᱜᱮ ᱵᱟᱝ᱾ ᱦᱟᱜᱷᱟᱱᱤ (Haghani) ᱟᱨ ᱰᱤᱣᱤ (Dewey) (2016) ᱫᱚ 61 ᱦᱚᱲ ᱠᱚ ᱢᱤᱫ ᱢᱤᱫ ᱦᱚᱲ $25 ᱠᱤᱱ ᱮᱢ ᱞᱮᱫᱟ ᱠᱚ, ᱟᱫᱷᱟ ᱜᱷᱟᱸᱴᱟ ᱦᱟᱹᱵᱤᱡ ᱢᱤᱫ ᱥᱤᱠᱟᱹ ᱨᱮ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱞᱟᱹᱜᱤᱫ, ᱡᱟᱦᱟᱸ ᱵᱟᱵᱚᱛ ᱠᱚ ᱞᱟᱹᱭ ᱞᱮᱫᱟ ᱡᱮ 60% ᱚᱠᱛᱚ ᱨᱮ ᱦᱮᱰ ᱩᱫᱩᱜᱚᱜ-ᱟ, ᱟᱨ ᱡᱤᱛ ᱫᱚ $250 ᱨᱮ ᱛᱷᱤᱨ ᱛᱟᱦᱮᱸᱱᱟ (ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱫᱚ ᱚᱱᱟ ᱥᱤᱢᱟᱹ ᱥᱮᱴᱮᱨ ᱛᱟᱭᱚᱢ ᱜᱮ ᱠᱚ ᱵᱟᱰᱟᱭ ᱞᱮᱫᱟ)᱾ ᱠᱮᱞᱤ ᱫᱚ ᱢᱮᱱᱟᱜ-ᱟ ᱡᱚᱛᱚ ᱫᱷᱟᱣ ᱦᱮᱰ ᱨᱮ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ 20% ᱵᱟᱡᱤ, ᱟᱨ ᱚᱞᱤᱭᱟᱹ ᱠᱚ ᱟᱸᱫᱟᱡᱽ ᱠᱚ ᱞᱮᱫᱟ ᱡᱮ 10–20% ᱨᱮᱭᱟᱜ ᱛᱷᱤᱨ ᱵᱟᱡᱤ ᱫᱚ ᱠᱚᱢ ᱵᱮᱥᱤ 95% ᱚᱠᱛᱚ ᱨᱮ ᱥᱤᱢᱟᱹ ᱥᱮᱴᱮᱨᱟ᱾ ᱠᱷᱟᱹᱞᱤ 21% ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱥᱮᱴᱮᱨ ᱞᱮᱱᱟ᱾ 28% ᱫᱚ ᱡᱚᱛᱚ ᱠᱚ ᱦᱟᱨᱟᱣ ᱞᱮᱫᱟ, 61 ᱠᱷᱚᱱ 18 ᱫᱚ ᱢᱤᱫ ᱩᱪᱷᱞᱟᱹᱣ ᱨᱮ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱠᱚ ᱞᱟᱜᱟᱣ ᱞᱮᱫᱟ, ᱠᱚᱢ ᱵᱮᱥᱤ ᱯᱮ ᱦᱟᱹᱴᱤᱧ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱦᱟᱹᱴᱤᱧ ᱫᱚ ᱮᱦᱚᱵ ᱨᱮᱭᱟᱜ $25 ᱠᱷᱚᱱ ᱠᱚᱢ ᱨᱮ ᱠᱚ ᱪᱟᱵᱟ ᱞᱮᱫᱟ, ᱟᱨ ᱟᱣᱥᱚᱛ ᱵᱷᱩᱜᱛᱟᱱᱴᱟᱠᱟᱵᱷᱩᱜᱛᱟᱱᱡᱤᱛ ᱵᱟᱡᱤ ᱪᱮᱫ ᱨᱩᱣᱟᱹᱲᱟ, ᱨᱩᱣᱟᱹᱲ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱪᱮᱛᱟᱱ “X ᱨᱮ 1” ᱞᱮᱠᱟ ᱨᱚᱲᱚᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ $91 ᱛᱟᱦᱮᱸᱱᱟ᱾ 61 ᱠᱷᱚᱱ ᱠᱷᱟᱹᱞᱤ ᱢᱚᱬᱮ ᱦᱚᱲ ᱜᱮ ᱠᱮᱞᱤ ᱠᱨᱟᱭᱴᱮᱨᱤᱭᱚᱱ ᱵᱟᱵᱚᱛ ᱟᱸᱡᱚᱢ ᱟᱠᱟᱫ ᱛᱟᱦᱮᱸᱫ ᱠᱚᱭ᱾ ᱵᱟᱲᱛᱤ ᱛᱟᱦᱮᱸᱱ ᱠᱷᱟᱱ, ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱢᱟᱯ ᱜᱮ ᱴᱷᱟᱹᱣᱠᱟᱹᱣᱟ ᱡᱮ ᱟᱯᱮ ᱚᱱᱟ ᱫᱚᱦᱚ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ ᱥᱮ ᱵᱟᱝ; ᱵᱟᱲᱛᱤ ᱵᱟᱹᱱᱩᱜ ᱠᱷᱟᱱ, ᱡᱮᱞᱮᱠᱟ ᱴᱷᱤᱠ ᱪᱟᱠᱟ ᱨᱮ, ᱡᱟᱦᱟᱸ ᱢᱟᱯ ᱦᱚᱸ ᱵᱟᱝ ᱜᱚᱲᱚᱭᱟ᱾

ᱢᱤᱫ ᱠᱷᱮᱞᱚᱸᱰ ᱢᱤᱫ ᱩᱪᱷᱞᱟᱹᱣ ᱨᱮ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱮ ᱞᱟᱜᱟᱣᱟ, ᱢᱮᱱᱠᱷᱟᱱ ᱩᱱᱤᱭᱟᱜ ᱯᱟᱲᱚᱥᱤ ᱫᱚ ᱦᱩᱰᱤᱧ ᱦᱟᱹᱴᱤᱧ ᱜᱮ ᱵᱟᱡᱤ ᱮ ᱞᱟᱜᱟᱣᱟ᱾

ᱚᱱᱟ ᱵᱚᱫᱚᱞ ᱛᱮ ᱪᱮᱫ ᱵᱮᱵᱷᱟᱨ ᱦᱩᱭᱩᱜ-ᱟ

ᱵᱟᱲᱛᱤ ᱵᱟᱹᱱᱩᱜ ᱠᱷᱟᱱ, ᱵᱟᱡᱤ ᱢᱟᱯ ᱫᱚ ᱵᱟᱡᱮᱴ ᱨᱮᱭᱟᱜ ᱠᱩᱠᱞᱤ ᱠᱟᱱᱟ, ᱵᱟᱹᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱫᱚ ᱵᱟᱝ: ᱵᱟᱡᱤ ᱴᱟᱠᱟ = ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱟᱯᱮ ᱛᱤᱱᱟᱹᱜ ᱠᱷᱚᱨᱚᱪ ᱥᱟᱱᱟᱭ ᱠᱟᱱᱟ ᱯᱮ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱢᱤᱫ ᱜᱷᱟᱸᱴᱟ ᱨᱮᱭᱟᱜ ᱵᱟᱡᱮᱴ ᱟᱨ ᱴᱮᱵᱩᱞ ᱨᱮᱭᱟᱜ ᱞᱚᱜᱚᱱ ᱠᱷᱚᱱ ᱦᱤᱥᱟᱹᱵ ᱦᱩᱭᱩᱜ-ᱟ (ᱨᱩᱞᱮᱴ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱥᱟᱢᱵᱷᱟᱞ ᱥᱟᱦᱴᱟ)᱾ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱠᱷᱮᱞᱚᱸᱰ ᱞᱟᱹᱜᱤᱫ ᱠᱮᱞᱤ ᱨᱮᱭᱟᱜ ᱮᱢ ᱫᱚ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱥᱟᱯᱷᱟ ᱛᱮᱞᱟ: ᱡᱤᱨᱚ᱾ ᱡᱤᱨᱚ ᱠᱷᱚᱱ ᱪᱮᱛᱟᱱ ᱡᱟᱦᱟᱸ ᱵᱟᱡᱤ ᱟᱯᱮ ᱞᱟᱜᱟᱣᱟ ᱯᱮ, ᱚᱱᱟ ᱫᱚ ᱠᱷᱮᱞ ᱨᱮᱭᱟᱜ ᱫᱟᱢ ᱠᱟᱱᱟ, ᱟᱯᱮ ᱛᱮ ᱵᱟᱪᱷᱟᱣ ᱟᱠᱟᱱ, ᱡᱟᱦᱟᱱᱟᱜ ᱯᱷᱚᱨᱢᱩᱞᱟ ᱛᱮ ᱵᱮᱥ ᱵᱮᱱᱟᱣ ᱟᱠᱟᱱ ᱫᱚ ᱵᱟᱝ᱾

ᱦᱟᱹᱴᱤᱧ ᱠᱮᱞᱤ ᱟᱨ “ᱴᱟᱠᱟ ᱥᱟᱢᱵᱷᱟᱞ” ᱵᱟᱵᱚᱛ ᱢᱤᱫ ᱠᱟᱛᱷᱟ

“ᱨᱩᱞᱮᱴ ᱞᱟᱹᱜᱤᱫ ᱠᱮᱞᱤ” ᱧᱩᱛᱩᱢ ᱛᱮ ᱟᱠᱤᱨᱤᱧ ᱥᱤᱥᱴᱮᱢ ᱡᱟᱦᱟᱸ ᱫᱚ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱨᱮ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ ᱛᱷᱤᱨ ᱯᱟᱨᱥᱮᱱᱴ ᱠᱚ ᱞᱟᱹᱭᱟ, ᱚᱱᱟ ᱫᱚ ᱦᱩᱰᱤᱧᱚᱜ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱥᱟᱶ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤᱥᱴᱨᱮᱴᱮᱡᱤᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱡᱚᱛᱚ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱱᱚᱶᱟ ᱥᱟᱶ ᱛᱩᱞᱟᱹᱣᱚᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱜᱮ ᱠᱟᱱᱟ᱾ ᱩᱱᱠᱩ ᱫᱚ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱦᱤᱥᱟᱹᱵᱴᱟᱠᱟᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱦᱤᱥᱟᱹᱵᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱟᱨᱵᱟᱝ ᱚᱠᱛᱚ ᱨᱮ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ, ᱫᱚᱦᱲᱟ ᱞᱟᱜᱟᱣ ᱡᱤᱛ ᱴᱟᱠᱟ ᱥᱮᱞᱮᱫ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱦᱮᱱᱰᱮᱞ, ᱮᱠᱥᱚᱱ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ 2.70% ᱠᱚ ᱦᱟᱨᱟᱣᱟ, ᱟᱨ ᱦᱟᱨᱟᱣ ᱡᱚᱠᱷᱚᱱ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱦᱩᱰᱤᱧᱚᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱯᱩᱸᱡᱤ ᱢᱩᱪᱟᱹᱫ ᱫᱚ ᱞᱟᱦᱟᱭ ᱠᱚ ᱵᱮᱱᱟᱣᱟ, ᱵᱟᱝ ᱦᱩᱭᱩᱜ ᱞᱮᱠᱟ ᱫᱚ ᱵᱟᱝ᱾ ᱵᱟᱡᱮᱴ ᱡᱮᱞᱮᱧ ᱚᱠᱛᱚ ᱫᱚᱦᱚ ᱞᱟᱹᱜᱤᱫ ᱱᱚᱶᱟ ᱫᱚ ᱴᱷᱤᱠ ᱦᱚᱨᱟ ᱠᱟᱱᱟ; ᱢᱮᱱᱠᱷᱟᱱ ᱱᱚᱶᱟ ᱫᱚ ᱠᱮᱞᱤ ᱫᱚ ᱵᱟᱝ, ᱠᱮᱞᱤ ᱫᱚ ᱛᱷᱤᱨ ᱞᱟᱹᱜᱤᱫ ᱮ ᱢᱮᱱ ᱛᱟᱦᱮᱸᱱᱟ᱾

ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤ ᱨᱩᱞᱮᱴ ᱥᱴᱨᱮᱴᱮᱡᱤ

ᱯᱷᱚᱨᱢᱩᱞᱟ

f* = (b·p − q) / b
ᱟᱨᱟᱜ: f* = −1/37 · ᱥᱴᱨᱮᱴ ᱚᱯ: f* = −1/1295
r ᱦᱟᱨ ᱨᱮ ᱵᱟᱭᱟᱥ ᱠᱷᱟᱱᱟ: f* = (35r − (1 − r)) / 35

ᱠᱩᱠᱞᱤ ᱠᱚ

ᱠᱮᱞᱤ ᱫᱚ ᱪᱮᱫ ᱡᱟᱦᱟᱸ ᱚᱠᱛᱚ ᱨᱩᱞᱮᱴ ᱨᱮ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱞᱟᱹᱜᱤᱫ ᱮ ᱢᱮᱱᱟ?

ᱠᱷᱟᱹᱞᱤ ᱵᱟᱭᱟᱥ ᱪᱟᱠᱟᱞᱮᱵᱵᱟᱭᱟᱥ ᱪᱟᱠᱟᱢᱤᱫ ᱪᱟᱠᱟ ᱡᱟᱦᱟᱸ ᱨᱮᱭᱟᱜ ᱦᱟᱛ ᱫᱚᱥ ᱛᱮ ᱛᱤᱱᱟᱹᱜ ᱜᱟᱱ ᱠᱷᱟᱱᱟ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ 1/37 ᱠᱷᱚᱱ ᱵᱟᱹᱲᱛᱤ᱾ ᱟᱹᱰᱤ ᱠᱚᱢ ᱧᱟᱢᱚᱜ-ᱟ, ᱦᱟᱡᱟᱨ ᱦᱟᱡᱟᱨ ᱚᱞ ᱟᱠᱟᱱ ᱜᱷᱩᱨᱟᱹᱣ ᱛᱮ ᱜᱮ ᱧᱟᱢ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱥᱮ ᱚᱠᱛᱚ ᱥᱟᱡ ᱠᱷᱚᱱ ᱢᱟᱯ ᱟᱠᱟᱱ ᱵᱟᱲᱛᱤ ᱛᱟᱦᱮᱸᱱ ᱠᱷᱟᱱ᱾ ᱴᱷᱤᱠ ᱪᱟᱠᱟ ᱨᱮ ᱫᱚ ᱵᱟᱝ᱾

ᱟᱫᱷᱟ-ᱠᱮᱞᱤ ᱪᱮᱫᱟᱜ?

ᱪᱮᱫᱟᱜ ᱥᱮ ᱵᱟᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱨᱮ ᱵᱷᱩᱞ ᱢᱮᱱᱟᱜ-ᱟ, ᱟᱨ ᱵᱮᱥᱤ ᱵᱟᱡᱤ ᱫᱚ ᱠᱚᱢ ᱵᱟᱡᱤ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱜᱟᱨᱟᱝ᱾ ᱟᱫᱷᱟ-ᱠᱮᱞᱤ ᱫᱚ ᱣᱮᱨᱤᱭᱮᱱᱥᱜᱚᱱᱤᱛᱣᱮᱨᱤᱭᱮᱱᱥᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱜᱷᱮᱨᱟᱣ ᱨᱮᱡᱟᱞᱴ ᱛᱤᱱᱟᱹᱜ ᱯᱟᱥᱱᱟᱣᱚᱜ-ᱟ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱥᱟᱯᱲᱟᱣ᱾ ᱥᱴᱨᱮᱴ ᱚᱯ ᱞᱟᱹᱜᱤᱫ ᱵᱟᱹᱲᱛᱤ, ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ ᱯᱩᱱ ᱦᱟᱹᱴᱤᱧ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱦᱟᱹᱴᱤᱧ ᱨᱮ ᱵᱟᱹᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱯᱩᱱ ᱦᱟᱹᱴᱤᱧ ᱨᱮᱭᱟᱜ ᱯᱮ ᱦᱟᱹᱴᱤᱧ ᱮᱢᱟ᱾

ᱠᱮᱞᱤ ᱟᱨ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱥᱟᱢᱵᱷᱟᱞ ᱫᱚ ᱢᱤᱫ ᱜᱮ ᱥᱮ?

ᱵᱟᱝ᱾ ᱠᱮᱞᱤ ᱫᱚ ᱵᱟᱲᱛᱤ ᱛᱟᱦᱮᱸᱱ ᱠᱷᱟᱱ ᱵᱟᱹᱲᱛᱤ ᱮ ᱵᱮᱥᱟᱭᱟ᱾ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱥᱟᱢᱵᱷᱟᱞ ᱫᱚ ᱵᱟᱲᱛᱤ ᱵᱟᱹᱱᱩᱜ ᱠᱷᱟᱱ ᱠᱷᱚᱨᱚᱪ ᱥᱟᱢᱵᱷᱟᱞᱟ᱾

ᱜᱚᱱᱤᱛ ᱥᱟᱶ ᱨᱟᱹᱥᱠᱟᱹ

ᱱᱚᱶᱟ ᱠᱚ ᱯᱩᱭᱞᱩ ᱟᱯᱮ ᱛᱮ ᱠᱩᱨᱩᱢᱩᱴᱩ ᱯᱮ᱾ ᱢᱤᱫ ᱢᱤᱫ ᱥᱚᱢᱟᱫᱷᱟᱱ ᱫᱚ ᱩᱠᱩ ᱢᱮᱱᱟᱜ-ᱟ; ᱛᱮᱭᱟᱨ ᱦᱩᱭ ᱠᱟᱛᱮ ᱡᱷᱤᱡᱽ ᱯᱮ᱾

  1. ᱛᱷᱚᱨᱯ (Thorp) ᱟᱨ ᱥᱮᱱᱚᱱ (Shannon) ᱠᱤᱱᱟᱜ ᱞᱟᱦᱟ ᱞᱟᱹᱭ ᱥᱟᱫᱷᱚᱱ ᱫᱚ ᱡᱟᱦᱟᱱ 44% ᱵᱟᱲᱛᱤ ᱮ ᱮᱢ ᱛᱟᱦᱮᱸᱱᱟ᱾ ᱢᱤᱫ ᱞᱟᱦᱟ ᱞᱟᱹᱭ ᱮᱞ ᱨᱮ, ᱠᱮᱞᱤ (Kelly) ᱢᱮᱱᱟᱭ ᱡᱮ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤᱴᱟᱠᱟᱠᱷᱮᱞ ᱯᱩᱸᱡᱤᱠᱷᱮᱞ ᱞᱟᱹᱜᱤᱫ ᱟᱞᱟᱜ ᱫᱚᱦᱚ ᱟᱠᱟᱱ ᱡᱚᱛᱚ ᱴᱟᱠᱟ᱾ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱥᱟᱢᱵᱷᱟᱞ ᱫᱚ ᱢᱮᱱᱮᱛ ᱢᱤᱫ ᱵᱟᱡᱤ ᱟᱨ ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱨᱮ ᱚᱱᱟ ᱠᱷᱚᱱ ᱛᱤᱱᱟᱹᱜ ᱡᱚᱠᱷᱤᱢ ᱨᱮ ᱫᱚᱦᱚᱭ ᱚᱱᱟ ᱴᱷᱟᱹᱣᱠᱟᱹ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ 1.26% ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱞᱟᱹᱠᱛᱤ᱾ ᱡᱩᱫᱤ ᱚᱱᱟ ᱜᱮ 44% ᱵᱟᱲᱛᱤ ᱢᱚᱬᱮ ᱯᱟᱲᱚᱥᱤ ᱮᱞ ᱨᱮ ᱦᱟᱹᱴᱤᱧ ᱢᱤᱫ ᱵᱟᱡᱤ ᱨᱮ ᱦᱤᱡᱩᱜ-ᱟ ᱠᱷᱟᱱ ᱪᱮᱫ ᱦᱩᱭᱩᱜ-ᱟ?

    ᱥᱚᱢᱟᱫᱷᱟᱱ ᱩᱫᱩᱜ

    ᱛᱮᱞᱟ ᱚᱱᱟ ᱚᱠᱛᱚ ᱠᱮᱞᱤ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ 7.1% ᱮ ᱢᱮᱱᱟ, ᱟᱨ ᱯᱩᱸᱡᱤ ᱫᱚ ᱡᱟᱦᱟᱱ ᱛᱩᱨᱩᱭ ᱫᱷᱟᱣ ᱞᱚᱜᱚᱱ ᱵᱟᱲᱦᱟᱣᱚᱜ-ᱟ: 1,000 ᱵᱟᱡᱤ ᱨᱮ ᱡᱟᱦᱟᱱ 1.25 ᱢᱤᱞᱤᱭᱚᱱ ᱫᱷᱟᱣ, ᱡᱟᱦᱟᱱ 11.5 ᱫᱷᱟᱣ ᱥᱟᱶ ᱛᱩᱞᱟᱹᱣ ᱠᱟᱛᱮ᱾

    44% ᱵᱟᱲᱛᱤ ᱢᱮᱱᱟᱜ ᱥᱴᱨᱮᱴ ᱚᱯᱵᱟᱡᱤᱥᱴᱨᱮᱴ ᱚᱯᱢᱤᱫ ᱮᱞ, ᱵᱷᱩᱜᱛᱟᱱ 35:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ 0.04 ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱛᱮ ᱡᱤᱛᱟᱹᱣᱚᱜ-ᱟ, ᱪᱮᱫᱟᱜ ᱥᱮ 36 × 0.04 = 1.44᱾ ᱠᱮᱞᱤ ᱨᱮᱭᱟᱜ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱵᱟᱲᱛᱤ ᱠᱮ ᱚᱰᱥ ᱛᱮ ᱦᱟᱹᱴᱤᱧ: 0.44/35 = 1.26%᱾ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱵᱟᱲᱦᱟᱣ ᱫᱚ 0.04 × ln(1 + 35 × 0.0126) + 0.96 × ln(1 − 0.0126) ≈ 0.00244, ᱚᱱᱟᱛᱮ 1,000 ᱵᱟᱡᱤ ᱯᱩᱸᱡᱤ ᱡᱟᱦᱟᱱ e^2.44 ≈ 11.5 ᱫᱷᱟᱣ ᱮ ᱜᱩᱬᱟ᱾

    ᱢᱤᱫ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱢᱚᱬᱮ ᱮᱞ ᱨᱮ ᱦᱟᱹᱴᱤᱧ ᱯᱮ, ᱟᱨ ᱵᱟᱡᱤ ᱫᱚ 0.20 ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱛᱮ ᱡᱤᱛᱟᱹᱣᱚᱜ-ᱟ ᱟᱨ 1 ᱞᱟᱹᱜᱤᱫ 36/5 ᱮᱢᱚᱜ-ᱟ, ᱵᱟᱝᱠᱷᱟᱱ 6.2 ᱨᱮ 1: ᱟᱡᱟᱦᱟᱸ 44% ᱵᱟᱲᱛᱤ, ᱪᱮᱫᱟᱜ ᱥᱮ 0.2 × 7.2 = 1.44᱾ ᱠᱮᱞᱤ ᱨᱮᱭᱟᱜ ᱵᱟᱡᱤ ᱴᱟᱠᱟ 0.44/6.2 = 7.10% ᱦᱩᱭᱩᱜ-ᱟ, ᱟᱨ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱵᱟᱲᱦᱟᱣ 0.01404, ᱡᱟᱦᱟᱱ 5.75 ᱫᱷᱟᱣ ᱵᱮᱥᱤ᱾ 1,000 ᱵᱟᱡᱤ ᱨᱮ ᱚᱱᱟ ᱫᱚ e^14.04, ᱡᱟᱦᱟᱱ 1.25 ᱢᱤᱞᱤᱭᱚᱱ᱾

    ᱵᱟᱲᱛᱤ ᱫᱚ ᱚᱱᱟ ᱜᱮ; ᱩᱪᱟᱹᱲ ᱞᱟᱛᱟᱨ ᱫᱚ ᱠᱚᱢ᱾ ᱢᱚᱬᱮ ᱫᱷᱟᱣ ᱨᱮ ᱢᱤᱫ ᱫᱷᱟᱣ ᱡᱤᱛᱟᱹᱣᱚᱜ ᱵᱟᱡᱤ ᱫᱚ ᱯᱩᱸᱡᱤ ᱢᱩᱪᱟᱹᱫ ᱡᱚᱠᱷᱤᱢ ᱵᱮᱜᱚᱨ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ ᱢᱟᱨᱟᱝ ᱦᱟᱹᱴᱤᱧ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ, ᱟᱨ ᱠᱮᱞᱤ ᱨᱮᱭᱟᱜ ᱵᱟᱲᱦᱟᱣ ᱚᱱᱟ ᱮ ᱮᱱᱟᱢᱟ᱾ ᱛᱷᱚᱨᱯ (Thorp, 1984) ᱱᱚᱣᱟ ᱫᱟᱹᱭᱠᱟᱹ ᱛᱮ ᱮ ᱩᱫᱩᱜ ᱟᱠᱟᱫᱟ ᱪᱮᱫᱟᱜ ᱞᱟᱦᱟ ᱞᱟᱹᱭ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱥᱮᱠᱴᱚᱨᱪᱟᱠᱟᱥᱮᱠᱴᱚᱨᱪᱟᱠᱟ ᱨᱮ ᱛᱟᱭᱚᱢ ᱛᱟᱭᱚᱢ ᱠᱷᱟᱱᱟ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱜᱩᱞᱟᱹᱭ ᱦᱟᱹᱴᱤᱧ, ᱞᱮᱭᱟᱣᱴ ᱨᱮᱭᱟᱜ ᱜᱩᱴᱤ ᱠᱷᱚᱱ ᱟᱞᱟᱜ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ ᱵᱟᱡᱤ ᱠᱚ ᱞᱟᱜᱟᱣᱟ᱾ ᱟᱹᱛᱩᱨ ᱨᱮ ᱢᱚᱬᱮ ᱯᱟᱲᱚᱥᱤᱵᱟᱡᱤᱯᱟᱲᱚᱥᱤᱪᱟᱠᱟ ᱨᱮ ᱢᱤᱫ ᱮᱞ ᱟᱨ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱵᱟᱨᱭᱟ ᱥᱮᱫ ᱵᱟᱨ-ᱵᱟᱨ ᱠᱷᱟᱱᱟ, ᱢᱚᱬᱮ ᱥᱴᱨᱮᱴ ᱚᱯ ᱪᱤᱯ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ ᱵᱟᱲᱛᱤ ᱫᱚ ᱡᱚᱛᱚ ᱠᱷᱚᱱ ᱵᱮᱥ ᱮᱠᱮᱞ ᱮᱞ ᱠᱷᱚᱱ ᱛᱤᱱᱟᱹᱜ ᱜᱟᱱ ᱠᱚᱢ (ᱮᱰᱣᱟᱱᱴᱮᱡ ᱯᱞᱮ ᱧᱮᱞ ᱯᱮ)᱾

  2. ᱢᱤᱫ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱟᱨ ᱯᱟᱲᱚᱥᱤ ᱠᱷᱟᱱᱟᱥᱟᱡ ᱥᱟᱢᱟᱱᱠᱷᱟᱱᱟᱨᱚᱴᱚᱨ ᱨᱮᱭᱟᱜ 37 ᱮᱞ ᱚᱞ ᱠᱷᱟᱱᱟ ᱠᱷᱚᱱ ᱢᱤᱫ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱞᱚᱴ, ᱠᱟᱯ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱮ ᱧᱟᱢ ᱟᱠᱟᱫᱟ ᱡᱟᱦᱟᱸ ᱫᱚ 37 ᱨᱮ 1 ᱵᱚᱫᱚᱞ 25 ᱨᱮ 1 ᱫᱷᱟᱣ ᱦᱤᱴ ᱠᱚ ᱦᱩᱭᱩᱜ-ᱟ᱾ ᱩᱱᱤ ᱫᱚ ᱵᱟᱨᱭᱟ ᱛᱟᱞᱟ ᱨᱮ ᱥᱯᱞᱤᱴᱵᱟᱡᱤᱥᱯᱞᱤᱴᱵᱟᱨ ᱥᱟᱵᱟᱫ ᱮᱞ, ᱵᱷᱩᱜᱛᱟᱱ 17:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ 17 ᱨᱮ 1 ᱛᱮ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱞᱟᱹᱠᱛᱤ ᱥᱮ ᱵᱟᱨᱭᱟ ᱮᱞ ᱥᱴᱨᱮᱴ ᱚᱯ? ᱠᱮᱞᱤ ᱛᱤᱱᱟᱹᱜ ᱮ ᱢᱮᱱᱟ, ᱟᱨ ᱱᱚᱣᱟ ᱞᱮᱠᱟᱱ ᱢᱤᱫ ᱠᱷᱟᱱᱟ ᱥᱟᱶ ᱛᱩᱞᱟᱹᱣ ᱠᱟᱛᱮ ᱯᱩᱸᱡᱤ ᱛᱤᱱᱟᱹᱜ ᱞᱚᱜᱚᱱ ᱵᱟᱲᱦᱟᱣᱚᱜ-ᱟ?

    ᱥᱚᱢᱟᱫᱷᱟᱱ ᱩᱫᱩᱜ

    ᱛᱮᱞᱟ ᱪᱮᱫ ᱦᱚᱸ ᱯᱷᱟᱨᱟᱠ ᱵᱟᱹᱱᱩᱜ-ᱟ: ᱥᱯᱞᱤᱴ ᱨᱮ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ 2.59%, ᱵᱟᱝᱠᱷᱟᱱ ᱡᱚᱛᱚ ᱮᱞ ᱨᱮ 1.29%᱾ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱯᱩᱸᱡᱤ 1,000 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱡᱟᱦᱟᱱ 155 ᱫᱷᱟᱣ ᱵᱟᱲᱦᱟᱣᱚᱜ-ᱟ, ᱢᱤᱫ ᱠᱷᱟᱱᱟ ᱥᱟᱶ 11.5 ᱫᱷᱟᱣ ᱛᱩᱞᱟᱹᱣ ᱠᱟᱛᱮ᱾

    ᱥᱯᱞᱤᱴ ᱫᱚ 2/25 = 0.08 ᱥᱚᱢᱵᱷᱟᱵᱱᱟᱜᱚᱱᱤᱛᱥᱚᱢᱵᱷᱟᱵᱱᱟᱢᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, 0 ᱠᱷᱚᱱ 1 ᱟᱨᱵᱟᱝ 0% ᱠᱷᱚᱱ 100%᱾ ᱢᱤᱫ ᱮᱞ: 1/37 = 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱛᱮ ᱡᱤᱛᱟᱹᱣᱚᱜ-ᱟ ᱟᱨ 17 ᱨᱮ 1 ᱵᱷᱩᱜᱛᱟᱱ ᱮᱢᱚᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱭᱩᱱᱤᱴᱴᱟᱠᱟᱭᱩᱱᱤᱴᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱟᱨᱵᱟᱝ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱮᱵᱷᱟᱨ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ᱾ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱠᱚ ᱭᱩᱱᱤᱴ ᱛᱮ ᱵᱩᱡᱷᱟᱹᱣᱚᱜ-ᱟ ᱡᱮᱢᱚᱱ ᱡᱟᱦᱟᱸᱱ ᱴᱮᱵᱩᱞ ᱨᱮ ᱞᱟᱹᱜᱩ ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱞᱟᱹᱜᱤᱫ 18 × 0.08 = 1.44 ᱨᱩᱣᱟᱹᱲ ᱮᱢᱟ: 44% ᱵᱟᱲᱛᱤ, ᱢᱤᱫ ᱵᱟᱭᱟᱥ ᱠᱷᱟᱱᱟ ᱞᱮᱠᱟ ᱜᱮ᱾ ᱠᱮᱞᱤ ᱨᱮᱭᱟᱜ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱵᱟᱲᱛᱤ ᱠᱮ ᱚᱰᱥ ᱛᱮ ᱦᱟᱹᱴᱤᱧ: 0.44/17 = 2.59%᱾

    1.29% ᱨᱮᱭᱟᱜ ᱵᱟᱨ ᱥᱴᱨᱮᱴ ᱚᱯ ᱵᱟᱡᱤ ᱫᱚ ᱴᱷᱤᱠ ᱚᱱᱟ ᱜᱮ ᱨᱮᱡᱟᱞᱴ ᱮᱢᱟ᱾ ᱡᱚᱠᱷᱚᱱ ᱡᱟᱦᱟᱸᱱᱟᱜ ᱮᱞ ᱩᱪᱟᱹᱲᱚᱜ-ᱟ, ᱢᱤᱫ ᱪᱤᱯᱴᱟᱠᱟᱪᱤᱯᱛᱷᱤᱠ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱪᱤᱱᱦᱟᱹ ᱴᱚᱠᱮᱱ, ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱞᱮᱭᱟᱣᱴ ᱨᱮ ᱫᱚᱦᱚᱜ-ᱟ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱪᱮᱠ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → 35 ᱨᱮ 1 ᱡᱤᱛᱟᱹᱣᱚᱜ-ᱟ ᱟᱨ ᱮᱴᱟᱜ ᱦᱟᱨᱟᱣᱚᱜ-ᱟ, ᱥᱩᱫᱽ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ 34 × 1.29% = 44%, ᱥᱯᱞᱤᱴ ᱞᱮᱠᱟ ᱜᱮ; ᱡᱚᱠᱷᱚᱱ ᱵᱟᱨᱭᱟ ᱮᱞ ᱵᱟᱝ ᱩᱪᱟᱹᱲᱚᱜ-ᱟ, ᱵᱟᱨᱭᱟ ᱜᱮ ᱦᱟᱨᱟᱣᱚᱜ-ᱟ᱾

    ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮᱭᱟᱜ ᱵᱟᱲᱦᱟᱣ 0.00505, ᱢᱤᱫ ᱠᱷᱟᱱᱟ ᱨᱮᱭᱟᱜ 0.00244 ᱥᱟᱶ ᱛᱩᱞᱟᱹᱣ ᱠᱟᱛᱮ, ᱚᱱᱟᱛᱮ 1,000 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱯᱩᱸᱡᱤ e^2.44 ≈ 11.5 ᱫᱷᱟᱣ ᱵᱚᱫᱚᱞ e^5.046 ≈ 155 ᱫᱷᱟᱣ ᱵᱟᱲᱦᱟᱣᱚᱜ-ᱟ᱾ ᱵᱟᱨ ᱵᱮᱥ ᱮᱞ ᱫᱚ ᱢᱤᱫ ᱮᱞ ᱨᱮᱭᱟᱜ ᱵᱟᱨ ᱫᱷᱟᱣ ᱠᱷᱚᱱ ᱟᱹᱰᱤ ᱵᱮᱥᱤ ᱜᱚᱱᱚᱝ ᱢᱮᱱᱟᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱵᱟᱭᱟᱥ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱮᱞ ᱜᱟᱫᱚᱞ ᱨᱮ ᱵᱟᱡᱤ ᱠᱚ ᱞᱟᱜᱟᱣᱟ᱾ ᱛᱷᱚᱨᱯ (Thorp, 1984) ᱚᱱᱟ ᱜᱮ ᱛᱩᱞᱟᱹᱣ ᱮ ᱦᱤᱥᱟᱹᱵ ᱟᱠᱟᱫᱟ᱾

ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ

ᱨᱩᱞᱮᱴ ᱨᱮ ᱵᱟᱹᱲᱛᱤ ᱞᱟᱹᱜᱤᱫ ᱥᱟᱱᱟᱢ ᱠᱷᱚᱱ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱡᱚᱛᱚ ᱦᱚᱲ ᱵᱟᱲᱟᱭ ᱟᱠᱟᱫ ᱮᱞ ᱠᱟᱱᱟ᱾

ᱨᱩᱞᱮᱴ ᱨᱮ ᱵᱟᱹᱲᱛᱤ ᱞᱟᱹᱜᱤᱫ ᱥᱟᱱᱟᱢ ᱠᱷᱚᱱ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱡᱚᱛᱚ ᱦᱚᱲ ᱵᱟᱲᱟᱭ ᱟᱠᱟᱫ ᱮᱞ ᱠᱟᱱᱟ᱾

ᱯᱷᱮᱰᱟᱛ

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