ᱨᱩᱞᱮᱴ ᱚᱰᱥ ᱟᱨ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱛᱟᱹᱞᱤᱠᱟᱹ
ᱥᱟᱱᱟᱢ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱵᱟᱡᱤ, ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, ᱵᱷᱩᱜᱛᱟᱱ, ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱜᱚᱱᱤᱛᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱡᱮᱞᱮᱧ ᱚᱠᱛᱚ ᱨᱮ ᱢᱤᱫ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱨᱮᱡᱟᱞᱴ᱾ ᱡᱚᱛᱚ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱭᱩᱨᱚᱯᱤᱭᱟᱱ ᱵᱟᱡᱤ ᱨᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ −1/37᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱟᱨ ᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱ ᱥᱟᱶ᱾
ᱥᱟᱱᱟᱢ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱢᱤᱫ ᱜᱮ, ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ −2.70%᱾ ᱩᱱᱠᱩ ᱫᱚ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱟᱨ ᱯᱟᱥᱱᱟᱣ ᱨᱮ ᱜᱮ ᱵᱷᱮᱜᱟᱨ᱾
ᱱᱚᱶᱟ ᱨᱩᱞᱮᱴ ᱚᱰᱥ ᱪᱟᱨᱴ ᱪᱮᱫ ᱞᱮᱠᱟ ᱯᱟᱲᱦᱟᱣ ᱦᱩᱭᱩᱜ-ᱟ
ᱥᱚᱢᱵᱷᱟᱵᱱᱟᱜᱚᱱᱤᱛᱥᱚᱢᱵᱷᱟᱵᱱᱟᱢᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, 0 ᱠᱷᱚᱱ 1 ᱟᱨᱵᱟᱝ 0% ᱠᱷᱚᱱ 100%᱾ ᱢᱤᱫ ᱮᱞ: 1/37 = 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱢᱮᱱᱟᱜ-ᱟ ᱡᱮ ᱛᱤᱱᱟᱹᱜ ᱫᱷᱟᱣ ᱟᱯᱮ ᱡᱤᱛᱟᱹᱣᱟ ᱯᱮ; ᱨᱩᱞᱮᱴ ᱚᱰᱥ ᱞᱮᱠᱟᱛᱮ ᱞᱟᱹᱭ ᱟᱠᱟᱱ ᱵᱷᱩᱜᱛᱟᱱᱴᱟᱠᱟᱵᱷᱩᱜᱛᱟᱱᱡᱤᱛ ᱵᱟᱡᱤ ᱪᱮᱫ ᱨᱩᱣᱟᱹᱲᱟ, ᱨᱩᱣᱟᱹᱲ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱪᱮᱛᱟᱱ “X ᱨᱮ 1” ᱞᱮᱠᱟ ᱨᱚᱲᱚᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱢᱮᱱᱟᱜ-ᱟ ᱛᱤᱱᱟᱹᱜ; σ ᱫᱚ ᱢᱮᱱᱟᱜ-ᱟ ᱡᱮ ᱥᱚᱯᱷᱚᱨ ᱫᱚ ᱛᱤᱱᱟᱹᱜ ᱪᱮᱛᱟᱱ-ᱞᱟᱛᱟᱨ᱾ EV ᱠᱚᱞᱚᱢ ᱫᱚ ᱵᱮᱱᱟᱣ ᱞᱮᱠᱟᱛᱮ ᱡᱚᱛᱚ ᱛᱟᱨᱤ ᱨᱮ ᱢᱤᱫ ᱜᱮ, ᱚᱱᱟᱛᱮ ᱱᱚᱶᱟ ᱛᱟᱹᱞᱤᱠᱟᱹ ᱫᱚ ᱥᱟᱹᱨᱤ ᱛᱮ ᱢᱤᱫ ᱜᱮ ᱫᱟᱢ ᱨᱮ ᱣᱮᱨᱤᱭᱮᱱᱥᱜᱚᱱᱤᱛᱣᱮᱨᱤᱭᱮᱱᱥᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱜᱷᱮᱨᱟᱣ ᱨᱮᱡᱟᱞᱴ ᱛᱤᱱᱟᱹᱜ ᱯᱟᱥᱱᱟᱣᱚᱜ-ᱟ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱥᱟᱯᱲᱟᱣ᱾ ᱥᱴᱨᱮᱴ ᱚᱯ ᱞᱟᱹᱜᱤᱫ ᱵᱟᱹᱲᱛᱤ, ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ ᱢᱮᱱᱩ ᱠᱟᱱᱟ᱾
ᱠᱚᱞ ᱵᱟᱡᱤ
ᱥᱮᱠᱴᱚᱨᱪᱟᱠᱟᱥᱮᱠᱴᱚᱨᱪᱟᱠᱟ ᱨᱮ ᱛᱟᱭᱚᱢ ᱛᱟᱭᱚᱢ ᱠᱷᱟᱱᱟ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱜᱩᱞᱟᱹᱭ ᱦᱟᱹᱴᱤᱧ, ᱞᱮᱭᱟᱣᱴ ᱨᱮᱭᱟᱜ ᱜᱩᱴᱤ ᱠᱷᱚᱱ ᱟᱞᱟᱜ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱵᱟᱡᱤ ᱫᱚ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱡᱩᱲᱟᱹᱣ ᱠᱟᱱᱟ ᱟᱨ ᱩᱱᱠᱩ ᱨᱮᱭᱟᱜ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱜᱮ ᱧᱟᱢᱟ᱾ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱡᱟᱜ ᱵᱷᱩᱜᱛᱟᱱ ᱨᱩᱯ ᱢᱮᱱᱟᱜ-ᱟ, ᱪᱮᱫᱟᱜ ᱥᱮ ᱪᱤᱯᱴᱟᱠᱟᱪᱤᱯᱛᱷᱤᱠ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱪᱤᱱᱦᱟᱹ ᱴᱚᱠᱮᱱ, ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱞᱮᱭᱟᱣᱴ ᱨᱮ ᱫᱚᱦᱚᱜ-ᱟ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱪᱮᱠ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱚ ᱫᱚ ᱥᱚᱢᱟᱱ ᱛᱮ ᱵᱟᱝ ᱦᱟᱛᱟᱣ ᱟᱠᱟᱱᱟ᱾
ᱟᱭᱢᱟ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ
k ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱠᱚᱢ ᱥᱮ ᱠᱚᱢ ᱢᱤᱫ ᱦᱤᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, ᱠᱚᱭᱢᱟ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱠᱩᱠᱞᱤ ᱞᱟᱹᱜᱤᱫ᱾
ᱥᱮᱥᱚᱱ ᱨᱮᱭᱟᱜ ᱯᱟᱥᱱᱟᱣ
$10 ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤ ᱛᱮ 100 ᱜᱷᱩᱨᱟᱹᱣ ᱥᱮᱥᱚᱱ ᱨᱮᱭᱟᱜ ᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱜᱚᱱᱤᱛᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱣᱮᱨᱤᱭᱮᱱᱥ ᱨᱮᱭᱟᱜ ᱵᱚᱜᱚ ᱢᱩᱞ; ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱠᱷᱚᱱ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱥᱟᱦᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ →, ᱵᱟᱡᱤ ᱞᱮᱠᱷᱟ ᱛᱮ; ᱥᱟᱱᱟᱢ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱨᱮᱡᱟᱞᱴ ᱢᱤᱫ ᱜᱮ: −$27᱾
ᱠᱩᱠᱞᱤ ᱠᱚ
ᱪᱮᱫᱟᱜ ᱥᱮ ᱡᱚᱛᱚ ᱵᱷᱩᱜᱛᱟᱱ ᱫᱚ 36/n − 1, ᱱᱤᱭᱟᱭ 37/n − 1 ᱵᱚᱫᱚᱞ ᱛᱮ᱾ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤᱜᱚᱱᱤᱛᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱠᱷᱚᱱ ᱠᱮᱥᱤᱱᱳ ᱟᱣᱥᱚᱛ ᱛᱮ ᱫᱚᱦᱚᱭ ᱦᱟᱹᱴᱤᱧ: ᱭᱩᱨᱚᱯᱤᱭᱟᱱ ᱨᱩᱞᱮᱴ ᱨᱮ 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱥᱟᱦᱴᱟ ᱧᱮᱞ ᱯᱮ᱾
ᱯᱷᱨᱮᱧᱪ ᱴᱮᱵᱩᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤᱵᱟᱡᱤᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤᱟᱨᱟᱜ/ᱦᱮᱸᱫᱮ, ᱵᱤᱡᱳᱲ/ᱡᱳᱲ, ᱢᱟᱨᱟᱝ/ᱦᱩᱰᱤᱧ᱾ 18 ᱮᱞ, ᱵᱷᱩᱜᱛᱟᱱ 1:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ →: p ᱟᱨ ᱵᱷᱩᱜᱛᱟᱱ ᱫᱚ ᱵᱟᱝ ᱵᱚᱫᱚᱞᱚᱜ-ᱟ, EV −1.35%, σ ≈ 0.99᱾
37 ᱵᱚᱫᱚᱞ ᱛᱮ 38 ᱛᱮ ᱦᱟᱹᱴᱤᱧ ᱯᱮ, ᱟᱨ EV ᱠᱚᱞᱚᱢ ᱫᱚ ᱡᱚᱛᱚ ᱛᱟᱨᱤ ᱨᱮ −5.26% ᱦᱩᱭᱩᱜ-ᱟ, ᱢᱚᱬᱮ ᱮᱞ ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ −7.89%᱾
ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ
ᱟᱨᱮ ᱵᱟᱡᱤ, ᱢᱤᱫ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ, ᱡᱟᱦᱟᱱᱟᱜ ᱦᱚᱸ ᱩᱭᱦᱟᱹᱨ ᱵᱟᱹᱱᱩᱜ-ᱟ᱾
ᱯᱷᱮᱰᱟᱛ
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.