ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ
ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱜᱩᱱ ᱟᱯᱮ ᱡᱟᱦᱟᱸ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱮᱫᱟ ᱯᱮ: ᱟᱣᱥᱚᱛ ᱛᱮ ᱥᱮᱥᱚᱱ ᱨᱮᱭᱟᱜ ᱠᱷᱚᱨᱚᱪ᱾
ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ = ᱡᱚᱛᱚ ᱵᱟᱡᱤ × 1/37᱾ $10 ᱵᱟᱡᱤ ᱴᱟᱠᱟ, 100 ᱜᱷᱩᱨᱟᱹᱣ: $1,000 ᱵᱟᱡᱤ, $27 ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ᱾ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱫᱚ ᱵᱮᱥᱤ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱮᱫᱟ, ᱚᱱᱟᱛᱮ ᱵᱮᱥᱤ ᱦᱟᱨᱟᱣᱚᱜ-ᱟ᱾
ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱦᱤᱥᱟᱹᱵ, ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱫᱚ ᱵᱟᱝ
ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤᱜᱚᱱᱤᱛᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱜᱩᱬ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ; ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱟᱨᱵᱟᱝ ᱚᱠᱛᱚ ᱨᱮ ᱟᱣᱥᱚᱛ ᱛᱮ ᱦᱟᱨᱟᱣᱚᱜ ᱴᱟᱠᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱴᱮᱵᱩᱞ ᱪᱮᱛᱟᱱ ᱛᱮ ᱪᱮᱫ ᱛᱤᱱ ᱴᱟᱠᱟ ᱯᱟᱨᱚᱢᱚᱜ-ᱟ ᱚᱱᱟ ᱪᱮᱛᱟᱱ ᱨᱮ ᱛᱷᱟᱯᱚᱱ, ᱟᱯᱮ ᱪᱮᱫ ᱛᱤᱱ ᱟᱹᱜᱩ ᱞᱮᱫᱟ ᱯᱮ ᱚᱱᱟ ᱪᱮᱛᱟᱱ ᱨᱮ ᱵᱟᱝ᱾ $100 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 → ᱡᱟᱦᱟᱸ ᱟᱭᱢᱟ ᱫᱷᱟᱣ ᱫᱚᱦᱲᱟ ᱵᱟᱡᱤ ᱨᱮ ᱞᱟᱜᱟᱣᱚᱜ-ᱟ, ᱚᱱᱟ ᱫᱚ $2,000 ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱦᱤᱥᱟᱹᱵᱴᱟᱠᱟᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱦᱤᱥᱟᱹᱵᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱟᱨᱵᱟᱝ ᱚᱠᱛᱚ ᱨᱮ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ, ᱫᱚᱦᱲᱟ ᱞᱟᱜᱟᱣ ᱡᱤᱛ ᱴᱟᱠᱟ ᱥᱮᱞᱮᱫ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱦᱮᱱᱰᱮᱞ, ᱮᱠᱥᱚᱱ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱟᱨ $54 ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ; $10,000 ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱡᱟᱦᱟᱸ ᱢᱤᱫ ᱫᱷᱟᱣ ᱟᱨᱟᱜᱵᱟᱡᱤᱟᱨᱟᱜ18 ᱟᱨᱟᱜ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱨᱩᱡᱽ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ ᱞᱟᱜᱟᱣᱚᱜ-ᱟ, ᱚᱱᱟ ᱫᱚ $10,000 ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱦᱤᱥᱟᱹᱵ ᱟᱨ $270 ᱦᱩᱭᱩᱜ-ᱟ᱾ ᱠᱮᱥᱤᱱᱳ ᱨᱮᱭᱟᱜ ᱟᱹᱢᱫᱟᱹᱱᱤ ᱫᱚ ᱦᱚᱨ ᱨᱮᱭᱟᱜ ᱪᱟᱞᱟᱜ ᱪᱟᱞᱟᱜ ᱪᱮᱛᱟᱱ ᱠᱚᱨ ᱠᱟᱱᱟ, ᱟᱨ ᱚᱱᱟ ᱪᱟᱞᱟᱜ ᱫᱚ ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱡᱚᱛᱚ ᱪᱤᱯᱴᱟᱠᱟᱪᱤᱯᱛᱷᱤᱠ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱪᱤᱱᱦᱟᱹ ᱴᱚᱠᱮᱱ, ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱞᱮᱭᱟᱣᱴ ᱨᱮ ᱫᱚᱦᱚᱜ-ᱟ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱪᱮᱠ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱟᱱᱟ᱾
ᱯᱷᱚᱨᱢᱩᱞᱟ
E[ᱦᱟᱹᱱᱤ] = Σ ᱵᱟᱡᱤ ᱴᱟᱠᱟ / 37᱾ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤ ᱠᱷᱮᱞᱚᱸᱰ ᱞᱟᱹᱜᱤᱫ ᱱᱚᱣᱟ ᱫᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ × ᱜᱷᱩᱨᱟᱹᱣ / 37 ᱠᱟᱱᱟ᱾ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱᱥᱴᱨᱮᱴᱮᱡᱤᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱᱢᱟᱨᱮ ᱨᱮᱡᱟᱞᱴ ᱞᱮᱠᱟ ᱛᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱵᱚᱫᱚᱞ ᱡᱟᱦᱟᱸᱱ ᱱᱤᱭᱚᱢ᱾ ᱱᱮᱜᱮᱴᱤᱵᱷ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱵᱟᱲᱦᱟᱣᱟ, ᱯᱚᱡᱤᱴᱤᱵᱷ ᱡᱤᱛ ᱛᱟᱭᱚᱢ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱞᱟᱹᱜᱤᱫ ᱱᱚᱣᱟ ᱫᱚ ᱟᱣᱥᱚᱛ ᱵᱟᱡᱤ ᱴᱟᱠᱟ × ᱜᱷᱩᱨᱟᱹᱣ / 37 ᱠᱟᱱᱟ, ᱟᱨ ᱟᱣᱥᱚᱛ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱵᱮᱥ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱜᱮᱭᱟ, ᱪᱮᱫᱟᱜ ᱥᱮ ᱦᱟᱹᱱᱤ ᱚᱠᱛᱚ ᱨᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱵᱟᱲᱦᱟᱣᱚᱜ-ᱟ᱾ $500 ᱥᱤᱢᱟᱹ ᱨᱮ $10 ᱵᱮᱥ ᱠᱷᱚᱱ ᱢᱟᱨᱴᱤᱝᱜᱮᱞᱥᱴᱨᱮᱴᱮᱡᱤᱢᱟᱨᱴᱤᱝᱜᱮᱞᱡᱚᱛᱚ ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱵᱟᱡᱤ ᱰᱚᱵᱚᱞ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ᱾ ᱱᱚᱶᱟ ᱪᱮᱫ ᱮ ᱠᱟᱹᱢᱤᱭᱟ ᱟᱨ ᱪᱮᱫ ᱵᱟᱭ ᱠᱟᱹᱢᱤᱭᱟ, ᱚᱱᱟ ᱥᱴᱨᱮᱴᱮᱡᱤ ᱦᱟᱹᱴᱤᱧ ᱨᱮ ᱧᱮᱞ ᱯᱮ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱢᱤᱫ ᱡᱮᱞᱮᱧ ᱥᱮᱥᱚᱱ ᱨᱮ ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱟᱣᱥᱚᱛ ᱛᱮ ᱠᱚᱢ ᱵᱮᱥᱤ $28 ᱦᱩᱭᱩᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱱᱚᱣᱟ ᱫᱚ ᱢᱤᱫ ᱞᱮᱠᱟᱱ $10 ᱵᱟᱡᱤ ᱠᱷᱚᱱ ᱡᱷᱚᱛᱚ ᱯᱮ ᱜᱩᱱ ᱵᱮᱥᱤ ᱦᱟᱨᱟᱣᱚᱜ-ᱟ, ᱢᱤᱫ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱦᱚᱸ ᱚᱰᱥ ᱵᱟᱝ ᱵᱚᱫᱚᱞ ᱠᱟᱛᱮ᱾
ᱞᱚᱜᱚᱱ
ᱞᱟᱭᱤᱵᱷ ᱴᱮᱵᱩᱞ ᱫᱚ ᱢᱤᱫ ᱜᱷᱟᱸᱴᱟ ᱨᱮ 40–60 ᱜᱷᱩᱨᱟᱹᱣ ᱠᱚ ᱪᱟᱞᱟᱣᱟ, ᱠᱮᱥᱤᱱᱳ ᱨᱮ 30–50, ᱞᱚᱜᱚᱱ ᱴᱮᱵᱩᱞ 90 ᱥᱮ ᱵᱮᱥᱤ, RNG ᱴᱮᱵᱩᱞ ᱫᱚ ᱟᱯᱮ ᱡᱟᱛᱮ ᱞᱚᱜᱚᱱ ᱠᱞᱤᱠ ᱮᱫᱟ ᱯᱮ᱾ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮ, ᱞᱚᱜᱚᱱ ᱫᱚ ᱡᱚᱛᱚ ᱜᱷᱟᱸᱴᱟ ᱨᱮ ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ ᱪᱮᱛᱟᱱ ᱡᱚᱛᱚ ᱠᱷᱚᱱ ᱢᱟᱨᱟᱝ ᱟᱹᱛᱩᱨ ᱠᱟᱱᱟ: ᱢᱤᱫ ᱞᱟᱦᱟᱭ ᱠᱮᱥᱤᱱᱳ ᱴᱮᱵᱩᱞ ᱠᱷᱚᱱ ᱢᱤᱫ ᱜᱷᱟᱸᱴᱟ ᱨᱮ 200 ᱜᱷᱩᱨᱟᱹᱣ ᱠᱷᱮᱞ RNG ᱴᱮᱵᱩᱞ ᱛᱮ ᱥᱮᱱ ᱫᱚ ᱧᱤᱫᱟᱹ ᱨᱮᱭᱟᱜ ᱠᱷᱚᱨᱚᱪ ᱯᱩᱱ ᱜᱩᱱ ᱵᱮᱱᱟᱣ ᱮᱫᱟ, ᱚᱰᱥ ᱵᱟᱝ ᱵᱚᱫᱚᱞ ᱠᱟᱛᱮ᱾
ᱢᱤᱫ ᱥᱮᱨᱢᱟ ᱨᱮ
ᱢᱤᱫ ᱥᱟᱵᱟᱫᱚ ᱦᱮᱡ ᱠᱷᱮᱞᱚᱸᱰ ᱡᱟᱦᱟᱸ ᱦᱟᱯᱛᱟ ᱨᱮ ᱵᱟᱨ ᱜᱷᱟᱸᱴᱟ 50 ᱜᱷᱩᱨᱟᱹᱣ ᱞᱟᱭᱤᱵᱷ ᱴᱮᱵᱩᱞ ᱨᱮ $10 ᱥᱟᱶ ᱮ ᱠᱷᱮᱞᱟ, ᱩᱱᱤ ᱫᱚ ᱢᱤᱫ ᱥᱮᱨᱢᱟ ᱨᱮ $52,000 ᱵᱟᱡᱤ ᱮ ᱞᱟᱜᱟᱣᱟ ᱟᱨ ᱭᱩᱨᱚᱯᱤᱭᱟᱱ ᱪᱟᱠᱟ ᱨᱮ ᱠᱚᱢ ᱵᱮᱥᱤ $1,400 ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ ᱮ ᱮᱢᱟ, ᱯᱷᱨᱮᱧᱪ ᱨᱮ $700, ᱟᱢᱮᱨᱤᱠᱟᱱ ᱨᱮ $2,700᱾ ᱦᱤᱥᱟᱹᱵ ᱫᱚ ᱵᱮᱥᱣᱟᱫ ᱜᱮᱭᱟ ᱢᱮᱱᱠᱷᱟᱱ ᱟᱠᱷᱨᱤ ᱠᱟᱛᱷᱟ ᱫᱚ ᱵᱟᱝ: ᱪᱟᱠᱟ ᱟᱨ ᱴᱮᱵᱩᱞ ᱵᱟᱪᱷᱟᱣ ᱫᱚ ᱡᱟᱦᱟᱸᱱ ᱥᱤᱥᱴᱮᱢ ᱠᱷᱚᱱ ᱟᱢᱟᱵ ᱜᱩᱱ ᱵᱮᱥᱤ ᱜᱚᱱᱚᱝ ᱜᱮᱭᱟ, ᱪᱮᱫᱟᱜ ᱥᱮ ᱥᱤᱥᱴᱮᱢ ᱨᱮᱭᱟᱜ ᱜᱚᱱᱚᱝ ᱫᱚ ᱴᱷᱤᱠ ᱡᱤᱨᱚᱪᱟᱠᱟᱡᱤᱨᱚᱢᱤᱫᱜᱮ ᱦᱟᱹᱨᱭᱟᱹᱲ ᱠᱷᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ, ᱰᱚᱡᱮᱱ ᱟᱨᱵᱟᱝ ᱠᱚᱞᱚᱢ ᱵᱟᱡᱤ ᱵᱟᱭ ᱠᱚᱵᱷᱟᱨᱟ; ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱢᱩᱞ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱤᱝᱜᱚᱞ ᱡᱤᱨᱚ, 0᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱟᱱᱟ᱾
ᱡᱟᱦᱟᱸᱱ ᱵᱮᱸᱠ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱜᱚᱱᱚᱝ ᱢᱤᱫ ᱠᱷᱮᱞ
ᱥᱮᱱᱴ ᱯᱤᱴᱟᱨᱥᱵᱟᱨᱜ ᱠᱷᱮᱞ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱱᱤᱠᱚᱞᱟᱥ ᱵᱮᱨᱱᱩᱞᱤ (Nicolaus Bernoulli) 1713 ᱨᱮ ᱮ ᱛᱮᱭᱟᱨ ᱞᱮᱫᱟ, ᱩᱯᱨᱩᱢ ᱫᱷᱟᱨᱮ ᱧᱩᱨ ᱦᱟᱹᱵᱤᱡ ᱥᱤᱠᱟᱹ ᱮ ᱪᱟᱞᱟᱜᱟ ᱟᱨ ᱢᱤᱫ ᱫᱷᱟᱣ ᱨᱮ ᱦᱩᱭ ᱞᱮᱠᱷᱟᱱ $2, ᱵᱟᱨ ᱫᱷᱟᱣ ᱨᱮ $4, ᱯᱮ ᱫᱷᱟᱣ ᱨᱮ $8 ᱮ ᱮᱢᱟ, ᱡᱚᱛᱚ ᱫᱷᱟᱣ ᱵᱟᱨ ᱜᱩᱱ᱾ ᱡᱚᱛᱚ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜ ᱡᱮᱞᱮᱧ ᱫᱚ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱜᱚᱱᱤᱛᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱡᱮᱞᱮᱧ ᱚᱠᱛᱚ ᱨᱮ ᱢᱤᱫ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱨᱮᱡᱟᱞᱴ᱾ ᱡᱚᱛᱚ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱭᱩᱨᱚᱯᱤᱭᱟᱱ ᱵᱟᱡᱤ ᱨᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ −1/37᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ $1 ᱡᱚᱲᱟᱣ ᱮᱫᱟ, ᱚᱱᱟᱛᱮ ᱠᱟᱜᱚᱡ ᱨᱮ ᱠᱷᱮᱞ ᱨᱮᱭᱟᱜ ᱜᱚᱱᱚᱝ ᱫᱚ ᱟᱢᱟᱵ ᱜᱮᱭᱟ᱾ ᱡᱟᱦᱟᱸᱱ ᱵᱮᱸᱠ ᱦᱚᱸ ᱟᱢᱟᱵ ᱤᱱᱟᱢ ᱵᱟᱝ ᱮᱢ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ, ᱟᱨ ᱤᱱᱟᱢ ᱠᱚ ᱵᱮᱸᱠ ᱨᱮ ᱢᱮᱱᱟᱜ ᱴᱟᱠᱟ ᱦᱟᱹᱵᱤᱡ ᱥᱤᱢᱟᱹ ᱦᱩᱭ ᱞᱮᱱ ᱛᱟᱭᱚᱢ, ᱜᱚᱱᱚᱝ ᱫᱚ ᱧᱩᱨᱩᱜ-ᱟ: $1 ᱢᱤᱞᱤᱭᱚᱱ ᱵᱮᱸᱠ ᱥᱟᱶ ᱠᱷᱮᱞ ᱨᱮᱭᱟᱜ ᱜᱚᱱᱚᱝ ᱫᱚ ᱠᱚᱢ ᱵᱮᱥᱤ $21, $1 ᱵᱤᱞᱤᱭᱚᱱ ᱥᱟᱶ ᱠᱚᱢ ᱵᱮᱥᱤ $31᱾ ᱢᱟᱨᱴᱤᱝᱜᱮᱞ ᱫᱚ ᱚᱱᱟ ᱜᱮ ᱠᱷᱮᱞ ᱮᱴᱟᱜ ᱫᱷᱟᱨᱮ ᱠᱷᱚᱱ ᱧᱮᱞ ᱠᱟᱛᱮ ᱠᱟᱱᱟ᱾ ᱱᱚᱣᱟ ᱫᱚ ᱡᱷᱚᱛᱚ ᱞᱮᱠᱟ ᱡᱚᱛᱚ ᱥᱟᱭᱠᱮᱞ ᱨᱮ ᱢᱤᱫ ᱭᱩᱱᱤᱴᱴᱟᱠᱟᱭᱩᱱᱤᱴᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱟᱨᱵᱟᱝ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱮᱵᱷᱟᱨ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ᱾ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱠᱚ ᱭᱩᱱᱤᱴ ᱛᱮ ᱵᱩᱡᱷᱟᱹᱣᱚᱜ-ᱟ ᱡᱮᱢᱚᱱ ᱡᱟᱦᱟᱸᱱ ᱴᱮᱵᱩᱞ ᱨᱮ ᱞᱟᱹᱜᱩ ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱡᱤᱛᱚᱜ-ᱟ ᱟᱨ ᱢᱤᱫ ᱜᱟᱱ ᱜᱟᱱ ᱦᱩᱭᱩᱜ ᱡᱮᱞᱮᱧ ᱞᱟᱜᱟᱛᱟᱨ ᱨᱮ ᱡᱚᱛᱚ ᱦᱟᱨᱟᱣᱚᱜ-ᱟ; ᱥᱤᱢᱟᱹ ᱵᱤᱱᱟᱹ ᱡᱮᱞᱮᱧ ᱞᱟᱜᱟᱛᱟᱨ ᱫᱚ ᱟᱨᱦᱚᱸ ᱢᱟᱨᱟᱝ ᱡᱤᱛ ᱛᱮ ᱥᱚᱫᱽᱫᱷᱚᱜ ᱛᱟᱦᱮᱸᱱᱟ, ᱟᱨ ᱥᱤᱢᱟᱹ ᱥᱟᱶ ᱵᱟᱝ, ᱚᱱᱟᱛᱮ ᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹᱴᱮᱵᱩᱞᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹᱦᱩᱠᱩᱢ ᱢᱮᱱᱟᱜ ᱠᱚᱢ ᱥᱮ ᱠᱚᱢ ᱟᱨ ᱵᱮᱥᱤ ᱥᱮ ᱵᱮᱥᱤ ᱵᱟᱡᱤ᱾ ᱵᱮᱥᱤ ᱥᱮ ᱵᱮᱥᱤ ᱥᱤᱢᱟᱹ ᱜᱮ ᱰᱚᱵᱚᱞ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱵᱚᱸᱫᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱢᱟᱨᱴᱤᱝᱜᱮᱞ ᱪᱮᱫ ᱞᱮᱠᱟ ᱦᱟᱨᱟᱣᱚᱜ-ᱟ ᱚᱱᱟ ᱛᱷᱤᱨ ᱮᱫᱟ, ᱦᱟᱨᱟᱣᱚᱜ-ᱟ ᱥᱮ ᱵᱟᱝ ᱚᱱᱟ ᱫᱚ ᱵᱟᱝ᱾
ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ ᱫᱚ ᱨᱮᱡᱟᱞᱴ ᱵᱟᱝ ᱠᱟᱱᱟ
ᱡᱟᱦᱟᱸᱱ ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱫᱚ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ ᱠᱷᱚᱱ ᱵᱷᱮᱜᱟᱨ ᱦᱩᱭᱩᱜ-ᱟ, ᱟᱭᱢᱟ ᱫᱷᱟᱣ ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ ᱠᱷᱚᱱ ᱦᱚᱸ ᱵᱮᱥᱤ᱾ $10 ᱥᱟᱶ 100 ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱜᱚᱱᱤᱛᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱣᱮᱨᱤᱭᱮᱱᱥ ᱨᱮᱭᱟᱜ ᱵᱚᱜᱚ ᱢᱩᱞ; ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱠᱷᱚᱱ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱥᱟᱦᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ $100 ᱠᱟᱱᱟ, ᱟᱸᱫᱟᱡᱽ −$27 ᱵᱤᱨᱩᱫᱷ ᱨᱮ; ᱡᱤᱛ ᱥᱮᱥᱚᱱ ᱫᱚ ᱵᱤᱥᱮᱥ ᱵᱟᱝ ᱠᱟᱱᱟ᱾ ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ ᱫᱚ ᱫᱟᱢ ᱠᱟᱱᱟ; ᱣᱮᱨᱤᱭᱮᱱᱥᱜᱚᱱᱤᱛᱣᱮᱨᱤᱭᱮᱱᱥᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱜᱷᱮᱨᱟᱣ ᱨᱮᱡᱟᱞᱴ ᱛᱤᱱᱟᱹᱜ ᱯᱟᱥᱱᱟᱣᱚᱜ-ᱟ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱥᱟᱯᱲᱟᱣ᱾ ᱥᱴᱨᱮᱴ ᱚᱯ ᱞᱟᱹᱜᱤᱫ ᱵᱟᱹᱲᱛᱤ, ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱵᱟᱸᱫᱷᱟᱣ ᱠᱟᱱᱟ; ᱢᱤᱫ ᱧᱤᱫᱟᱹ ᱨᱮᱭᱟᱜ ᱨᱮᱡᱟᱞᱴ ᱫᱚ ᱢᱤᱫ ᱜᱚᱴᱟᱝ ᱱᱢᱩᱱᱟ ᱠᱟᱱᱟ᱾
ᱯᱷᱚᱨᱢᱩᱞᱟ
ᱠᱩᱠᱞᱤ ᱠᱚ
ᱵᱟᱝ᱾ ᱟᱯᱮ ᱡᱟᱦᱟᱸ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱮᱫᱟ ᱯᱮ ᱚᱱᱟ ᱨᱮᱭᱟᱜ 2.70%᱾ ᱡᱤᱛ ᱴᱟᱠᱟ ᱫᱚᱦᱲᱟ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱞᱮᱠᱷᱟᱱ ᱚᱱᱟ ᱫᱚᱦᱲᱟ ᱵᱟᱡᱤ ᱨᱮ ᱞᱟᱜᱟᱣᱚᱜ-ᱟ᱾
ᱡᱚᱛᱚ ᱜᱷᱟᱸᱴᱟ ᱨᱮ, ᱦᱮᱸ, ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱞᱚᱜᱚᱱ ᱨᱮ᱾ ᱡᱚᱛᱚ ᱥᱮᱴᱮᱨ ᱡᱚᱠᱷᱟ ᱨᱮ, ᱵᱟᱝ: ᱯᱩᱸᱡᱤ ᱢᱩᱪᱟᱹᱫ ᱡᱚᱠᱷᱤᱢᱜᱚᱱᱤᱛᱯᱩᱸᱡᱤ ᱢᱩᱪᱟᱹᱫ ᱡᱚᱠᱷᱤᱢᱡᱚᱠᱷᱟ ᱟᱨᱵᱟᱝ ᱜᱷᱩᱨᱟᱹᱣ ᱞᱮᱠᱷᱟ ᱦᱟᱹᱵᱤᱡ ᱥᱮᱴᱮᱨ ᱞᱟᱦᱟ ᱡᱚᱛᱚ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱦᱟᱨᱟᱣ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱧᱮᱞ ᱯᱮ᱾
ᱠᱮᱥᱤᱱᱳ ᱫᱚ ᱟᱣᱥᱚᱛ ᱵᱟᱡᱤ ᱟᱨ ᱠᱷᱮᱞ ᱚᱠᱛᱚ ᱠᱷᱚᱱ ᱟᱯᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ ᱠᱚ ᱟᱸᱫᱟᱡᱽ ᱠᱚ ᱠᱚᱨᱟᱣᱟ ᱟᱨ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱦᱟᱹᱴᱤᱧ ᱠᱚᱢᱯ ᱞᱮᱠᱟ ᱠᱚ ᱨᱩᱣᱟᱹᱲ ᱮᱫᱟ᱾ ᱩᱱᱠᱩ ᱫᱚ ᱫᱟᱢ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱦᱟᱹᱴᱤᱧ ᱠᱚ ᱨᱩᱣᱟᱹᱲ ᱮᱫᱟ, ᱟᱯᱮ ᱵᱟᱲᱛᱤ ᱫᱚ ᱵᱟᱝ ᱠᱚ ᱮᱢ ᱮᱫᱟ ᱯᱮᱭᱟ᱾
ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ
ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱦᱤᱥᱟᱹᱵ × 1/37᱾ ᱜᱷᱚᱰᱤ ᱫᱚ ᱯᱷᱚᱨᱢᱩᱞᱟ ᱨᱮ ᱢᱮᱱᱟᱜ-ᱟ᱾
ᱯᱷᱮᱰᱟᱛ
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.