ᱨᱩᱞᱮᱴ ᱰᱚᱡᱮᱱ ᱵᱟᱡᱤ
ᱨᱩᱞᱮᱴ ᱰᱚᱡᱮᱱ ᱵᱟᱡᱤ ᱫᱚ ᱞᱟᱜᱟᱛᱟᱨ ᱜᱮᱞ ᱵᱟᱨ ᱮᱞ ᱠᱚᱵᱷᱟᱨᱟ: 1–12, 13–24 ᱟᱨᱵᱟᱝ 25–36᱾
ᱜᱮᱞ ᱵᱟᱨ ᱮᱞ, 2:1 ᱵᱷᱩᱜᱛᱟᱱ᱾ ᱥᱚᱢᱵᱷᱟᱵᱱᱟᱜᱚᱱᱤᱛᱥᱚᱢᱵᱷᱟᱵᱱᱟᱢᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, 0 ᱠᱷᱚᱱ 1 ᱟᱨᱵᱟᱝ 0% ᱠᱷᱚᱱ 100%᱾ ᱢᱤᱫ ᱮᱞ: 1/37 = 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → 32.43%᱾ ᱡᱤᱨᱚ ᱨᱮ ᱦᱟᱨᱟᱣᱚᱜ-ᱟ᱾
ᱨᱩᱞᱮᱴ ᱴᱮᱵᱩᱞ ᱨᱮ ᱰᱚᱡᱮᱱ ᱠᱚ ᱚᱠᱟ ᱨᱮ ᱢᱮᱱᱟᱜ-ᱟ?
ᱞᱮᱭᱟᱣᱴᱥᱟᱡ ᱥᱟᱢᱟᱱᱞᱮᱭᱟᱣᱴᱴᱮᱵᱩᱞ ᱪᱮᱛᱟᱱ ᱪᱷᱟᱯᱟ ᱵᱟᱡᱤ ᱡᱟᱹᱞᱤ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱴᱮᱵᱩᱞ, ᱯᱷᱮᱞᱴ, ᱠᱟᱯᱲᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ ᱡᱮᱞᱮᱧ ᱫᱷᱟᱨᱮ ᱥᱮᱫ ᱯᱮ ᱵᱟᱠᱥᱚ, ᱡᱟᱦᱟᱸ ᱨᱮ 1st 12, 2nd 12, 3rd 12 ᱚᱞ ᱢᱮᱱᱟᱜ-ᱟ, ᱟᱨᱵᱟᱝ ᱯᱷᱨᱮᱧᱪ ᱴᱮᱵᱩᱞ ᱨᱮ P12 (ᱯᱨᱮᱢᱤᱭᱮᱨ), M12 (ᱢᱚᱭᱮᱱ), D12 (ᱫᱮᱨᱱᱤᱭᱮᱨ)᱾ ᱡᱚᱛᱚ ᱵᱟᱠᱥᱚ ᱫᱚ ᱟᱡ ᱛᱮ ᱴᱮᱵᱩᱞ ᱨᱮᱭᱟᱜ ᱠᱚᱢ ᱥᱮ ᱠᱚᱢ ᱥᱤᱢᱟᱹ ᱯᱩᱨᱟᱹᱣ ᱞᱟᱹᱠᱛᱤ᱾ ᱡᱤᱨᱚᱪᱟᱠᱟᱡᱤᱨᱚᱢᱤᱫᱜᱮ ᱦᱟᱹᱨᱭᱟᱹᱲ ᱠᱷᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ, ᱰᱚᱡᱮᱱ ᱟᱨᱵᱟᱝ ᱠᱚᱞᱚᱢ ᱵᱟᱡᱤ ᱵᱟᱭ ᱠᱚᱵᱷᱟᱨᱟ; ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱢᱩᱞ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱤᱝᱜᱚᱞ ᱡᱤᱨᱚ, 0᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱡᱟᱦᱟᱱ ᱰᱚᱡᱮᱱᱵᱟᱡᱤᱰᱚᱡᱮᱱ1–12, 13–24 ᱟᱨᱵᱟᱝ 25–36, ᱵᱷᱩᱜᱛᱟᱱ 2:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ ᱦᱚᱸ ᱵᱟᱹᱱᱩᱜ-ᱟ᱾
ᱨᱩᱞᱮᱴ ᱰᱚᱡᱮᱱ ᱨᱮᱭᱟᱜ ᱵᱷᱩᱜᱛᱟᱱ ᱟᱨ ᱟᱸᱫᱟᱡᱽ
37 ᱠᱷᱚᱱ ᱜᱮᱞ ᱵᱟᱨ ᱮᱞ ᱞᱟᱹᱜᱤᱫ ᱱᱤᱭᱟᱭ ᱚᱰᱥ ᱫᱚ 2.083 ᱨᱮ 1 ᱠᱟᱱᱟ; ᱴᱮᱵᱩᱞ ᱫᱚ 2 ᱜᱮ ᱮᱢᱟᱭ᱾ ᱡᱤᱛ $10 ᱰᱚᱡᱮᱱ ᱫᱚ $20 ᱨᱩᱣᱟᱹᱲ ᱮᱢᱟᱭ᱾ ᱟᱣᱥᱚᱛ 37 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ: 12 ᱡᱤᱛ (+$240), 25 ᱦᱟᱨᱟᱣ (−$250), ᱥᱩᱫᱽ −$10᱾
ᱢᱤᱫ ᱫᱷᱟᱣ ᱨᱮ ᱵᱟᱨ ᱰᱚᱡᱮᱱ
ᱥᱚᱢᱟᱱ ᱪᱤᱯᱴᱟᱠᱟᱪᱤᱯᱛᱷᱤᱠ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱪᱤᱱᱦᱟᱹ ᱴᱚᱠᱮᱱ, ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱞᱮᱭᱟᱣᱴ ᱨᱮ ᱫᱚᱦᱚᱜ-ᱟ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱪᱮᱠ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱛᱮ ᱵᱟᱨ ᱰᱚᱡᱮᱱ ᱠᱚᱵᱷᱟᱨ ᱫᱚ 37 ᱠᱷᱚᱱ 24 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱡᱤᱛᱟᱹᱣᱚᱜ-ᱟ (64.9%) ᱢᱮᱱᱠᱷᱟᱱ ᱥᱩᱫᱽ ᱞᱟᱵᱷ ᱫᱚ ᱢᱤᱫ ᱭᱩᱱᱤᱴᱴᱟᱠᱟᱭᱩᱱᱤᱴᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱟᱨᱵᱟᱝ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱮᱵᱷᱟᱨ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ᱾ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱠᱚ ᱭᱩᱱᱤᱴ ᱛᱮ ᱵᱩᱡᱷᱟᱹᱣᱚᱜ-ᱟ ᱡᱮᱢᱚᱱ ᱡᱟᱦᱟᱸᱱ ᱴᱮᱵᱩᱞ ᱨᱮ ᱞᱟᱹᱜᱩ ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱜᱮ: ᱢᱤᱫ ᱨᱮ 2 ᱡᱤᱛᱟᱹᱣ ᱟᱨ ᱮᱴᱟᱜ ᱨᱮ 1 ᱦᱟᱨᱟᱣ᱾ 13 ᱦᱟᱨᱟᱣ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱡᱚᱛᱚ ᱨᱮ ᱵᱟᱨ ᱭᱩᱱᱤᱴ ᱞᱟᱜᱟ᱾ (24 × 1 − 13 × 2)/37 = ᱵᱟᱨ ᱭᱩᱱᱤᱴ ᱯᱨᱚᱛᱤ −2/37, ᱥᱟᱫᱷᱟᱨᱚᱬ 2.70%᱾ ᱨᱩᱯ ᱫᱚ ᱧᱮᱞ ᱨᱮ ᱵᱮᱥ, ᱡᱷᱟᱞᱟ ᱯᱮ ᱜᱷᱩᱨᱟᱹᱣ ᱠᱷᱚᱱ ᱵᱟᱨ ᱨᱮ ᱡᱤᱛ, ᱟᱨ ᱵᱟᱲᱛᱤ ᱫᱚ ᱵᱟᱝ ᱵᱚᱫᱚᱞᱚᱜ-ᱟ᱾
ᱨᱩᱞᱮᱴ ᱰᱚᱡᱮᱱ ᱟᱨ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ
ᱰᱚᱡᱮᱱ ᱨᱮ ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱰᱚᱵᱚᱞ ᱫᱚ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱞᱮᱠᱟ ᱵᱟᱝ ᱨᱩᱣᱟᱹᱲᱚᱜ-ᱟ: ᱰᱚᱵᱚᱞ ᱛᱟᱭᱚᱢ 2 ᱨᱮ 1 ᱵᱷᱩᱜᱛᱟᱱᱴᱟᱠᱟᱵᱷᱩᱜᱛᱟᱱᱡᱤᱛ ᱵᱟᱡᱤ ᱪᱮᱫ ᱨᱩᱣᱟᱹᱲᱟ, ᱨᱩᱣᱟᱹᱲ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱪᱮᱛᱟᱱ “X ᱨᱮ 1” ᱞᱮᱠᱟ ᱨᱚᱲᱚᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱵᱟᱨ ᱦᱟᱹᱱᱤ ᱜᱮ ᱨᱩᱣᱟᱹᱲᱟ, ᱡᱚᱛᱚ ᱫᱚ ᱵᱟᱝ, ᱚᱱᱟᱛᱮ ᱥᱟᱫᱷᱟᱨᱚᱬ “ᱰᱚᱡᱮᱱ ᱢᱟᱨᱴᱤᱝᱜᱮᱞᱥᱴᱨᱮᱴᱮᱡᱤᱢᱟᱨᱴᱤᱝᱜᱮᱞᱡᱚᱛᱚ ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱵᱟᱡᱤ ᱰᱚᱵᱚᱞ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ᱾ ᱱᱚᱶᱟ ᱪᱮᱫ ᱮ ᱠᱟᱹᱢᱤᱭᱟ ᱟᱨ ᱪᱮᱫ ᱵᱟᱭ ᱠᱟᱹᱢᱤᱭᱟ, ᱚᱱᱟ ᱥᱴᱨᱮᱴᱮᱡᱤ ᱦᱟᱹᱴᱤᱧ ᱨᱮ ᱧᱮᱞ ᱯᱮ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ →” ᱫᱚ ᱵᱚᱫᱚᱞ ᱛᱮ ᱯᱮ ᱫᱷᱟᱣ ᱮᱫᱟ᱾ ᱯᱮ ᱫᱷᱟᱣ ᱛᱮ $5 ᱠᱷᱚᱱ ᱢᱚᱬᱮ ᱫᱷᱟᱯ ᱨᱮ $500 ᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹᱴᱮᱵᱩᱞᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹᱦᱩᱠᱩᱢ ᱢᱮᱱᱟᱜ ᱠᱚᱢ ᱥᱮ ᱠᱚᱢ ᱟᱨ ᱵᱮᱥᱤ ᱥᱮ ᱵᱮᱥᱤ ᱵᱟᱡᱤ᱾ ᱵᱮᱥᱤ ᱥᱮ ᱵᱮᱥᱤ ᱥᱤᱢᱟᱹ ᱜᱮ ᱰᱚᱵᱚᱞ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱵᱚᱸᱫᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱥᱮᱴᱮᱨᱚᱜ-ᱟ, ᱟᱨᱟᱜᱵᱟᱡᱤᱟᱨᱟᱜ18 ᱟᱨᱟᱜ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱨᱩᱡᱽ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ ᱰᱚᱵᱚᱞ ᱞᱟᱹᱜᱤᱫ ᱮᱭᱟᱭ ᱫᱷᱟᱯ᱾ ᱚᱠᱟ ᱰᱚᱡᱮᱱ ᱵᱟᱹᱜᱤ ᱨᱮᱭᱟᱜ ᱚᱞᱟᱣ ᱥᱤᱥᱴᱮᱢ ᱠᱚ ᱫᱚ ᱪᱮᱫ ᱦᱚᱸ ᱵᱟᱝ ᱵᱚᱫᱚᱞᱟ, ᱪᱮᱫᱟᱜ ᱥᱮ ᱜᱷᱩᱨᱟᱹᱣ ᱠᱚ ᱫᱚ ᱟᱡᱟᱫ ᱠᱟᱱᱟ᱾
ᱪᱟᱠᱟ ᱨᱮ
ᱰᱚᱡᱮᱱ ᱨᱮᱭᱟᱜ ᱜᱮᱞ ᱵᱟᱨ ᱮᱞ ᱫᱚ ᱪᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱫᱷᱟᱨᱮ ᱜᱷᱮᱨᱟ ᱪᱤᱛᱟᱹᱨ ᱢᱮᱱᱟᱜ-ᱟ; ᱯᱟᱹᱦᱤᱞ ᱰᱚᱡᱮᱱ ᱫᱚ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ᱨᱮᱭᱟᱜ ᱠᱷᱟᱱᱟᱥᱟᱡ ᱥᱟᱢᱟᱱᱠᱷᱟᱱᱟᱨᱚᱴᱚᱨ ᱨᱮᱭᱟᱜ 37 ᱮᱞ ᱚᱞ ᱠᱷᱟᱱᱟ ᱠᱷᱚᱱ ᱢᱤᱫ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱞᱚᱴ, ᱠᱟᱯ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱚ ᱦᱟᱛᱟᱣᱟ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱥᱟᱱᱟᱢ ᱪᱟᱠᱟ ᱜᱷᱮᱨᱟ ᱪᱤᱛᱟᱹᱨ ᱴᱷᱟᱶ ᱨᱮ ᱢᱮᱱᱟᱜ-ᱟ᱾ ᱰᱚᱡᱮᱱ ᱫᱚ ᱢᱤᱫ ᱞᱮᱭᱟᱣᱴ ᱵᱟᱡᱤ ᱠᱟᱱᱟ, ᱚᱱᱟ ᱨᱮ ᱡᱟᱦᱟᱱ ᱥᱟᱹᱨᱤ ᱥᱮᱠᱴᱚᱨᱪᱟᱠᱟᱥᱮᱠᱴᱚᱨᱪᱟᱠᱟ ᱨᱮ ᱛᱟᱭᱚᱢ ᱛᱟᱭᱚᱢ ᱠᱷᱟᱱᱟ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱜᱩᱞᱟᱹᱭ ᱦᱟᱹᱴᱤᱧ, ᱞᱮᱭᱟᱣᱴ ᱨᱮᱭᱟᱜ ᱜᱩᱴᱤ ᱠᱷᱚᱱ ᱟᱞᱟᱜ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱵᱟᱹᱱᱩᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱵᱟᱭᱟᱥ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱱᱚᱶᱟ ᱵᱟᱝ ᱠᱚ ᱵᱮᱵᱷᱟᱨᱟ᱾
ᱠᱩᱠᱞᱤ ᱠᱚ
ᱵᱟᱝ᱾ ᱡᱚᱛᱚ ᱜᱮ 37 ᱠᱷᱚᱱ 12 ᱠᱟᱱᱟ᱾ ᱫᱚᱥᱟᱨ ᱰᱚᱡᱮᱱ ᱨᱮ 17 ᱢᱮᱱᱟᱜ-ᱟ, ᱡᱟᱦᱟᱸ ᱨᱮ ᱡᱟᱦᱟᱸ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣᱚᱜ-ᱟ, ᱢᱮᱱᱠᱷᱟᱱ ᱚᱱᱟ ᱫᱚ ᱪᱮᱫ ᱦᱚᱸ ᱵᱟᱝ ᱵᱚᱫᱚᱞᱟ᱾
ᱦᱮᱸ, ᱟᱨ 37 ᱠᱷᱚᱱ 36 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱟᱯᱮ ᱢᱤᱫ ᱡᱤᱛᱟᱹᱣ ᱟᱨ ᱵᱟᱨ ᱦᱟᱨᱟᱣ ᱟᱯᱮ, ᱟᱨ ᱡᱤᱨᱚ ᱨᱮ ᱯᱮᱭᱟᱜ ᱦᱟᱨᱟᱣ ᱟᱯᱮ᱾
ᱵᱟᱨᱭᱟ ᱜᱮ ᱜᱮᱞ ᱵᱟᱨ ᱮᱞ ᱠᱚᱵᱷᱟᱨᱟ᱾ ᱵᱷᱩᱜᱛᱟᱱ ᱱᱤᱭᱚᱢ ᱫᱚ ᱠᱚᱵᱷᱟᱨ ᱜᱮ ᱞᱮᱠᱷᱟ ᱮᱫᱟ᱾
ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ
64.9% ᱜᱷᱩᱨᱟᱹᱣ ᱡᱤᱛᱟᱹᱣ᱾ 2.70% ᱴᱟᱠᱟ ᱦᱟᱨᱟᱣ᱾
ᱯᱷᱮᱰᱟᱛ
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.