ᱨᱩᱞᱮᱴ ᱥᱤᱥᱴᱮᱢ ᱨᱮᱭᱟᱜ ᱤᱛᱤᱦᱟᱹᱥ
ᱵᱟᱨ ᱥᱟᱭ ᱥᱮᱨᱢᱟ ᱦᱚᱲ ᱠᱚ ᱟᱡᱟᱜ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱵᱚᱫᱚᱞ ᱨᱮᱭᱟᱜ ᱱᱤᱭᱚᱢ ᱠᱚ ᱚᱞ ᱮᱫᱟ᱾
ᱢᱟᱨᱴᱤᱝᱜᱮᱞ ᱫᱚ 18 ᱥᱟᱭ ᱥᱮᱨᱢᱟ ᱨᱮᱭᱟᱜ ᱠᱟᱱᱟ; ᱫᱟᱞᱟᱸᱵᱮᱨ ᱫᱚ ᱢᱤᱫ ᱜᱚᱱᱤᱛ ᱵᱤᱫᱽ ᱧᱩᱛᱩᱢ ᱛᱮ ᱠᱟᱱᱟ ᱡᱟᱦᱟᱸᱭ ᱱᱚᱶᱟ ᱵᱟᱭ ᱠᱩᱥᱤᱭᱟᱜ ᱛᱟᱦᱮᱸᱫ; ᱞᱟᱵᱩᱥᱮᱨ ᱫᱚ ᱵᱷᱤᱠᱴᱳᱨᱤᱭᱟᱱ ᱚᱠᱛᱚ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱨᱟᱡᱽᱱᱤᱛᱤ ᱦᱚᱲ ᱨᱮᱭᱟᱜ ᱥᱟᱹᱠ ᱠᱟᱱᱟ᱾ ᱚᱱᱟ ᱚᱠᱛᱚ ᱦᱚᱸ ᱱᱚᱶᱟ ᱠᱚ ᱢᱤᱫᱴᱟᱝ ᱦᱚᱸ ᱵᱟᱝ ᱠᱟᱹᱢᱤ ᱞᱮᱫᱟ᱾
ᱢᱟᱨᱴᱤᱝᱜᱮᱞ
ᱧᱩᱛᱩᱢ ᱫᱚ ᱫᱩᱱᱟ ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱯᱨᱚᱵᱷᱟᱸᱥᱟᱞ ᱡᱩᱣᱟ ᱠᱟᱛᱷᱟ ᱠᱷᱚᱱ ᱦᱮᱡ ᱟᱠᱟᱱᱟ (à la martegalo, “ᱢᱟᱨᱴᱤᱜ ᱦᱚᱲ ᱠᱚ ᱞᱮᱠᱟ”, ᱡᱟᱦᱟᱸ ᱠᱚ ᱫᱚ ᱵᱮᱯᱚᱨᱚᱣᱟ ᱧᱩᱛᱩᱢᱟᱜ ᱛᱟᱦᱮᱸᱫ ᱠᱚᱣᱟ), 1760 ᱫᱚᱥᱚᱠ ᱠᱷᱚᱱ ᱯᱷᱨᱮᱧᱪ ᱟᱹᱲᱟᱹ ᱯᱚᱛᱷᱤ ᱨᱮ ᱚᱞ ᱢᱮᱱᱟᱜ-ᱟ᱾ ᱛᱷᱚᱨᱯ (1984), American Heritage Dictionary ᱛᱟᱭᱚᱢ, ᱢᱤᱫ ᱫᱚᱥᱟᱨ ᱞᱟᱠᱪᱟᱨ ᱵᱩᱡᱷᱟᱹᱣ ᱮᱢ ᱮᱫᱟᱭ: ᱢᱟᱨᱴᱤᱜ ᱦᱚᱲ ᱠᱚ ᱟᱡᱟᱵ ᱟᱹᱫᱚᱛ ᱠᱷᱟᱹᱛᱤᱨ ᱵᱤᱨᱞᱟᱹᱣᱚᱜ ᱛᱟᱦᱮᱸᱫ ᱠᱚᱣᱟ, ᱚᱱᱟ ᱢᱩᱫᱽ ᱨᱮ ᱢᱤᱫ ᱫᱚ ᱫᱷᱚᱛᱤ-ᱯᱮᱱᱴ ᱛᱟᱭᱚᱢ ᱥᱮᱫ ᱛᱮ ᱛᱚᱞ, ᱚᱱᱟᱛᱮ ᱠᱟᱛᱷᱟ ᱫᱚ “ᱦᱟᱥᱟᱭ ᱞᱮᱠᱟᱛᱮ” ᱢᱮᱱᱮᱛ ᱦᱩᱭ ᱮᱱᱟ᱾ 18 ᱥᱟᱭ ᱥᱮᱨᱢᱟ ᱨᱮᱭᱟᱜ ᱯᱮᱨᱤᱥ ᱨᱮ ᱱᱚᱶᱟ ᱫᱚ ᱟᱜᱟᱢ ᱜᱮ ᱦᱩᱥᱤᱭᱟᱹᱨ ᱠᱟᱹᱦᱱᱤ ᱛᱟᱦᱮᱸᱫ: ᱠᱟᱥᱟᱱᱚᱵᱷᱟ 1750 ᱫᱚᱥᱚᱠ ᱨᱮ ᱵᱷᱮᱱᱤᱥ ᱨᱮ ᱯᱷᱮᱨᱳ ᱨᱮ ᱫᱩᱱᱟ ᱠᱟᱛᱮ ᱟᱹᱰᱤ ᱫᱷᱚᱱ ᱦᱟᱨᱟᱣ ᱨᱮᱭᱟᱜ ᱠᱟᱛᱷᱟ ᱚᱞ ᱟᱠᱟᱫᱟᱭ᱾ ᱱᱚᱶᱟ ᱪᱮᱫᱟᱜ ᱵᱟᱝ ᱠᱟᱹᱢᱤᱭᱟ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱜᱚᱱᱤᱛ, ᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹᱴᱮᱵᱩᱞᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹᱦᱩᱠᱩᱢ ᱢᱮᱱᱟᱜ ᱠᱚᱢ ᱥᱮ ᱠᱚᱢ ᱟᱨ ᱵᱮᱥᱤ ᱥᱮ ᱵᱮᱥᱤ ᱵᱟᱡᱤ᱾ ᱵᱮᱥᱤ ᱥᱮ ᱵᱮᱥᱤ ᱥᱤᱢᱟᱹ ᱜᱮ ᱰᱚᱵᱚᱞ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱵᱚᱸᱫᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱟᱨ ᱥᱤᱢᱟᱹ ᱢᱮᱱᱟᱜ 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 →, 1770 ᱫᱚᱥᱚᱠ ᱦᱟᱹᱵᱤᱡ ᱵᱩᱡᱷᱟᱹᱣ ᱦᱩᱭ ᱟᱠᱟᱱ ᱛᱟᱦᱮᱸᱫ᱾ ᱥᱚᱢᱵᱷᱟᱵᱱᱟᱜᱚᱱᱤᱛᱥᱚᱢᱵᱷᱟᱵᱱᱟᱢᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, 0 ᱠᱷᱚᱱ 1 ᱟᱨᱵᱟᱝ 0% ᱠᱷᱚᱱ 100%᱾ ᱢᱤᱫ ᱮᱞ: 1/37 = 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱛᱚᱛᱷ ᱨᱮ 1930 ᱫᱚᱥᱚᱠ ᱨᱮ “ᱢᱟᱨᱴᱤᱝᱜᱮᱞᱥᱴᱨᱮᱴᱮᱡᱤᱢᱟᱨᱴᱤᱝᱜᱮᱞᱡᱚᱛᱚ ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱵᱟᱡᱤ ᱰᱚᱵᱚᱞ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ᱾ ᱱᱚᱶᱟ ᱪᱮᱫ ᱮ ᱠᱟᱹᱢᱤᱭᱟ ᱟᱨ ᱪᱮᱫ ᱵᱟᱭ ᱠᱟᱹᱢᱤᱭᱟ, ᱚᱱᱟ ᱥᱴᱨᱮᱴᱮᱡᱤ ᱦᱟᱹᱴᱤᱧ ᱨᱮ ᱧᱮᱞ ᱯᱮ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ →” ᱫᱚ ᱱᱤᱭᱟᱭ ᱠᱷᱮᱞᱜᱚᱱᱤᱛᱱᱤᱭᱟᱭ ᱠᱷᱮᱞᱚᱠᱟ ᱠᱷᱮᱞ ᱨᱮ ᱡᱟᱦᱟᱸᱱ ᱥᱮᱫ ᱦᱚᱸ ᱵᱟᱲᱛᱤ ᱵᱟᱹᱱᱩᱜ-ᱟ: ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱡᱤᱨᱚ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱞᱟᱹᱜᱤᱫ ᱢᱤᱫ ᱴᱮᱠᱱᱤᱠᱟᱞ ᱥᱟᱵᱫᱚ ᱦᱩᱭ ᱮᱱᱟ, ᱟᱨ ᱨᱩᱞᱮᱴ ᱢᱟᱨᱴᱤᱝᱜᱮᱞ ᱫᱚ ᱴᱷᱤᱠ ᱚᱱᱟ ᱜᱮ ᱵᱟᱝ ᱠᱟᱱᱟ᱾
ᱫᱟᱞᱟᱸᱵᱮᱨ
ᱡᱟᱸ ᱞᱚ ᱨᱚᱸ ᱫᱟᱞᱟᱸᱵᱮᱨ (Jean le Rond d’Alembert) Encyclopédie (1754) ᱨᱮ ᱜᱟᱞᱚᱪ ᱠᱮᱫᱟᱭ ᱡᱮ ᱢᱤᱫ ᱫᱷᱟᱣ ᱞᱟᱜᱟᱛᱟᱨ ᱢᱚᱦᱚᱨ ᱛᱟᱭᱚᱢ ᱯᱚᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱵᱟᱹᱲᱛᱤᱜ-ᱟ, ᱢᱤᱫ ᱢᱟᱨᱟᱝ ᱜᱚᱱᱤᱛ ᱵᱤᱫᱽ ᱴᱷᱮᱱ ᱠᱷᱚᱱ ᱡᱩᱣᱟᱲᱤᱭᱟᱜ ᱵᱷᱩᱞ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱥᱟᱵᱮᱫ ᱢᱟᱲᱟᱝ ᱠᱟᱛᱷᱟ᱾ ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱭᱩᱱᱤᱴᱴᱟᱠᱟᱭᱩᱱᱤᱴᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱟᱨᱵᱟᱝ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱮᱵᱷᱟᱨ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ᱾ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱠᱚ ᱭᱩᱱᱤᱴ ᱛᱮ ᱵᱩᱡᱷᱟᱹᱣᱚᱜ-ᱟ ᱡᱮᱢᱚᱱ ᱡᱟᱦᱟᱸᱱ ᱴᱮᱵᱩᱞ ᱨᱮ ᱞᱟᱹᱜᱩ ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱥᱮᱞᱮᱫ ᱟᱨ ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱩᱪᱟᱹᱲ ᱵᱟᱡᱤ ᱥᱤᱥᱴᱮᱢ ᱫᱚ ᱛᱟᱭᱚᱢ ᱨᱮᱭᱟᱜ ᱡᱩᱣᱟᱲᱤ ᱠᱚ ᱩᱱᱤᱭᱟᱜ ᱧᱩᱛᱩᱢ ᱛᱮ ᱧᱩᱛᱩᱢ ᱠᱮᱫᱟ, ᱡᱟᱦᱟᱸ ᱠᱚ ᱦᱚᱸ ᱚᱱᱟ ᱜᱮ ᱵᱤᱥᱣᱟᱥ ᱛᱟᱦᱮᱸᱫ ᱠᱚᱣᱟ᱾ ᱩᱱᱤ ᱱᱚᱶᱟ ᱵᱟᱭ ᱞᱟᱹᱭ ᱞᱮᱫᱟ ᱟᱨ, ᱩᱱᱤᱭᱟᱜ ᱵᱮᱥ ᱫᱤᱱ ᱨᱮ, ᱵᱟᱝ ᱟᱠᱟᱨᱤᱭᱟ ᱛᱟᱦᱮᱸᱫᱟᱭ᱾
ᱞᱟᱵᱩᱥᱮᱨ
ᱦᱮᱱᱨᱤ ᱞᱟᱵᱩᱥᱮᱨᱥᱴᱨᱮᱴᱮᱡᱤᱞᱟᱵᱩᱥᱮᱨᱠᱟᱴᱟᱣ ᱥᱤᱥᱴᱮᱢ: ᱢᱤᱫ ᱞᱟᱭᱤᱱ ᱮᱞ ᱚᱞ ᱯᱮ, ᱵᱟᱨᱭᱟ ᱢᱩᱪᱟᱹᱫ ᱮᱞ ᱨᱮᱭᱟᱜ ᱡᱚᱲᱟᱣ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱯᱮ, ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱚᱱᱟ ᱠᱚ ᱠᱟᱴᱟᱣ ᱯᱮ, ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱦᱟᱨᱟᱣ ᱟᱠᱟᱱ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱥᱮᱞᱮᱫ ᱯᱮ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → (Henry Labouchère, 1831–1912), ᱠᱷᱚᱵᱚᱨ ᱚᱞᱤᱭᱟᱹ, ᱛᱷᱤᱭᱮᱴᱟᱨ ᱢᱟᱞᱤᱠ ᱟᱨ ᱞᱤᱵᱟᱨᱟᱞ MP, 1870 ᱫᱚᱥᱚᱠ ᱨᱮ ᱞᱚᱸᱰᱚᱱ ᱥᱚᱢᱟᱡ ᱨᱮ ᱠᱟᱴᱟᱣ ᱥᱤᱥᱴᱮᱢ ᱧᱩᱛᱩᱢ ᱠᱮᱫᱟᱭ ᱟᱨ ᱢᱮᱱᱟᱜ-ᱟ ᱡᱮ ᱢᱚᱱᱴᱮ ᱠᱟᱨᱞᱚ ᱨᱮ ᱵᱮᱵᱷᱟᱨ ᱞᱮᱫᱟᱭ᱾ ᱦᱚᱨᱟ, ᱮᱞ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱛᱷᱟᱨ ᱚᱞ ᱠᱟᱛᱮ ᱵᱟᱨ ᱢᱩᱪᱟᱹᱫ ᱮᱞ ᱨᱮᱭᱟᱜ ᱡᱚᱲ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ, ᱩᱱᱤ ᱠᱷᱚᱱ ᱢᱟᱲᱟᱝ ᱜᱮ ᱛᱟᱦᱮᱸᱫ᱾ ᱩᱱᱤᱭᱟᱜ ᱧᱩᱛᱩᱢ ᱥᱟᱵ ᱮᱱᱟ ᱪᱮᱫᱟᱜ ᱡᱮ ᱩᱱᱤ ᱮᱴᱟᱜ ᱠᱟᱹᱢᱤ ᱞᱟᱹᱜᱤᱫ ᱧᱩᱛᱩᱢ ᱛᱟᱦᱮᱸᱫᱟᱭ ᱟᱨ ᱥᱤᱥᱴᱮᱢ ᱨᱮ ᱢᱤᱫ ᱟᱡᱟᱵ ᱜᱩᱱ ᱢᱮᱱᱟᱜ-ᱟ ᱡᱮ ᱟᱹᱰᱤ ᱫᱷᱟᱣ ᱠᱟᱹᱢᱤᱭᱟ, ᱚᱱᱟᱛᱮ ᱧᱤᱫᱟᱹ ᱫᱟᱠᱟ ᱴᱮᱵᱩᱞ ᱨᱮ ᱠᱟᱛᱷᱟ ᱨᱮᱭᱟᱜ ᱵᱤᱥᱚᱭ ᱦᱩᱭ ᱮᱱᱟ᱾
ᱠᱟᱥᱟᱱᱚᱵᱷᱟ ᱯᱷᱮᱨᱳ ᱨᱮ ᱫᱩᱱᱟ ᱠᱟᱛᱮ ᱦᱟᱨᱟᱣ ᱮᱫᱟᱭ᱾ ᱢᱟᱨᱴᱤᱝᱜᱮᱞ ᱫᱚ ᱟᱜᱟᱢ ᱜᱮ ᱢᱟᱨᱮ ᱠᱟᱱᱟ᱾
ᱫᱟᱞᱟᱸᱵᱮᱨ ᱚᱱᱟ ᱵᱷᱩᱞ ᱪᱷᱟᱯᱟᱣ ᱮᱫᱟᱭ ᱡᱟᱦᱟᱸ ᱛᱟᱭᱚᱢ ᱛᱮ ᱥᱤᱥᱴᱮᱢ ᱞᱮᱠᱟ ᱩᱱᱤᱭᱟᱜ ᱧᱩᱛᱩᱢ ᱦᱟᱛᱟᱣᱟ᱾
“ᱢᱟᱨᱴᱤᱝᱜᱮᱞ” ᱡᱩᱣᱟ ᱨᱮᱭᱟᱜ ᱠᱚᱛᱷᱟ ᱞᱮᱠᱟ ᱯᱷᱨᱮᱧᱪ ᱟᱹᱲᱟᱹ ᱯᱚᱛᱷᱤ ᱨᱮ ᱵᱚᱞᱚ ᱮᱱᱟ᱾
ᱞᱟᱵᱩᱥᱮᱨ ᱞᱚᱸᱰᱚᱱ ᱨᱮ ᱠᱟᱴᱟᱣ ᱥᱤᱥᱴᱮᱢ ᱧᱩᱛᱩᱢ ᱮᱫᱟᱭ᱾
ᱯᱷᱤᱵᱚᱱᱟᱪᱤ ᱟᱨ ᱯᱟᱨᱚᱞᱤ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱡᱩᱣᱟ ᱯᱚᱛᱷᱤ ᱠᱚ ᱨᱮ ᱧᱮᱞᱚᱜ ᱠᱟᱱᱟ᱾
ᱪᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱮᱞ ᱛᱟᱹᱞᱤᱠᱟᱹ ᱨᱮ ᱛᱷᱤᱨ “ᱥᱮᱠᱴᱚᱨ” ᱥᱤᱥᱴᱮᱢ ᱰᱟᱠ ᱛᱮ ᱟᱠᱷᱨᱤᱧᱚᱜ ᱠᱟᱱᱟ᱾
ᱰᱩᱵ ᱨᱮᱭᱟᱜ ᱪᱮᱞᱟ ᱦᱟᱞᱢᱚᱥ ᱥᱟᱵᱩᱫ ᱮᱫᱟᱭ ᱡᱮ ᱡᱟᱦᱟᱸ ᱵᱟᱡᱤ ᱥᱤᱥᱴᱮᱢ ᱦᱚᱸ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱤᱨᱩᱫᱽ ᱠᱷᱮᱞ ᱫᱚ ᱠᱷᱮᱞᱚᱸᱰ ᱥᱮᱫ ᱠᱷᱮᱞ ᱨᱮ ᱵᱟᱭ ᱵᱚᱫᱚᱞ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾
ᱠᱚᱢᱯᱭᱩᱴᱟᱨ ᱡᱚᱛᱚ ᱥᱤᱥᱴᱮᱢ ᱥᱤᱢᱩᱞᱮᱴ ᱮᱫᱟ᱾ ᱡᱚᱛᱚ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱦᱤᱥᱟᱹᱵ ᱨᱮᱭᱟᱜ −1/37 ᱩᱫᱩᱜ ᱮᱫᱟ᱾
ᱚᱱᱟ ᱜᱮ ᱥᱤᱥᱴᱮᱢ ᱠᱚ ᱚᱱᱟ ᱜᱮ ᱯᱷᱚᱞ ᱥᱟᱶ ᱚᱱᱞᱟᱭᱤᱱ ᱟᱠᱷᱨᱤᱧᱚᱜ ᱠᱟᱱᱟ, ᱱᱚᱶᱟ ᱥᱟᱭᱤᱴ ᱨᱮ ᱵᱽᱨᱟᱣᱡᱟᱨ ᱨᱮ ᱥᱤᱢᱩᱞᱮᱴ ᱟᱠᱟᱱ᱾
20 ᱥᱟᱭ ᱥᱮᱨᱢᱟ
ᱯᱷᱤᱵᱚᱱᱟᱪᱤᱥᱴᱨᱮᱴᱮᱡᱤᱯᱷᱤᱵᱚᱱᱟᱪᱤ1, 1, 2, 3, 5, 8, 13… ᱥᱤᱨᱤᱡᱽ ᱯᱟᱧᱡᱟ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ: ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱫᱷᱟᱯ ᱞᱟᱦᱟ, ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱵᱟᱨ ᱫᱷᱟᱯ ᱛᱟᱭᱚᱢ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱟᱨ ᱯᱟᱨᱚᱞᱤᱥᱴᱨᱮᱴᱮᱡᱤᱯᱟᱨᱚᱞᱤᱯᱚᱡᱤᱴᱤᱵᱷ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ: ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱰᱚᱵᱚᱞ, ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱟᱨᱵᱟᱝ ᱞᱟᱜᱟᱛᱟᱨ ᱯᱮ ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱫᱚᱦᱲᱟ ᱮᱛᱚᱦᱚᱵ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱩᱞᱴᱟᱹ ᱢᱟᱨᱴᱤᱝᱜᱮᱞ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱯᱟᱥᱮ 1900 ᱨᱮ ᱡᱩᱣᱟ ᱯᱚᱛᱷᱤ ᱠᱚ ᱨᱮ ᱵᱚᱞᱚ ᱮᱱᱟ᱾ ᱥᱟᱭ ᱥᱮᱨᱢᱟ ᱛᱟᱞᱟ ᱨᱮ ᱰᱟᱠ ᱛᱮ ᱟᱠᱷᱨᱤᱧ ᱥᱤᱥᱴᱮᱢ ᱠᱚ ᱦᱮᱡ ᱞᱮᱱᱟ, ᱡᱚᱛᱚ ᱥᱟᱶ ᱢᱤᱫ ᱥᱟᱠᱷᱤ ᱟᱨ ᱴᱟᱠᱟ ᱨᱩᱣᱟᱹᱲ ᱨᱮᱭᱟᱜ ᱠᱟᱛᱷᱟ, ᱟᱨ ᱯᱟᱦᱤᱞ ᱠᱚᱢᱯᱭᱩᱴᱟᱨ ᱥᱤᱢᱩᱞᱮᱥᱚᱱ ᱠᱚ, ᱡᱟᱦᱟᱸ ᱠᱚ ᱫᱚ ᱜᱚᱱᱤᱛ ᱟᱜᱟᱢ ᱜᱮ ᱡᱟᱦᱟᱸ ᱞᱟᱹᱭ ᱟᱠᱟᱫᱟ ᱚᱱᱟ ᱜᱮ ᱩᱫᱩᱜ ᱠᱮᱫᱟ᱾ ᱡᱟᱦᱟᱸ ᱥᱤᱥᱴᱮᱢ ᱦᱚᱸ ᱵᱟᱝ ᱠᱟᱹᱢᱤᱭᱟ, ᱱᱚᱶᱟ ᱨᱮᱭᱟᱜ ᱥᱟᱵᱩᱫ ᱟᱜᱟᱢ ᱜᱮ ᱛᱟᱦᱮᱸᱫ: ᱡᱚᱥᱮᱯᱷ ᱰᱩᱵ (1936) ᱟᱨ ᱯᱚᱞ ᱦᱟᱞᱢᱚᱥ (1939) ᱩᱫᱩᱜ ᱠᱤᱱ ᱠᱮᱫᱟ ᱡᱮ ᱚᱠᱛᱮ ᱟᱨ ᱡᱟᱦᱟᱸᱱᱤᱡ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱦᱩᱭᱩᱜ-ᱟ ᱚᱱᱟ ᱵᱟᱪᱷᱟᱣ ᱨᱮᱭᱟᱜ ᱡᱟᱦᱟᱸ ᱱᱤᱭᱚᱢ ᱦᱚᱸ ᱢᱤᱫ ᱱᱤᱭᱟᱭ ᱟᱨᱵᱟᱝ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱤᱨᱩᱫᱽ ᱠᱷᱮᱞ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱯᱷᱚᱞ ᱵᱟᱭ ᱵᱚᱫᱚᱞ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ, ᱟᱨ ᱛᱷᱚᱨᱯ ᱟᱜ 1969 ᱨᱮᱭᱟᱜ ᱥᱟᱨᱣᱮ ᱫᱚ ᱡᱩᱣᱟᱲᱤ ᱠᱚ ᱡᱟᱦᱟᱸ ᱞᱮᱠᱟ ᱥᱟᱢᱟᱝ ᱨᱮ ᱧᱟᱢᱟ ᱚᱱᱟ ᱞᱮᱠᱟ ᱛᱮ ᱥᱚᱨᱛᱚ ᱠᱚ ᱩᱫᱩᱜ ᱠᱮᱫᱟ᱾ ᱚᱱᱟ ᱠᱷᱚᱱ ᱥᱤᱥᱴᱮᱢ ᱠᱚ ᱵᱟᱝ ᱵᱚᱫᱚᱞ ᱟᱠᱟᱱᱟ; ᱯᱨᱚᱪᱟᱨ ᱫᱚ ᱯᱚᱛᱷᱤ ᱠᱷᱚᱱ ᱵᱷᱤᱰᱤᱭᱳ ᱛᱮ ᱥᱮᱱ ᱟᱠᱟᱱᱟ᱾
ᱪᱮᱫᱟᱜ ᱵᱟᱧᱪᱟᱣ ᱢᱮᱱᱟᱜ ᱠᱟᱱᱟ
ᱥᱤᱥᱴᱮᱢ ᱫᱚ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱪᱮᱫ ᱦᱚᱸ ᱠᱟᱹᱢᱤ ᱟᱨ ᱞᱟᱹᱭ ᱞᱟᱹᱜᱤᱫ ᱢᱤᱫ ᱠᱟᱹᱦᱱᱤ ᱮᱢᱟ᱾ ᱟᱹᱰᱤ ᱥᱤᱥᱴᱮᱢ ᱨᱮ ᱟᱹᱰᱤ ᱥᱮᱥᱚᱱ ᱢᱤᱫ ᱦᱩᱰᱤᱧ ᱡᱤᱛ ᱛᱮ ᱢᱩᱪᱟᱹᱫᱚᱜ-ᱟ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱦᱤᱥᱟᱹᱵ ᱠᱷᱚᱱ ᱵᱮᱥ ᱠᱟᱹᱦᱱᱤ ᱠᱟᱱᱟ᱾ ᱦᱟᱨᱟᱣ ᱥᱮᱥᱚᱱ ᱠᱚ ᱠᱚᱢ ᱦᱩᱭᱩᱜ-ᱟ ᱟᱨ ᱵᱷᱟᱹᱜᱭᱚ ᱵᱟᱝ ᱵᱮᱥ ᱞᱮᱠᱟ ᱩᱭᱦᱟᱹᱨᱚᱜ-ᱟ᱾ ᱯᱨᱚᱪᱟᱨ ᱞᱟᱹᱜᱤᱫ ᱚᱰᱥ ᱵᱟᱵᱚᱫ ᱢᱤᱪᱷᱟ ᱞᱟᱹᱭ ᱵᱟᱝ ᱞᱟᱹᱠᱛᱤᱭᱟ; ᱢᱤᱫ ᱡᱤᱛ ᱥᱮᱥᱚᱱ ᱩᱫᱩᱜ ᱜᱮ ᱡᱚᱛᱚ ᱠᱟᱱᱟ, ᱟᱨ ᱚᱱᱟ ᱟᱹᱰᱤ ᱢᱮᱱᱟᱜ-ᱟ᱾ ᱩᱞᱴᱟᱹ ᱜᱟᱞᱚᱪ, 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%, 1843 ᱠᱷᱚᱱ ᱢᱮᱱᱟᱜ-ᱟ ᱢᱮᱱᱠᱷᱟᱱ ᱡᱟᱣᱽᱨᱟ ᱢᱤᱫ ᱵᱷᱟᱹᱜᱭᱚ ᱧᱤᱫᱟᱹ ᱞᱮᱠᱟ ᱵᱟᱭ ᱞᱚᱵᱷᱟᱣ ᱫᱟᱲᱮᱭᱟᱜ ᱞᱮᱱᱟ᱾
ᱟᱠᱷᱨᱤᱧ ᱞᱟᱹᱜᱤᱫ ᱥᱤᱥᱴᱮᱢ
20 ᱥᱟᱭ ᱥᱮᱨᱢᱟ ᱨᱮᱭᱟᱜ ᱵᱮᱯᱟᱨ ᱫᱚ ᱟᱡᱟᱜ ᱦᱚᱨᱟ ᱠᱚ ᱥᱮᱞᱮᱫ ᱠᱮᱫᱟ, ᱡᱚᱛᱚ ᱫᱚ ᱚᱱᱟ ᱜᱮ ᱦᱟᱹᱱᱤ ᱟᱸᱫᱟᱡᱽ ᱵᱟᱡᱤ ᱠᱚ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱱᱟᱣᱟ ᱥᱟᱡᱟᱣ᱾ ᱯᱷᱮᱡᱽ ᱣᱟᱱ (Phase One) ᱫᱚ $25 ᱟᱨ ᱠᱤᱨᱤᱧᱤᱭᱟᱹ ᱨᱮᱭᱟᱜ ᱡᱤᱛ ᱨᱮᱭᱟᱜ 10% ᱨᱮ ᱟᱠᱷᱨᱤᱧᱚᱜ ᱛᱟᱦᱮᱸᱫ, $500 ᱮᱢ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱯᱷᱮᱡᱽ ᱴᱩ ᱟᱨ $5,000 ᱨᱮ ᱢᱤᱫ “ᱤᱱᱟᱨ ᱥᱟᱨᱠᱮᱞ” ᱨᱮᱭᱟᱜ ᱠᱟᱛᱷᱟ ᱥᱟᱶ᱾ ᱱᱚᱶᱟ ᱠᱚ ᱢᱩᱫᱽ ᱨᱮ ᱢᱤᱫᱴᱟᱝ ᱦᱚᱸ ᱦᱤᱥᱟᱹᱵ ᱵᱟᱭ ᱵᱚᱫᱚᱞᱟ: ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱛᱟᱹᱞᱤᱠᱟᱹ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱜᱚᱱᱤᱛᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱡᱮᱞᱮᱧ ᱚᱠᱛᱚ ᱨᱮ ᱢᱤᱫ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱨᱮᱡᱟᱞᱴ᱾ ᱡᱚᱛᱚ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱭᱩᱨᱚᱯᱤᱭᱟᱱ ᱵᱟᱡᱤ ᱨᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ −1/37᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱩᱱᱠᱩᱣᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱨᱮᱭᱟᱜ ᱡᱚᱲ ᱠᱟᱱᱟ᱾
ᱡᱟᱦᱟᱸ ᱫᱚ ᱥᱤᱥᱴᱮᱢ ᱵᱟᱝ ᱠᱟᱱᱟ
ᱛᱤᱝᱜᱩ ᱱᱤᱭᱚᱢ: ᱢᱟᱲᱟᱝ ᱠᱷᱚᱱ ᱡᱟᱦᱟᱸᱱᱤᱡ ᱦᱟᱨᱟᱣ ᱟᱨᱵᱟᱝ ᱡᱤᱛᱟᱹᱣ ᱞᱟᱹᱜᱤᱫ ᱛᱷᱤᱨ ᱠᱟᱛᱮ ᱵᱟᱹᱜᱤ᱾ ᱟᱹᱰᱤ ᱫᱷᱟᱣ ᱱᱚᱶᱟ ᱠᱚ ᱥᱤᱥᱴᱮᱢ ᱨᱮᱭᱟᱜ ᱦᱟᱹᱴᱤᱧ ᱞᱮᱠᱟ ᱟᱠᱷᱨᱤᱧᱚᱜ-ᱟ ᱟᱨ ᱱᱚᱶᱟ ᱜᱮ ᱢᱤᱫ ᱜᱚᱴᱟ ᱦᱟᱹᱴᱤᱧ ᱡᱟᱦᱟᱸ ᱫᱚ ᱪᱮᱫ ᱦᱚᱸ ᱠᱟᱹᱢᱤᱭᱟ, ᱪᱮᱫᱟᱜ ᱡᱮ ᱱᱚᱶᱟ ᱠᱚ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱦᱤᱥᱟᱹᱵ ᱠᱚᱢ ᱮᱫᱟ᱾ ᱱᱚᱶᱟ ᱠᱚᱣᱟᱜ ᱡᱟᱦᱟᱸ ᱧᱩᱛᱩᱢ ᱦᱚᱲ ᱵᱟᱹᱱᱩᱜ-ᱟ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱴᱷᱤᱠ ᱜᱮ ᱠᱟᱱᱟ᱾
ᱠᱩᱠᱞᱤ ᱠᱚ
ᱢᱟᱨᱴᱤᱝᱜᱮᱞ, ᱢᱤᱫ ᱥᱟᱭ ᱥᱮᱨᱢᱟ ᱟᱨᱵᱟᱝ ᱡᱟᱹᱥᱛᱤ ᱛᱮ᱾ ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱫᱩᱱᱟ ᱫᱚ ᱡᱚᱛᱚᱭ ᱦᱚᱲ ᱨᱮᱭᱟᱜ ᱯᱟᱦᱤᱞ ᱵᱤᱪᱟᱹᱨ ᱠᱟᱱᱟ᱾
ᱫᱟᱞᱟᱸᱵᱮᱨ ᱡᱟᱹᱥᱛᱤ ᱥᱮᱴᱮᱨ ᱮᱱᱟᱭ, ᱵᱷᱩᱞ ᱛᱮ᱾ ᱯᱟᱥᱠᱟᱞ, ᱯᱷᱮᱨᱢᱟ, ᱦᱟᱭᱜᱮᱱᱥ, ᱵᱮᱨᱱᱩᱞᱤ ᱟᱨ ᱞᱟᱯᱞᱟᱥ ᱡᱚᱛᱚ ᱠᱚ ᱵᱩᱡᱷᱟᱹᱣ ᱠᱮᱫᱟ ᱪᱮᱫᱟᱜ ᱥᱤᱥᱴᱮᱢ ᱠᱚ ᱵᱷᱟᱝᱜᱚᱱᱚᱜ-ᱟ᱾
ᱪᱮᱫᱟᱜ ᱡᱮ ᱟᱹᱰᱤ ᱥᱮᱥᱚᱱ ᱡᱤᱛᱚᱜ-ᱟ, ᱟᱨ ᱢᱤᱫ ᱡᱤᱛ ᱥᱮᱥᱚᱱ ᱨᱮᱭᱟᱜ ᱵᱷᱤᱰᱤᱭᱳ ᱛᱮᱭᱟᱨ ᱫᱚ ᱥᱚᱥᱛᱟ ᱠᱟᱱᱟ᱾
ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ
ᱵᱟᱨ ᱥᱟᱭ ᱥᱮᱨᱢᱟ ᱨᱮᱭᱟᱜ ᱧᱩᱛᱩᱢ ᱠᱚ᱾ ᱢᱤᱫ ᱜᱚᱴᱟ ᱮᱞ᱾
ᱯᱷᱮᱰᱟᱛ
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- d’Alembert, J. “Croix ou pile.”
- Schwartz, D. G. Roll the Bones: The History of Gambling.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.