ᱨᱩᱞᱮᱴ ᱦᱟᱨᱟᱣ ᱫᱟᱲᱮᱭᱟᱜ ᱟᱯᱮ ᱥᱮ? ᱨᱩᱞᱮᱴ ᱨᱮ ᱪᱮᱫ ᱞᱮᱠᱟ ᱡᱤᱛᱚᱜ-ᱟ
ᱨᱩᱞᱮᱴ ᱨᱮ ᱪᱮᱫ ᱞᱮᱠᱟ ᱡᱤᱛᱚᱜ-ᱟ? ᱢᱤᱫ ᱵᱟᱡᱤ ᱦᱚᱨᱟ ᱛᱮ ᱫᱚ ᱵᱟᱝ᱾ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ, ᱤᱛᱤᱦᱟᱹᱥ ᱨᱮ, ᱢᱤᱫ ᱠᱷᱟᱹᱢᱤ ᱪᱟᱠᱟ ᱥᱮ ᱟᱸᱫᱟᱡᱽ ᱫᱟᱲᱮᱭᱟᱜ ᱰᱤᱞᱟᱨ ᱥᱟᱶ, ᱟᱨ ᱟᱹᱰᱤ ᱢᱟᱨᱟᱝ ᱠᱟᱹᱢᱤ ᱛᱮ ᱜᱮ᱾
ᱵᱟᱡᱤ ᱥᱤᱥᱴᱮᱢ ᱫᱚ ᱨᱩᱞᱮᱴ ᱵᱟᱝ ᱦᱟᱨᱟᱣ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ: ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱜᱚᱱᱤᱛᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱡᱮᱞᱮᱧ ᱚᱠᱛᱚ ᱨᱮ ᱢᱤᱫ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱨᱮᱡᱟᱞᱴ᱾ ᱡᱚᱛᱚ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱭᱩᱨᱚᱯᱤᱭᱟᱱ ᱵᱟᱡᱤ ᱨᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ −1/37᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱡᱚᱲᱚᱜ-ᱟ ᱟᱨ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱱᱮᱜᱮᱴᱤᱵᱷ ᱜᱮᱭᱟ᱾ ᱚᱞ ᱟᱠᱟᱱ ᱡᱤᱛ ᱠᱚ ᱫᱚ ᱯᱷᱤᱡᱤᱠᱥ ᱵᱮᱵᱷᱟᱨ ᱠᱷᱚᱱ ᱦᱮᱡ ᱟᱠᱟᱱᱟ, ᱦᱚᱨᱟ ᱠᱷᱚᱱ ᱫᱚ ᱵᱟᱝ᱾
ᱥᱤᱥᱴᱮᱢ ᱠᱚ ᱪᱮᱫᱟᱜ ᱵᱷᱮᱜᱟᱨᱚᱜ-ᱟ
ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ EV = ᱟᱡᱟᱜ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ −1/37᱾ ᱞᱟᱦᱟ ᱨᱮᱡᱟᱞᱴ ᱠᱷᱚᱱ ᱡᱮᱞᱮᱠᱟ ᱦᱚᱸ ᱵᱟᱪᱷᱟᱣ ᱞᱮᱱ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱡᱟᱦᱟᱸᱱ ᱫᱷᱟᱨᱟ ᱨᱮᱭᱟᱜ EV = ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ −1/37᱾ ᱱᱚᱶᱟ ᱫᱚ ᱥᱟᱹᱜᱩᱱ ᱵᱮᱨᱤᱭᱮᱵᱚᱞ ᱨᱮᱭᱟᱜ ᱡᱚᱲ ᱵᱟᱵᱚᱫ ᱢᱤᱫ ᱛᱷᱤᱭᱳᱨᱮᱢ ᱠᱟᱱᱟ, ᱢᱤᱫ ᱧᱮᱞ ᱠᱷᱚᱱ ᱧᱟᱢ ᱠᱟᱛᱷᱟ ᱫᱚ ᱵᱟᱝ ᱡᱟᱦᱟᱸ ᱢᱤᱫ ᱵᱮᱥ ᱥᱤᱥᱴᱮᱢ ᱩᱞᱴᱟᱹᱣ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾ ᱡᱚᱥᱮᱯᱷ ᱰᱩᱵ (Joseph Doob) ᱟᱨ ᱯᱚᱞ ᱦᱟᱞᱢᱚᱥ (Paul Halmos) 1930 ᱥᱮᱨᱢᱟ ᱠᱚ ᱨᱮ ᱱᱚᱶᱟ ᱥᱟᱵᱩᱫ ᱞᱮᱫᱟ ᱠᱤᱱ, ᱟᱨ ᱮᱰᱣᱟᱨᱰ ᱛᱷᱚᱨᱯ (Edward Thorp), ᱡᱟᱦᱟᱸᱭ ᱠᱟᱨᱰ ᱞᱮᱠᱷᱟ ᱠᱟᱛᱮ ᱵᱞᱮᱠᱡᱮᱠ ᱦᱟᱨᱟᱣ ᱞᱮᱫᱟ, ᱚᱱᱟ ᱞᱟᱹᱜᱤᱫ ᱞᱟᱹᱠᱛᱤᱭᱟᱱ ᱥᱚᱨᱛᱚ ᱠᱚ ᱮ ᱚᱞ ᱞᱮᱫᱟ: ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱱᱮᱜᱮᱴᱤᱵᱷ, ᱟᱡᱟᱫ ᱜᱷᱩᱨᱟᱹᱣᱜᱚᱱᱤᱛᱟᱡᱟᱫ ᱜᱷᱩᱨᱟᱹᱣᱢᱟᱨᱮ ᱪᱮᱫ ᱦᱚᱸ ᱦᱩᱭ ᱠᱷᱟᱱ ᱦᱚᱸ ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱢᱤᱫ ᱞᱮᱠᱟ ᱜᱮ᱾ ᱱᱚᱶᱟ ᱥᱟᱭᱤᱴ ᱨᱮᱭᱟᱜ ᱡᱚᱛᱚ ᱦᱤᱥᱟᱹᱵ ᱨᱮᱭᱟᱜ ᱵᱮᱥ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ →, ᱢᱤᱫ ᱴᱮᱵᱩᱞ ᱵᱮᱥᱤ ᱥᱮ ᱵᱮᱥᱤ ᱟᱨ ᱢᱤᱫ ᱴᱮᱵᱩᱞ ᱠᱚᱢ ᱥᱮ ᱠᱚᱢ᱾ ᱩᱱᱤᱭᱟᱜ 1966 ᱥᱮᱨᱢᱟ ᱨᱮᱭᱟᱜ ᱯᱟᱲᱦᱟᱣ ᱯᱩᱛᱷᱤ ᱫᱚ ᱢᱤᱫ ᱥᱚᱡᱷᱮ ᱥᱟᱵᱩᱫ ᱮᱢ ᱮᱫᱟ᱾
ᱪᱮᱫ ᱠᱟᱹᱢᱤ ᱞᱮᱱᱟ
ᱯᱮ ᱜᱚᱴᱟᱝ ᱡᱤᱱᱤᱥ, ᱡᱚᱛᱚ ᱥᱟᱨᱤᱨ ᱪᱟᱠᱟ ᱥᱟᱶ ᱡᱚᱲᱟᱣ᱾ ᱵᱟᱭᱟᱥ: ᱢᱤᱫ ᱪᱟᱠᱟ ᱡᱟᱦᱟᱸ ᱨᱮᱭᱟᱜ ᱠᱷᱟᱱᱟᱥᱟᱡ ᱥᱟᱢᱟᱱᱠᱷᱟᱱᱟᱨᱚᱴᱚᱨ ᱨᱮᱭᱟᱜ 37 ᱮᱞ ᱚᱞ ᱠᱷᱟᱱᱟ ᱠᱷᱚᱱ ᱢᱤᱫ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱞᱚᱴ, ᱠᱟᱯ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱚ ᱥᱚᱢᱟᱱ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱵᱟᱝ ᱠᱟᱱᱟ, ᱦᱟᱡᱟᱨ ᱦᱟᱡᱟᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱚᱞ ᱠᱟᱛᱮ ᱧᱟᱢ ᱟᱠᱟᱱᱟ᱾ ᱟᱸᱫᱟᱡᱽ: ᱵᱚᱞᱥᱟᱡ ᱥᱟᱢᱟᱱᱵᱚᱞᱨᱚᱴᱚᱨ ᱨᱮᱭᱟᱜ ᱩᱞᱴᱟᱹ ᱥᱮᱫ ᱴᱨᱮᱠ ᱨᱮ ᱜᱤᱰᱤ ᱦᱩᱰᱤᱧ ᱵᱚᱞ᱾ ᱱᱤᱛᱚᱜᱟᱜ ᱵᱚᱞ ᱫᱚ ᱟᱭᱣᱚᱨᱤᱱ ᱟᱨᱵᱟᱝ ᱴᱮᱯᱷᱞᱚᱱ ᱨᱮᱭᱟᱜ, 18–21 mm᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱟᱨ ᱨᱚᱴᱚᱨᱥᱟᱡ ᱥᱟᱢᱟᱱᱨᱚᱴᱚᱨᱪᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱜᱷᱩᱨᱟᱹᱣᱚᱜ ᱦᱟᱹᱴᱤᱧ ᱡᱟᱦᱟᱸ ᱨᱮ ᱠᱷᱟᱱᱟ ᱠᱚ ᱢᱮᱱᱟᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ ᱚᱠᱛᱚ ᱢᱟᱯ ᱠᱟᱛᱮ ᱵᱚᱞ ᱧᱩᱨᱩᱜ ᱥᱮᱠᱴᱚᱨᱪᱟᱠᱟᱥᱮᱠᱴᱚᱨᱪᱟᱠᱟ ᱨᱮ ᱛᱟᱭᱚᱢ ᱛᱟᱭᱚᱢ ᱠᱷᱟᱱᱟ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱜᱩᱞᱟᱹᱭ ᱦᱟᱹᱴᱤᱧ, ᱞᱮᱭᱟᱣᱴ ᱨᱮᱭᱟᱜ ᱜᱩᱴᱤ ᱠᱷᱚᱱ ᱟᱞᱟᱜ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱟᱸᱫᱟᱡᱽ, 1970 ᱥᱮᱨᱢᱟ ᱠᱚ ᱠᱷᱚᱱ ᱩᱠᱩ ᱠᱚᱢᱯᱭᱩᱴᱟᱨ ᱥᱟᱶ ᱦᱩᱭ ᱟᱠᱟᱱᱟ᱾ ᱰᱤᱞᱟᱨ ᱥᱟᱦᱤ: ᱢᱤᱫ ᱩᱭᱦᱟᱹᱨ ᱡᱮ ᱰᱤᱞᱟᱨ ᱨᱮᱭᱟᱜ ᱵᱚᱞ ᱮᱫᱮᱫ ᱫᱚ ᱵᱚᱞ ᱧᱩᱨ ᱟᱸᱫᱟᱡᱽ ᱞᱟᱹᱜᱤᱫ ᱡᱩᱛ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱜᱮᱭᱟ, ᱛᱤᱥ ᱦᱚᱸ ᱯᱚᱛᱭᱟᱣ ᱞᱮᱠᱟᱛᱮ ᱵᱟᱝ ᱩᱫᱩᱜ ᱟᱠᱟᱱᱟ᱾ ᱯᱮᱭᱟ ᱞᱟᱹᱜᱤᱫ ᱢᱤᱫ ᱥᱟᱨᱤᱨ ᱪᱟᱠᱟ, ᱡᱮᱞᱮᱧ ᱧᱮᱞ ᱟᱨ ᱢᱤᱫ ᱠᱮᱥᱤᱱᱳ ᱡᱟᱦᱟᱸ ᱵᱟᱭ ᱧᱮᱞ ᱧᱟᱢ ᱞᱮᱫᱟ ᱞᱟᱹᱠᱛᱤᱭᱟ᱾
ᱡᱚᱥᱮᱯᱷ ᱡᱮᱜᱟᱨ (Joseph Jagger) ᱫᱚ ᱢᱚᱱᱴᱮ ᱠᱟᱨᱞᱚ ᱨᱮᱭᱟᱜ ᱪᱟᱠᱟ ᱠᱚ ᱚᱞ ᱪᱷᱚᱭ ᱮᱫᱟᱭ, ᱟᱹᱰᱤ ᱦᱤᱡᱩᱜ ᱮᱞ ᱠᱚ ᱧᱟᱢ ᱮᱫᱟᱭ, ᱟᱨ ᱠᱮᱥᱤᱱᱳ ᱟᱡᱟᱜ ᱪᱟᱠᱟ ᱠᱚ ᱥᱟᱨᱮᱡ ᱟᱨ ᱛᱟᱭᱚᱢ ᱵᱚᱫᱚᱞ ᱦᱟᱹᱵᱤᱡ ᱟᱹᱰᱤ ᱡᱤᱛᱟᱹᱣ ᱮᱫᱟᱭ᱾
ᱪᱟᱨᱞᱥ ᱣᱮᱞᱥ (Charles Wells) ᱫᱚ ᱟᱹᱰᱤ ᱥᱟᱜᱩᱱ ᱟᱨ ᱛᱤᱥ ᱦᱚᱸ ᱵᱟᱭ ᱵᱩᱡᱷᱟᱹᱣ ᱞᱮᱫᱟ ᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱥᱟᱶ “ᱵᱮᱸᱠ ᱨᱟᱹᱯᱩᱫ ᱮᱫᱟᱭ”᱾ ᱚᱱᱟ ᱨᱟᱵᱟᱝ ᱨᱮ ᱩᱱᱤ ᱨᱩᱣᱟᱹᱲ ᱠᱟᱛᱮ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱦᱟᱹᱴᱤᱧ ᱫᱚᱦᱲᱟ ᱦᱟᱹᱱᱤ ᱮᱫᱟᱭ᱾
ᱮᱰᱣᱟᱨᱰ ᱛᱷᱚᱨᱯ ᱟᱨ ᱠᱞᱳᱰ ᱥᱮᱱᱚᱱ (Claude Shannon) ᱫᱚ ᱨᱩᱞᱮᱴ ᱵᱚᱞ ᱨᱮᱭᱟᱜ ᱚᱠᱛᱚ ᱢᱟᱯ ᱞᱟᱹᱜᱤᱫ ᱯᱟᱦᱤᱞ ᱦᱚᱲᱢᱚ ᱨᱮ ᱫᱚᱦᱚ ᱠᱚᱢᱯᱭᱩᱴᱟᱨ ᱵᱮᱱᱟᱣ ᱮᱫᱟ ᱠᱤᱱ᱾ ᱡᱚᱱᱛᱚᱨ ᱫᱚ ᱡᱚᱦᱚᱢ ᱡᱚᱦᱚᱢ ᱠᱟᱹᱢᱤᱭ-ᱟ; ᱯᱨᱚᱡᱮᱠᱴ ᱫᱚ ᱵᱟᱹᱜᱤᱚᱜ-ᱟ᱾
ᱥᱟᱱᱴᱟ ᱠᱨᱩᱡᱽ ᱨᱮᱭᱟᱜ ᱭᱩᱰᱮᱢᱚᱱᱥ (Eudaemons) ᱫᱚ ᱱᱮᱵᱷᱟᱰᱟ ᱨᱮᱭᱟᱜ ᱠᱮᱥᱤᱱᱳ ᱠᱚ ᱨᱮ ᱩᱠᱩ ᱠᱚᱢᱯᱭᱩᱴᱟᱨ ᱵᱮᱵᱷᱟᱨ ᱮᱫᱟ ᱠᱚ᱾ ᱥᱟᱹᱨᱤ ᱵᱟᱲᱛᱤ, ᱵᱟᱝ ᱯᱚᱛᱭᱟᱣ ᱞᱮᱠᱟᱱ ᱤᱞᱮᱠᱴᱨᱚᱱᱤᱠᱥ, ᱡᱟᱦᱟᱸᱱ ᱫᱷᱚᱱ ᱵᱟᱝ᱾
ᱜᱚᱱᱡᱟᱞᱳ ᱜᱟᱨᱥᱤᱭᱟ-ᱯᱮᱞᱟᱭᱳ (Gonzalo García-Pelayo) ᱟᱨ ᱩᱱᱤᱭᱟᱜ ᱜᱷᱟᱨᱚᱧᱡᱽ ᱫᱚ ᱢᱟᱰᱨᱤᱰ ᱥᱮᱴᱮᱨ ᱡᱚᱛᱚ ᱪᱟᱠᱟ ᱨᱮ ᱡᱚᱦᱚᱢ 5,000 ᱜᱷᱩᱨᱟᱹᱣ ᱚᱞ ᱮᱫᱟ ᱠᱚ, ᱵᱟᱭᱟᱥ ᱪᱟᱠᱟ ᱧᱟᱢ ᱮᱫᱟ ᱠᱚ, ᱡᱤᱛᱚᱜ-ᱟ ᱠᱚ, ᱵᱟᱨᱚᱱᱚᱜ-ᱟ ᱠᱚ, ᱟᱨ ᱠᱳᱨᱴ ᱨᱮ ᱵᱟᱨᱚᱱ ᱵᱟᱹᱛᱤᱞ ᱦᱩᱭᱩᱜ ᱧᱮᱞ ᱮᱫᱟ ᱠᱚ᱾
ᱯᱮ ᱠᱷᱮᱞᱚᱸᱰ ᱞᱚᱱᱰᱚᱱ ᱨᱮᱭᱟᱜ ᱨᱤᱴᱡᱽ (Ritz) ᱨᱮ ᱵᱚᱞ ᱧᱩᱨ ᱟᱸᱫᱟᱡᱽ ᱠᱟᱛᱮ £1.3 ᱢᱤᱞᱤᱭᱚᱱ ᱡᱤᱛᱟᱹᱣ ᱮᱫᱟ ᱠᱚ᱾ ᱞᱮᱡᱟᱨ ᱨᱮᱭᱟᱜ ᱠᱟᱛᱷᱟ ᱟᱹᱲᱟᱹᱜ ᱞᱮᱱᱟ ᱢᱮᱱᱠᱷᱟᱱ ᱛᱤᱥ ᱦᱚᱸ ᱵᱟᱝ ᱩᱫᱩᱜ ᱞᱮᱱᱟ; ᱩᱱᱠᱩ ᱫᱚ ᱡᱤᱛ ᱴᱟᱠᱟ ᱫᱚᱦᱚ ᱮᱫᱟ ᱠᱚ᱾
ᱥᱢᱚᱞ (Small) ᱟᱨ ᱥᱮ (Tse) ᱫᱚ ᱢᱤᱫ ᱯᱷᱤᱡᱤᱠᱥ ᱚᱱᱚᱞ ᱪᱷᱟᱯᱟ ᱮᱫᱟ ᱠᱤᱱ ᱡᱟᱦᱟᱸ ᱫᱚ ᱩᱫᱩᱜ ᱮᱫᱟ ᱡᱮ ᱞᱮᱵ ᱦᱟᱹᱞᱚᱛ ᱨᱮ ᱚᱠᱛᱚ ᱢᱟᱯ ᱥᱟᱶ ᱛᱤᱱᱟᱹᱜ ᱯᱟᱹᱨᱥᱮᱱᱴ ᱵᱟᱲᱛᱤ ᱧᱟᱢ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾
ᱱᱚᱶᱟ ᱱᱤᱛ ᱪᱮᱫᱟᱜ ᱵᱟᱝ ᱠᱟᱹᱢᱤᱭ-ᱟ
ᱠᱮᱥᱤᱱᱳ ᱠᱚ ᱵᱚᱣᱞᱥᱟᱡ ᱥᱟᱢᱟᱱᱵᱚᱣᱞᱪᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱛᱷᱤᱨ ᱵᱟᱦᱨᱮ ᱦᱟᱹᱴᱤᱧ: ᱠᱟᱴ ᱟᱨᱵᱟᱝ ᱠᱚᱢᱯᱚᱡᱤᱴ ᱫᱷᱟᱨᱮ ᱡᱟᱦᱟᱸ ᱨᱮ ᱵᱚᱞ ᱴᱨᱮᱠ ᱟᱨ ᱮᱯᱨᱚᱱ ᱢᱮᱱᱟᱜ-ᱟ, ᱟᱨ ᱡᱟᱦᱟᱸ ᱵᱷᱤᱛᱤᱨ ᱨᱮ ᱨᱚᱴᱚᱨ ᱜᱷᱩᱨᱟᱹᱣᱚᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱛᱟᱞᱟ ᱨᱮ ᱪᱟᱠᱟ ᱵᱚᱦᱚᱜᱥᱟᱡ ᱥᱟᱢᱟᱱᱪᱟᱠᱟ ᱵᱚᱦᱚᱜᱨᱚᱴᱚᱨ ᱨᱮᱭᱟᱜ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱮᱞ ᱠᱚ ᱫᱚᱦᱚ ᱜᱷᱩᱨᱟᱹᱣᱚᱜ ᱦᱟᱹᱴᱤᱧ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱵᱚᱫᱚᱞ ᱮᱫᱟ ᱠᱚ, ᱵᱚᱣᱞ ᱥᱚᱢᱟᱱ ᱮᱫᱟ ᱠᱚ, ᱠᱷᱟᱱᱟ ᱢᱟᱯ ᱮᱫᱟ ᱠᱚ ᱟᱨ ᱴᱷᱤᱠ ᱚᱠᱛᱚ ᱨᱮ ᱯᱷᱨᱮᱴᱥᱟᱡ ᱥᱟᱢᱟᱱᱯᱷᱨᱮᱴᱪᱟᱠᱟ ᱨᱮ ᱵᱟᱨ ᱠᱷᱟᱱᱟ ᱛᱟᱞᱟ ᱨᱮᱭᱟᱜ ᱞᱚᱦᱟ ᱟᱲ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱵᱚᱫᱚᱞ ᱮᱫᱟ ᱠᱚ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱵᱟᱭᱟᱥ ᱦᱟᱨᱟᱣ ᱮᱫᱟ᱾ ᱞᱟᱭᱤᱵᱷ ᱥᱴᱩᱰᱤᱭᱳ ᱫᱚ ᱵᱚᱞ ᱞᱟᱦᱟᱭ ᱞᱟᱦᱟ ᱵᱟᱡᱤ ᱵᱚᱸᱫ ᱮᱫᱟ ᱟᱨ ᱥᱴᱨᱤᱢ ᱨᱮᱭᱟᱜ ᱵᱤᱞᱚᱢ ᱴᱷᱤᱠ ᱮᱫᱟ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱚᱠᱛᱚ ᱢᱟᱯ ᱦᱟᱨᱟᱣ ᱮᱫᱟ᱾ ᱡᱟᱹᱥᱛᱤ ᱮᱞᱟᱠᱟ ᱨᱮ ᱟᱸᱫᱟᱡᱽ ᱡᱚᱱᱛᱚᱨ ᱫᱚ ᱫᱚᱥ ᱠᱟᱱᱟ᱾ ᱰᱤᱞᱟᱨ ᱠᱚ ᱵᱚᱞ ᱮᱫᱮᱫ ᱵᱚᱫᱚᱞ ᱞᱟᱹᱜᱤᱫ ᱦᱩᱠᱩᱢ ᱧᱟᱢ ᱮᱫᱟ ᱠᱚ᱾ ᱢᱤᱫ ᱞᱟᱭᱤᱥᱮᱱᱥ ᱠᱮᱥᱤᱱᱳ ᱥᱮ ᱥᱴᱩᱰᱤᱭᱳ ᱨᱮ ᱢᱤᱫ ᱱᱟᱣᱟ, ᱥᱟᱢᱵᱷᱟᱞ ᱪᱟᱠᱟ ᱞᱟᱹᱜᱤᱫ ᱥᱟᱹᱨᱤ ᱛᱮᱞᱟ ᱫᱚ ᱵᱟᱝ᱾
ᱨᱩᱞᱮᱴ ᱪᱮᱫ ᱞᱮᱠᱟ ᱦᱟᱨᱟᱣ, ᱮᱠᱮᱞ ᱵᱤᱪᱟᱨ ᱞᱮᱠᱟᱛᱮ: ᱪᱮᱫ ᱞᱟᱹᱠᱛᱤᱭᱟ
ᱢᱮᱱ ᱞᱮ ᱢᱤᱫ ᱠᱷᱟᱱᱟ ᱫᱚ 37 ᱨᱮ 1 ᱵᱚᱫᱚᱞ ᱨᱮ 33 ᱨᱮ 1 ᱦᱤᱴ ᱮᱫᱟ᱾ ᱚᱱᱟ ᱨᱮ ᱢᱤᱫ ᱥᱴᱨᱮᱴ ᱚᱯᱵᱟᱡᱤᱥᱴᱨᱮᱴ ᱚᱯᱢᱤᱫ ᱮᱞ, ᱵᱷᱩᱜᱛᱟᱱ 35:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ EV = 35/33 − 32/33 = +3/33 ≈ +9%᱾ ᱠᱷᱟᱱᱟ ᱫᱚ ᱥᱟᱜᱩᱱ ᱵᱟᱝ, ᱵᱟᱭᱟᱥ ᱠᱟᱱᱟ ᱚᱱᱟ ᱵᱟᱰᱟᱭ ᱞᱟᱹᱜᱤᱫ ᱚᱱᱟ ᱪᱟᱠᱟ ᱠᱷᱚᱱ ᱡᱚᱦᱚᱢ 10,000 ᱚᱞ ᱟᱠᱟᱱ ᱜᱷᱩᱨᱟᱹᱣ ᱞᱟᱹᱠᱛᱤᱭᱟ; ᱚᱱᱟ ᱵᱮᱵᱷᱟᱨ ᱞᱟᱹᱜᱤᱫ ᱟᱯᱮ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱚᱠᱛᱚ ᱪᱟᱠᱟ ᱵᱟᱝ ᱵᱚᱫᱚᱞᱚᱜ ᱞᱟᱹᱠᱛᱤᱭᱟ᱾ ᱞᱮᱵ ᱥᱟᱦᱴᱟ ᱠᱚ ᱫᱚ ᱥᱴᱮᱴᱤᱥᱴᱤᱠᱥ ᱵᱩᱡᱷᱟᱹᱣ ᱮᱫᱟ; ᱤᱛᱤᱦᱟᱹᱥ ᱥᱟᱦᱴᱟ ᱠᱚ ᱫᱚ ᱱᱚᱶᱟ ᱠᱟᱹᱢᱤ ᱦᱚᱲ ᱠᱚ ᱥᱟᱶ ᱪᱮᱫ ᱦᱩᱭᱮᱱᱟ ᱚᱱᱟ ᱵᱩᱡᱷᱟᱹᱣ ᱮᱫᱟ᱾
ᱥᱟᱹᱨᱤ ᱛᱮᱞᱟ
ᱥᱤᱥᱴᱮᱢ ᱢᱮᱱᱟᱜ ᱯᱟᱲᱦᱟᱣᱤᱭᱟᱹ ᱞᱟᱹᱜᱤᱫ: ᱱᱚᱶᱟ ᱵᱟᱝ ᱠᱟᱹᱢᱤᱭᱟ, ᱟᱨ ᱟᱯᱮ ᱱᱚᱶᱟ ᱥᱟᱭᱤᱴ ᱨᱮᱭᱟᱜ ᱥᱤᱢᱩᱞᱮᱴᱚᱨ ᱥᱟᱶ ᱢᱤᱫ ᱫᱤᱱ ᱛᱟᱭᱚᱢ ᱵᱮᱞᱟ ᱨᱮ ᱚᱱᱟ ᱪᱮᱠᱟᱣ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ ᱯᱮ᱾ ᱠᱷᱟᱛᱟ ᱟᱨ ᱫᱷᱤᱨᱡᱚ ᱢᱮᱱᱟᱜ ᱯᱟᱲᱦᱟᱣᱤᱭᱟᱹ ᱞᱟᱹᱜᱤᱫ: ᱵᱤᱪᱟᱨ ᱞᱮᱠᱟᱛᱮ ᱵᱟᱭᱟᱥ ᱢᱮᱱᱟᱜ-ᱟ ᱟᱨ ᱵᱮᱵᱷᱟᱨ ᱨᱮ ᱚᱱᱟ ᱢᱮᱴᱟᱣ ᱦᱩᱭᱩᱜ-ᱟ᱾ ᱡᱚᱛᱚ ᱦᱚᱲ ᱞᱟᱹᱜᱤᱫ: ᱨᱩᱞᱮᱴ ᱫᱚ ᱢᱤᱫ ᱠᱤᱨᱤᱧ ᱠᱟᱱᱟ᱾ ᱟᱯᱮ ᱠᱩᱥᱤ ᱢᱮᱱᱟᱜ ᱫᱟᱢ ᱮᱢ ᱯᱮ, ᱟᱯᱮ ᱵᱟᱪᱷᱟᱣ ᱞᱚᱜᱚᱱ ᱨᱮ, ᱢᱤᱫ ᱡᱤᱨᱚᱪᱟᱠᱟᱡᱤᱨᱚᱢᱤᱫᱜᱮ ᱦᱟᱹᱨᱭᱟᱹᱲ ᱠᱷᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ, ᱰᱚᱡᱮᱱ ᱟᱨᱵᱟᱝ ᱠᱚᱞᱚᱢ ᱵᱟᱡᱤ ᱵᱟᱭ ᱠᱚᱵᱷᱟᱨᱟ; ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱢᱩᱞ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱤᱝᱜᱚᱞ ᱡᱤᱨᱚ, 0᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱟᱨ ᱧᱟᱢ ᱫᱟᱲᱮᱭᱟᱜ ᱞᱮᱠᱷᱟᱱ ᱞᱟ ᱯᱟᱨᱛᱟᱡᱽᱱᱤᱭᱚᱢᱞᱟ ᱯᱟᱨᱛᱟᱡᱽᱯᱷᱨᱮᱧᱪ ᱱᱤᱭᱚᱢ: ᱡᱤᱨᱚ ᱦᱤᱡᱩᱜ ᱞᱮᱠᱷᱟᱱ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱫᱷᱟ ᱨᱩᱣᱟᱹᱲᱚᱜ-ᱟ᱾ ᱚᱱᱟ ᱵᱟᱡᱤ ᱠᱚ ᱨᱮ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱟᱫᱷᱟ, 1.35% ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱢᱮᱱᱟᱜ ᱪᱟᱠᱟ ᱨᱮ᱾
ᱠᱩᱠᱞᱤ ᱠᱚ
ᱵᱟᱝ᱾ ᱪᱟᱨᱞᱥ ᱣᱮᱞᱥ ᱞᱮᱠᱟᱱ ᱵᱟᱰᱟᱭ ᱥᱤᱥᱴᱮᱢ “ᱡᱤᱛᱚᱜ ᱦᱚᱲ” ᱠᱚ ᱫᱚ ᱥᱟᱜᱩᱱ ᱛᱮ ᱡᱤᱛᱟᱹᱣ ᱞᱮᱫᱟ ᱠᱚ ᱟᱨ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱦᱟᱹᱴᱤᱧ ᱫᱚᱦᱲᱟ ᱦᱟᱹᱱᱤ ᱞᱮᱫᱟ ᱠᱚ᱾
ᱵᱤᱪᱟᱨ ᱞᱮᱠᱟᱛᱮ᱾ ᱢᱤᱫ ᱱᱟᱣᱟ ᱠᱮᱥᱤᱱᱳ ᱥᱮ ᱥᱴᱩᱰᱤᱭᱳ ᱨᱮ ᱚᱱᱟ ᱵᱮᱵᱷᱟᱨ ᱞᱟᱹᱜᱤᱫ ᱟᱯᱮ ᱡᱩᱛ ᱰᱟᱴᱟ ᱧᱟᱢ ᱞᱟᱦᱟ ᱜᱮ ᱚᱱᱟ ᱧᱮᱞ ᱧᱟᱢ ᱟᱨ ᱥᱟᱵᱟᱲ ᱦᱩᱭᱩᱜ-ᱟ᱾
ᱡᱟᱹᱥᱛᱤ ᱮᱞᱟᱠᱟ ᱨᱮ ᱵᱟᱝ, ᱟᱨ ᱵᱚᱞ ᱞᱟᱦᱟᱭ ᱞᱟᱦᱟ ᱵᱟᱡᱤ ᱵᱚᱸᱫ ᱮᱫᱟ ᱞᱟᱭᱤᱵᱷ ᱴᱮᱵᱩᱞ ᱵᱤᱨᱩᱫᱷ ᱦᱚᱸ ᱵᱟᱝ ᱵᱮᱵᱷᱟᱨ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾
ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ
ᱯᱷᱤᱡᱤᱠᱥ, ᱦᱚᱨᱟ ᱫᱚ ᱵᱟᱝ᱾ ᱟᱨ ᱱᱤᱛ ᱫᱚ ᱚᱱᱟ ᱦᱚᱸ ᱵᱟᱝ᱾
ᱯᱷᱮᱰᱟᱛ
- RouletteDoc. Roulette strategies overview.
- Roulette77. Roulette strategies overview.
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. Elementary Probability.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- Bass, T. A. The Eudaemonic Pie.
- Small, M. & Tse, C. K. “Predicting the outcome of roulette.”
- Barnhart, R. T. Beating the Wheel.
- Chellel, K. “The Gambler Who Beat Roulette.”