ꯗꯕꯜ ꯕꯣꯜ ꯔꯨꯂꯦꯠ
ꯆꯛꯔ ꯑꯃꯗ ꯕꯣꯜ ꯑꯅꯤ꯫ ꯃꯅꯨꯡꯒꯤ ꯕꯦꯠꯁꯤꯡꯅꯕꯦꯠꯃꯅꯨꯡꯒꯤ ꯕꯦꯠꯒ꯭ꯔꯤꯗꯀꯤ ꯃꯁꯤꯡꯁꯤꯡꯒꯤ ꯃꯊꯛꯇ ꯅꯠꯔꯒ ꯃꯈꯣꯌꯒꯤ ꯃꯔꯛꯇ ꯊꯝꯕ ꯕꯦꯠ ꯀꯔꯤꯒꯨꯝꯕ: ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ, ꯁ꯭ꯞꯂꯤꯠ, ꯁ꯭ꯇ꯭ꯔꯤꯠ, ꯀꯣꯔꯅꯔ, ꯁꯤꯛꯁ ꯂꯥꯏꯟ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯕꯣꯜ ꯑꯃꯥ ꯃꯊꯧ ꯇꯥꯏ; ꯃꯄꯥꯟꯒꯤ ꯕꯦꯠꯁꯤꯡꯅ ꯑꯅꯤꯃꯛ ꯃꯊꯧ ꯇꯥꯏ꯫
ꯗꯕꯜ ꯕꯣꯜ ꯔꯨꯂꯦꯠꯇ, ꯕꯣꯜ ꯑꯅꯤ ꯄꯨꯟꯅ ꯊꯥꯗꯣꯀꯏ ꯑꯃꯁꯨꯡ ꯃꯁꯥ ꯃꯊꯟꯇ ꯂꯦꯞꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯇꯝ ꯈꯔꯗ ꯃꯈꯣꯌ ꯄꯣꯀꯦꯠ ꯑꯃꯃꯛꯇ ꯂꯦꯞꯂꯤ꯫ ꯃꯅꯨꯡꯒꯤ ꯕꯦꯠꯁꯤꯡ ꯕꯣꯜ ꯑꯃꯍꯦꯛꯇ ꯊꯣꯀꯄꯗ ꯃꯥꯏꯄꯥꯀꯏ, ꯃꯍꯧꯁꯥꯒꯤ ꯄꯦꯑꯥꯎꯠꯀꯤ ꯁꯔꯨꯛ ꯄꯤ, ꯑꯃꯁꯨꯡ ꯑꯅꯤꯃꯛ ꯊꯣꯀꯄꯗ ꯀꯌꯥꯗꯒꯤ ꯑꯅꯤ ꯄꯤ꯫ ꯃꯄꯥꯟꯒꯤ ꯕꯦꯠꯁꯤꯡ ꯕꯣꯜ ꯑꯅꯤꯃꯛ ꯌꯥꯅꯔꯕꯗꯈꯛ ꯃꯥꯏꯄꯥꯀꯏ, ꯃꯁꯤꯅ ꯃꯈꯣꯌꯕꯨ ꯕꯣꯜ ꯑꯃꯥ ꯂꯩꯕ ꯇꯦꯕꯜꯗꯒꯤ ꯀꯌꯥꯗꯒꯤ ꯑꯅꯤ ꯃꯃꯜ ꯋꯥꯡꯍꯜꯂꯤ꯫ ꯖꯦꯀꯄꯣꯠ ꯕꯦꯠ ꯑꯃꯅ ꯕꯣꯜ ꯑꯅꯤꯃꯛ ꯅꯍꯥꯛꯀꯤ ꯃꯁꯤꯡꯗ ꯂꯦꯞꯂꯕꯗꯤ ꯄꯤ꯫
ꯃꯅꯨꯡꯒꯤ ꯕꯦꯠꯁꯤꯡ
ꯅꯍꯥꯛꯀꯤ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯃꯁꯤꯡ ꯑꯃꯈꯛꯇ, 35:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯕꯣꯜꯈꯨꯠꯂꯥꯏꯕꯣꯜꯔꯣꯇꯔꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯇ꯭ꯔꯦꯛꯇ ꯊꯥꯗꯣꯛꯄ ꯑꯄꯤꯛꯄ ꯕꯣꯜ꯫ ꯍꯧꯖꯤꯛꯀꯤ ꯕꯣꯜꯁꯤꯡ ꯑꯥꯏꯚꯣꯔꯤꯟ ꯅꯠꯔꯒ ꯇꯦꯐ꯭ꯂꯣꯅꯅ ꯁꯦꯝꯃꯤ, 18–21 mm꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯍꯦꯛꯇ ꯃꯗꯨꯗ ꯂꯦꯞꯂꯕꯗꯤ ꯃꯥꯏꯄꯥꯀꯏ ꯑꯃꯁꯨꯡ ꯂꯦꯞꯄ ꯕꯣꯜ ꯈꯨꯗꯤꯡꯃꯛꯀꯤꯗꯃꯛ 17:1 ꯄꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯑꯅꯤꯃꯛ ꯂꯦꯞꯂꯕꯗꯤ 34:1꯫ ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯆꯛꯔ ꯑꯃꯗ, ꯆꯞ ꯃꯥꯟꯅꯕ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯂꯩꯕ ꯄꯦꯌꯔ 1,369ꯒꯤ ꯃꯅꯨꯡꯗ 72ꯗ ꯕꯣꯜ ꯑꯃꯥ ꯅꯍꯥꯛꯀꯤ ꯃꯁꯤꯡꯗ ꯂꯦꯞꯏ ꯑꯃꯁꯨꯡ 1ꯗ ꯕꯣꯜ ꯑꯅꯤꯃꯛ ꯂꯦꯞꯏ꯫ ꯕꯦꯠ ꯑꯁꯤꯅ 72 × 17 + 34 = 1,258 ꯃꯥꯏꯄꯥꯀꯏ ꯑꯃꯁꯨꯡ 1,296 ꯃꯥꯡꯏ, 1,369ꯒꯤ ꯃꯅꯨꯡꯗ ꯃꯄꯨꯡ ꯐꯥꯕ ꯃꯥꯡꯕ 38: ꯑꯦꯖ 2.78%, 2.70%ꯗꯒꯤ ꯈꯔꯈꯛ ꯍꯦꯟꯅ꯫ ꯕꯣꯜ ꯑꯅꯤꯃꯛ ꯊꯣꯀꯄꯗ 35:1 ꯄꯤꯔꯕꯗꯤ ꯃꯗꯨ ꯆꯨꯝꯅ 2.70%ꯗ ꯍꯜꯂꯛꯀꯅꯤ꯫ ꯁꯔꯨꯛ ꯍꯟꯊꯍꯜꯂꯕ ꯄꯦꯑꯥꯎꯠꯁꯤꯡꯁꯦꯜꯄꯦꯑꯥꯎꯠꯃꯥꯏꯄꯥꯛꯄ ꯕꯦꯠ ꯑꯃꯅ ꯍꯜꯂꯛꯄ ꯁꯦꯜ, ꯍꯜꯂꯀꯄ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯊꯛꯇ “X ꯗꯒꯤ 1” ꯍꯥꯌꯅ ꯍꯥꯌꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯅꯨꯡꯒꯤ ꯕꯦꯠꯀꯤ ꯇꯦꯕꯜ ꯄꯨꯝꯕꯗ ꯂꯩ꯫ ꯀꯣꯔꯅꯔꯕꯦꯠꯀꯣꯔꯅꯔꯂꯦꯑꯥꯎꯠꯇ ꯀꯣꯟꯅꯥ ꯑꯃꯥ ꯁꯦꯌꯔ ꯇꯧꯅꯔꯤꯕ ꯃꯁꯤꯡ ꯃꯔꯤ, 8:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯊꯥꯡꯖꯤꯟꯅꯕꯅꯤ: 3:1ꯗ ꯃꯁꯤꯒꯤ ꯃꯃꯜ 14.7%, ꯆꯨꯝꯃꯤꯟꯅꯕ ꯃꯃꯜ ꯑꯗꯨ ꯌꯥꯃꯗ꯭ꯔꯕꯗꯥ 3.7:1 ꯑꯣꯏꯒꯗꯕꯅꯤ꯫
ꯃꯄꯥꯟꯒꯤ ꯕꯦꯠꯁꯤꯡ
ꯑꯉꯥꯡꯕꯅꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯕꯣꯜ ꯑꯅꯤꯃꯛ ꯑꯉꯥꯡꯕ ꯃꯊꯧ ꯇꯥꯏ: (18/37)² = 23.7%, 3:1 ꯄꯤ꯫ ꯕꯦꯠ ꯑꯁꯤꯅ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ 4 × 23.7% = 94.7% ꯍꯜꯂꯛꯏ, ꯑꯦꯖ 5.33%, ꯌꯨꯔꯣꯄꯤꯌꯟ ꯃꯁꯤꯡꯒꯤ ꯀꯌꯥꯗꯒꯤ ꯑꯅꯤ꯫ ꯗꯖꯟꯕꯦꯠꯗꯖꯟ1–12, 13–24 ꯅꯠꯔꯒ 25–36, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯅ ꯕꯣꯜ ꯑꯅꯤꯃꯛ ꯃꯁꯤꯗ ꯂꯩꯕ ꯃꯊꯧ ꯇꯥꯏ, (12/37)² = 10.5%, ꯑꯃꯁꯨꯡ 8:1 ꯄꯤ: ꯑꯃꯨꯛ ꯍꯟꯅꯥ 5.33%꯫ ꯕꯣꯜ ꯑꯃꯥ ꯑꯉꯥꯡꯕꯗ ꯑꯃꯁꯨꯡ ꯑꯇꯣꯞꯄ ꯑꯗꯨ ꯑꯃꯨꯕꯗꯕꯦꯠꯑꯃꯨꯕꯑꯃꯨꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯅꯣꯌꯥꯔ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯂꯦꯞꯄꯒꯤ ꯕꯦꯠ, ꯆꯞ ꯃꯥꯟꯅꯕ ꯄꯦꯑꯥꯎꯠꯇ, ꯃꯁꯤꯁꯨ ꯑꯗꯨꯃꯛꯅꯤ꯫ ꯑꯍꯨꯝ ꯄꯨꯝꯅꯃꯛꯀꯤ ꯃꯃꯜ 1 − (36/37)² = 5.33%, ꯖꯤꯔꯣꯕꯨ ꯑꯃꯨꯛ ꯑꯅꯤ ꯂꯥꯟꯊꯣꯛꯀꯗꯕ ꯕꯦꯠ ꯑꯃꯒꯤ ꯃꯃꯜꯅꯤ꯫
ꯀꯗꯥꯏꯗ ꯐꯪꯒꯅꯤ
ꯁꯥꯟꯅꯕ ꯑꯁꯤ 2013ꯗ ꯒ꯭ꯂꯣꯕꯦꯜ ꯒꯦꯃꯤꯡ ꯑꯦꯛꯁꯄꯣꯗ ꯎꯠꯈꯤ ꯑꯃꯁꯨꯡ 2014ꯗꯒꯤ ꯂꯥꯁ ꯚꯦꯒꯥꯁꯀꯤ ꯇ꯭ꯔꯣꯄꯤꯀꯥꯅꯥꯗ ꯗꯕꯜ ꯖꯤꯔꯣ ꯆꯛꯔꯗ ꯁꯥꯟꯈꯤ꯫ ꯃꯐꯝ ꯑꯗꯨꯗ ꯑꯉꯥꯡꯕꯒꯤ ꯃꯃꯜ 10.25% ꯑꯃꯁꯨꯡ 1,200:1ꯒꯤ ꯖꯦꯀꯄꯣꯠꯀꯤ 16.83%꯫ ꯂꯥꯏꯕ ꯁ꯭ꯇꯨꯗꯤꯑꯣꯁꯤꯡꯅ ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ ꯃꯈꯂꯁꯤꯡ ꯆꯂꯥꯏ ꯑꯃꯁꯨꯡ ꯖꯦꯀꯄꯣꯠꯇ 1,300:1 ꯄꯤ꯫ ꯕꯣꯜꯁꯤꯡ ꯑꯁꯤ ꯇ꯭ꯌꯨꯕ ꯑꯃꯗꯒꯤ ꯅꯝꯊꯔꯕ ꯅꯨꯡꯁꯤꯠꯅ ꯃꯤꯟꯠ ꯈꯔꯒꯤ ꯈꯥꯌꯗꯅꯕꯗ ꯊꯥꯗꯣꯀꯏ; ꯁꯦꯝꯕꯤꯕꯥ ꯃꯤꯑꯣꯏꯒꯤ ꯆꯥꯡꯌꯦꯡꯁꯤꯡꯗ ꯃꯈꯣꯌ ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯃꯛꯇ ꯂꯦꯞꯄ ꯑꯁꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯅ ꯍꯥꯌꯔꯤꯕꯒꯨꯝꯅ ꯊꯣꯛꯂꯤ ꯍꯥꯌꯅ ꯐꯪꯈꯤ꯫
ꯁꯥꯟꯅꯗ꯭ꯔꯤꯕ ꯌꯥꯗ꯭ꯔꯕꯗꯤ, ꯀꯔꯝꯅ ꯁꯥꯟꯒꯗꯒꯦ
3%ꯗꯒꯤ ꯅꯦꯝꯕ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯁꯤꯡ ꯑꯃꯁꯨꯡ ꯁ꯭ꯞꯂꯤꯠꯁꯤꯡꯕꯦꯠꯁ꯭ꯞꯂꯤꯠꯌꯨꯝꯂꯣꯟꯅꯕ ꯃꯁꯤꯡ ꯑꯅꯤ, 17:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯑꯆꯨꯝꯕ ꯁꯔꯨꯛꯅꯤ꯫ ꯃꯄꯥꯟꯒꯤ ꯕꯦꯠꯁꯤꯡꯒꯤꯕꯦꯠꯃꯄꯥꯟꯒꯤ ꯕꯦꯠꯒ꯭ꯔꯤꯗꯀꯤ ꯃꯄꯥꯟꯗ ꯂꯩꯕ ꯕꯀꯁꯁꯤꯡꯗ ꯊꯝꯕ ꯕꯦꯠ: ꯗꯖꯟꯁꯤꯡ, ꯀꯂꯝꯁꯤꯡ ꯑꯃꯁꯨꯡ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯃꯜ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯇꯦꯕꯜꯒꯤ ꯀꯌꯥꯗꯒꯤ ꯑꯅꯤꯅꯤ꯫ 3:1ꯒꯤ ꯀꯣꯔꯅꯔꯁꯤꯡꯒꯤ ꯃꯃꯜ ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔꯒꯤ ꯕꯦꯠ ꯑꯃꯍꯦꯛꯇꯗꯒꯤ ꯍꯦꯟꯅ ꯋꯥꯡꯏ꯫ ꯖꯦꯀꯄꯣꯠ ꯕꯦꯠ ꯑꯁꯤ ꯂꯣꯇꯔꯤ ꯇꯤꯀꯦꯠ ꯑꯃꯅꯤ, ꯃꯁꯤꯒꯤ ꯃꯃꯜ ꯇꯦꯕꯜꯗ ꯃꯈꯥ ꯄꯣꯜꯂꯤ: 1,300:1ꯗ 4.97%, 1,200ꯗ 12.27%꯫
ꯋꯥꯍꯪꯁꯤꯡ
ꯌꯥꯏ꯫ ꯃꯈꯣꯌ ꯃꯁꯥ ꯃꯊꯟꯇ ꯂꯦꯞꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯑꯦꯚꯔꯦꯖꯗ ꯁ꯭ꯄꯤꯟ 37ꯗ ꯑꯃꯨꯛ ꯑꯅꯤꯃꯛ ꯄꯣꯀꯦꯠ ꯑꯃꯗ ꯂꯦꯞꯏ, ꯑꯃꯁꯨꯡ ꯅꯍꯥꯛꯅ ꯈꯅꯈꯤꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯗ 1,369ꯗ ꯑꯃꯨꯛ꯫ ꯖꯦꯀꯄꯣꯠ ꯕꯦꯠꯅ ꯄꯤꯔꯤꯕꯁꯤ ꯃꯁꯤꯒꯤꯗꯃꯛꯅꯤ꯫
ꯃꯔꯃꯗꯤ 3.22:1 ꯑꯁꯤ 23.7%ꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯒꯤ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯄꯦꯑꯥꯎꯠꯅꯤ, ꯑꯃꯁꯨꯡ ꯀꯦꯁꯤꯅꯣꯅ ꯈꯦꯠꯅꯕ ꯑꯗꯨ ꯊꯃꯖꯤꯜꯂꯤ, ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ 5.33%꯫
ꯆꯨꯝꯃꯤꯟꯅꯕ ꯃꯃꯜ 1,368:1 ꯑꯣꯏꯒꯗꯕꯅꯤ꯫ 1,300ꯗ ꯃꯁꯤꯒꯤ ꯃꯃꯜ 4.97%, ꯇꯦꯕꯜ ꯑꯗꯨꯃꯛꯇ ꯑꯉꯥꯡꯕꯗꯒꯤ ꯈꯔꯈꯛ ꯅꯦꯝꯏ; 1,200ꯗ ꯃꯃꯜ 12.27%꯫
ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯥ ꯁꯥꯟꯅꯕ
ꯃꯁꯤꯁꯤꯡ ꯑꯍꯥꯅꯕꯗ ꯅꯍꯥꯛ ꯃꯁꯥꯃꯛꯅ ꯍꯣꯠꯅꯕꯤꯌꯨ꯫ ꯄꯥꯎꯈꯨꯝ ꯈꯨꯗꯤꯡꯃꯛ ꯊꯨꯡꯗꯨꯅ ꯊꯝꯂꯤ; ꯁꯦꯝ ꯁꯥꯔꯕ ꯃꯇꯃꯗ ꯍꯥꯡꯗꯣꯛꯄꯤꯌꯨ꯫
ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯆꯛꯔ ꯑꯃꯗ ꯗꯕꯜ ꯕꯣꯜꯈꯨꯠꯂꯥꯏꯕꯣꯜꯔꯣꯇꯔꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯇ꯭ꯔꯦꯛꯇ ꯊꯥꯗꯣꯛꯄ ꯑꯄꯤꯛꯄ ꯕꯣꯜ꯫ ꯍꯧꯖꯤꯛꯀꯤ ꯕꯣꯜꯁꯤꯡ ꯑꯥꯏꯚꯣꯔꯤꯟ ꯅꯠꯔꯒ ꯇꯦꯐ꯭ꯂꯣꯅꯅ ꯁꯦꯝꯃꯤ, 18–21 mm꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯔꯨꯂꯦꯠꯇ, ꯑꯉꯥꯡꯕꯅꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯕꯣꯜ ꯑꯅꯤꯃꯛ ꯑꯉꯥꯡꯕ ꯑꯣꯏꯕ ꯃꯊꯧ ꯇꯥꯏ ꯑꯃꯁꯨꯡ 3 ꯗꯒꯤ 1 ꯄꯤ, ꯗꯖꯟꯕꯦꯠꯗꯖꯟ1–12, 13–24 ꯅꯠꯔꯒ 25–36, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯅ ꯕꯣꯜ ꯑꯅꯤꯃꯛ ꯃꯗꯨꯗ ꯂꯩꯕ ꯃꯊꯧ ꯇꯥꯏ ꯑꯃꯁꯨꯡ 8 ꯗꯒꯤ 1 ꯄꯤ, ꯑꯃꯁꯨꯡ ꯑꯉꯥꯡꯕ ꯑꯃꯥ ꯑꯃꯁꯨꯡ ꯑꯃꯨꯕꯕꯦꯠꯑꯃꯨꯕꯑꯃꯨꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯅꯣꯌꯥꯔ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗ ꯊꯝꯕ ꯕꯦꯠ ꯑꯃꯅ ꯆꯞ ꯃꯥꯟꯅꯕ ꯁꯦꯜ ꯄꯤ꯫ ꯀꯔꯤꯒꯤ ꯑꯍꯨꯝ ꯄꯨꯝꯅꯃꯛꯀꯤ ꯃꯃꯜ ꯆꯞ ꯃꯥꯟꯅꯅ 5.33% ꯂꯩꯕꯅꯣ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯊꯝꯂꯕ $1,369 ꯈꯨꯗꯤꯡꯗ $1,296 ꯍꯜꯂꯛꯏ: ꯖꯤꯔꯣ ꯑꯗꯨ ꯑꯃꯨꯛ ꯑꯅꯤ ꯂꯥꯟꯊꯣꯀꯄꯒꯤ ꯃꯃꯜ꯫
ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 37 ꯗ ꯕꯣꯜ ꯑꯅꯤꯅ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯃꯥꯟꯅꯕ ꯄꯦꯌꯔ 37 × 37 = 1,369 ꯁꯦꯝꯃꯤ꯫
ꯕꯣꯜ ꯑꯅꯤꯃꯛꯇ ꯑꯉꯥꯡꯕ: ꯄꯦꯌꯔ 18 × 18 = 324꯫ 3 ꯗꯒꯤ 1 ꯗ ꯃꯥꯏꯄꯥꯛꯂꯕ $1 ꯑꯃꯅ $4 ꯍꯜꯂꯛꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯕꯦꯠ ꯑꯗꯨꯅ 324 × 4 = 1,296 ꯍꯜꯂꯛꯏ꯫
ꯗꯖꯟ ꯑꯃꯥ: 8 ꯗꯒꯤ 1 ꯗ ꯄꯦꯌꯔ 12 × 12 = 144, $9 ꯍꯜꯂꯛꯄ: 144 × 9 = 1,296꯫
ꯑꯉꯥꯡꯕ ꯑꯃꯥ ꯑꯃꯁꯨꯡ ꯑꯃꯨꯕ ꯑꯃꯥ: ꯃꯥꯌꯀꯩ ꯑꯃꯃꯃꯗ ꯄꯦꯌꯔ 18 × 18, ꯄꯨꯝꯅꯃꯛ 648, ꯆꯞ ꯃꯥꯟꯅꯕ ꯁꯦꯜꯗ, $2 ꯍꯜꯂꯛꯄ: 648 × 2 = 1,296꯫
ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯊꯝꯂꯕ $1,369 ꯗ $1,296 ꯍꯜꯂꯛꯏ꯫ ꯃꯥꯡꯕ ꯑꯗꯨ 73/1,369 = 5.33% ꯅꯤ꯫ ꯑꯃꯁꯨꯡ 1,296 = 36 × 36: ꯄꯦꯑꯥꯎꯠꯁꯦꯜꯄꯦꯑꯥꯎꯠꯃꯥꯏꯄꯥꯛꯄ ꯕꯦꯠ ꯑꯃꯅ ꯍꯜꯂꯛꯄ ꯁꯦꯜ, ꯍꯜꯂꯀꯄ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯊꯛꯇ “X ꯗꯒꯤ 1” ꯍꯥꯌꯅ ꯍꯥꯌꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯈꯨꯗꯤꯡꯃꯛ ꯕꯣꯜ ꯑꯅꯤꯃꯛꯅ ꯖꯤꯔꯣ ꯂꯥꯛꯂꯣꯏꯗꯕꯅꯤ ꯍꯥꯌꯕꯒꯨꯝ ꯁꯦꯃꯈꯤꯕꯅꯤ, ꯃꯗꯨ 1 − (36/37)² ꯅꯤ꯫ ꯗꯕꯜ ꯖꯤꯔꯣ ꯆꯛꯔꯗ ꯃꯇꯧ ꯑꯁꯨꯝꯕ ꯍꯤꯁꯥꯕ ꯑꯗꯨꯅ 1 − (36/38)² = 10.25% ꯄꯤ꯫
ꯗꯕꯜ ꯕꯣꯜ ꯇꯦꯕꯜꯒꯤ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯃꯁꯤꯡ ꯑꯃꯈꯛꯇ, 35:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯅ ꯅꯍꯥꯛꯀꯤ ꯃꯁꯤꯡꯗ ꯂꯥꯛꯄ ꯕꯣꯜ ꯈꯨꯗꯤꯡꯃꯛꯀꯤꯗꯃꯛ 17 ꯗꯒꯤ 1 ꯄꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯑꯅꯤꯃꯛ ꯂꯥꯛꯂꯕꯗ 34 ꯗꯒꯤ 1꯫ ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ ꯆꯛꯔꯗ ꯃꯁꯤꯒꯤ ꯃꯃꯜ ꯀꯌꯥ ꯂꯩꯕꯒꯦ, ꯑꯃꯁꯨꯡ ꯀꯔꯤꯅ ꯃꯁꯤꯕꯨ 2.70% ꯗ ꯍꯜꯂꯛꯍꯅꯒꯅꯤ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ 2.78%꯫ ꯕꯣꯜ ꯑꯅꯤꯃꯛ ꯂꯥꯛꯂꯕꯗ 35 ꯗꯒꯤ 1 ꯄꯤꯔꯕꯗ ꯆꯞ ꯃꯥꯟꯅꯅ 2.70% ꯑꯣꯏꯒꯅꯤ꯫
ꯄꯦꯌꯔ 1,369 ꯒꯤ ꯃꯅꯨꯡꯗ, ꯅꯍꯥꯛꯀꯤ ꯃꯁꯤꯡ ꯑꯗꯨ 36 ꯗ ꯑꯍꯥꯅꯕ ꯕꯣꯜꯗ ꯈꯛꯇ, 36 ꯗ ꯑꯅꯤꯁꯨꯕꯥ ꯕꯣꯜꯗ ꯈꯛꯇ, 1 ꯗ ꯑꯅꯤꯃꯛꯇ, ꯑꯃꯁꯨꯡ 36 × 36 = 1,296 ꯗ ꯑꯃꯠꯇꯗ ꯂꯩꯇꯦ꯫
ꯕꯣꯜ ꯑꯃꯥ: ꯄꯦꯌꯔ 72, +17 ꯗ, ꯃꯔꯝ ꯑꯗꯨꯅ +1,224꯫ ꯕꯣꯜ ꯑꯅꯤꯃꯛ: ꯄꯦꯌꯔ 1, +34 ꯗ꯫ ꯑꯃꯠꯇꯥ ꯅꯠꯇꯕ: ꯄꯦꯌꯔ 1,296, −1 ꯗ꯫ ꯄꯨꯝꯅꯃꯛ: 1,224 + 34 − 1,296 = −38, 38/1,369 = 2.78% ꯒꯤ ꯑꯦꯖ꯫
ꯑꯅꯤꯃꯛ ꯂꯥꯛꯄꯗ 35 ꯗꯒꯤ 1 ꯄꯤꯔꯕꯗꯤ, ꯄꯨꯝꯅꯃꯛ −37 ꯑꯣꯏꯒꯅꯤ, ꯑꯃꯁꯨꯡ 37/1,369 = 1/37 = 2.70%, ꯌꯨꯔꯣꯄꯤꯌꯟ ꯃꯃꯜ꯫ ꯀꯦꯁꯤꯅꯣꯅ 1,369 ꯗ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯥ ꯍꯦꯟꯅꯥ ꯊꯝꯖꯤꯜꯂꯤ꯫
ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ
ꯃꯅꯨꯡꯒꯤ ꯕꯦꯠꯁꯤꯡ ꯑꯆꯨꯝꯕ; ꯃꯄꯥꯟꯒꯤ ꯕꯦꯠꯁꯤꯡꯒꯤ ꯃꯃꯜ ꯀꯌꯥꯗꯒꯤ ꯑꯅꯤ꯫
ꯍꯧꯔꯛꯐꯃꯁꯤꯡ
- Wizard of Odds. “Double Ball Roulette.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.