ꯔꯨꯂꯦꯠ ꯗꯖꯟ ꯕꯦꯠ
ꯔꯨꯂꯦꯠꯀꯤ ꯗꯖꯟ ꯕꯦꯠꯅ ꯃꯇꯨꯡ ꯏꯟꯅꯥ ꯂꯥꯛꯄ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ ꯀꯨꯞꯏ: 1–12, 13–24 ꯅꯠꯔꯒ 25–36꯫

ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ, ꯄꯦꯑꯥꯎꯠ 2:1꯫ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 32.43%꯫ ꯖꯤꯔꯣ ꯂꯥꯛꯂꯕꯗ ꯃꯥꯏꯊꯤꯕ ꯐꯪꯏ꯫
ꯔꯨꯂꯦꯠ ꯇꯦꯕꯜꯗ ꯗꯖꯟꯁꯤꯡ ꯀꯗꯥꯏꯗ ꯂꯩꯕꯒꯦ?
ꯂꯦꯑꯥꯎꯠꯈꯨꯠꯂꯥꯏꯂꯦꯑꯥꯎꯠꯇꯦꯕꯜꯗ ꯏꯔꯕ ꯕꯦꯠ ꯊꯝꯕꯒꯤ ꯒ꯭ꯔꯤꯗ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯇꯦꯕꯜ, ꯐꯦꯜꯠ, ꯀ꯭ꯂꯣꯊ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯀꯤ ꯁꯥꯡꯕ ꯃꯥꯏꯀꯩꯗ ꯂꯩꯕ ꯕꯛꯁ ꯑꯍꯨꯝ, 1st 12, 2nd 12, 3rd 12 ꯍꯥꯌꯅ ꯏꯔꯤꯕ, ꯅꯠꯔꯒ ꯐ꯭ꯔꯦꯟꯆ ꯇꯦꯕꯜꯁꯤꯡꯗ P12 (ꯄ꯭ꯔꯦꯃꯤꯌꯦꯔ), M12 (ꯃꯣꯌꯦꯟ), D12 (ꯗꯔꯅꯤꯌꯦꯔ)꯫ ꯃꯈꯣꯌ ꯑꯃꯃꯃꯅ ꯇꯦꯕꯜꯒꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯦꯝꯕ ꯉꯝꯈꯩ ꯃꯁꯥ ꯃꯊꯟꯇ ꯐꯪꯒꯗꯕꯅꯤ꯫ ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯀꯔꯝꯕ ꯗꯖꯟꯕꯦꯠꯗꯖꯟ1–12, 13–24 ꯅꯠꯔꯒ 25–36, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗꯁꯨ ꯌꯥꯎꯗꯦ꯫
ꯔꯨꯂꯦꯠ ꯗꯖꯟꯒꯤ ꯄꯦꯑꯥꯎꯠ ꯑꯃꯁꯨꯡ ꯐꯪꯒꯗꯕ ꯃꯃꯜ
37 ꯒꯤ ꯃꯅꯨꯡꯗꯒꯤ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯑꯣꯗꯁ 2.083 ꯗꯒꯤ 1 ꯅꯤ; ꯇꯦꯕꯜꯅ 2 ꯈꯛ ꯄꯤ꯫ ꯃꯥꯏꯄꯥꯛꯂꯕ $10 ꯒꯤ ꯗꯖꯟ ꯑꯃꯅ $20 ꯍꯜꯂꯀꯏ꯫ ꯑꯦꯚꯔꯦꯖ ꯁ꯭ꯄꯤꯟ 37 ꯗ: ꯃꯥꯏꯄꯥꯛꯄ 12 (+$240), ꯃꯥꯏꯊꯤꯕ 25 (−$250), ꯅꯦꯠ −$10꯫
ꯗꯖꯟ ꯑꯅꯤ ꯑꯃꯨꯛꯇ
ꯗꯖꯟ ꯑꯅꯤꯗ ꯃꯥꯟꯅꯕ ꯆꯤꯞꯁꯤꯡꯁꯦꯜꯆꯤꯞꯂꯦꯞꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯃꯜ ꯇꯥꯛꯄ ꯇꯣꯀꯟ, ꯕꯦꯠ ꯊꯝꯅꯕ ꯂꯦꯑꯥꯎꯠꯇ ꯊꯝꯃꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯆꯦꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯊꯝꯂꯕꯗ ꯁ꯭ꯄꯤꯟ 37 ꯒꯤ ꯃꯅꯨꯡꯗꯒꯤ 24 (64.9%) ꯃꯥꯏꯄꯥꯛꯏ, ꯑꯗꯨꯕꯨ ꯅꯦꯠ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯈꯛ ꯐꯪꯏ: ꯑꯃꯗ 2 ꯃꯥꯏꯄꯥꯛꯏ ꯑꯃꯁꯨꯡ ꯑꯇꯣꯞꯄ ꯑꯗꯨꯗ 1 ꯃꯥꯡꯏ꯫ ꯃꯥꯏꯊꯤꯕ ꯁ꯭ꯄꯤꯟ 13 ꯈꯨꯗꯤꯡꯗ ꯌꯨꯅꯤꯠ ꯑꯅꯤ ꯃꯥꯡꯏ꯫ (24 × 1 − 13 × 2)/37 = ꯌꯨꯅꯤꯠ ꯑꯅꯤ ꯈꯨꯗꯤꯡꯗ −2/37, ꯃꯇꯧ ꯑꯣꯏꯕ 2.70%꯫ ꯃꯑꯣꯡ ꯑꯁꯤ ꯌꯦꯡꯕꯗ ꯐꯖꯩ, ꯁ꯭ꯄꯤꯟ ꯑꯍꯨꯃꯗ ꯑꯅꯤ ꯃꯇꯃꯗ ꯃꯥꯏꯄꯥꯛꯏ, ꯑꯗꯨꯕꯨ ꯑꯦꯖ ꯑꯗꯨ ꯍꯣꯡꯗꯦ꯫
ꯔꯨꯂꯦꯠ ꯗꯖꯟ ꯑꯃꯁꯨꯡ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟꯁꯤꯡ
ꯗꯖꯟꯗ ꯃꯥꯏꯊꯤꯕ ꯐꯪꯔꯕꯥ ꯃꯇꯨꯡꯗ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯟꯅꯥ ꯊꯝꯕꯅ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯇ ꯍꯟꯅꯥ ꯐꯪꯕꯒꯨꯝꯅ ꯍꯟꯅꯥ ꯐꯪꯍꯟꯗꯦ: ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯟꯅꯥ ꯊꯝꯂꯕꯥ ꯃꯇꯨꯡꯗ 2 ꯗꯒꯤ 1 ꯒꯤ ꯄꯦꯑꯥꯎꯠꯁꯦꯜꯄꯦꯑꯥꯎꯠꯃꯥꯏꯄꯥꯛꯄ ꯕꯦꯠ ꯑꯃꯅ ꯍꯜꯂꯛꯄ ꯁꯦꯜ, ꯍꯜꯂꯀꯄ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯊꯛꯇ “X ꯗꯒꯤ 1” ꯍꯥꯌꯅ ꯍꯥꯌꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯅ ꯃꯥꯏꯊꯤꯕ ꯑꯅꯤ ꯈꯛ ꯍꯟꯅꯥ ꯐꯪꯍꯜꯂꯤ, ꯄꯨꯝꯅꯃꯛ ꯅꯠꯇꯦ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯇꯧ ꯑꯣꯏꯕ “ꯗꯖꯟ ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯊꯧꯔꯥꯡꯃꯥꯔꯇꯤꯟꯒꯦꯜꯃꯥꯏꯊꯤꯕ ꯈꯨꯗꯤꯡꯒꯤ ꯃꯇꯨꯡꯗ ꯕꯦꯠ ꯑꯗꯨ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯟꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ꯫ ꯃꯁꯤꯅ ꯀꯔꯤ ꯇꯧꯕꯒꯦ ꯑꯃꯁꯨꯡ ꯀꯔꯤ ꯇꯧꯗꯕꯒꯦ ꯍꯥꯌꯕ ꯊꯧꯔꯥꯡꯒꯤ ꯁꯦꯛꯁꯅꯗ ꯌꯦꯡꯕꯤꯌꯨ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →”ꯅ ꯑꯍꯨꯝ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯜꯂꯤ꯫ ꯑꯍꯨꯝ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯟꯕꯅ $5 ꯗꯒꯤ ꯈꯣꯡꯊꯥꯡ ꯃꯉꯥꯗ $500 ꯒꯤ ꯇꯦꯕꯜꯒꯤ ꯉꯝꯈꯩꯇꯦꯕꯜꯇꯦꯕꯜꯒꯤ ꯉꯝꯈꯩꯌꯥꯍꯜꯂꯤꯕ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯦꯝꯕ ꯑꯃꯁꯨꯡ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯕ ꯕꯦꯠ꯫ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯕ ꯉꯝꯈꯩ ꯑꯗꯨꯅ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯟꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯊꯤꯡꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯗ ꯌꯧꯏ, ꯑꯉꯥꯡꯕꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯗ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯟꯅꯥ ꯊꯝꯕꯅ ꯈꯣꯡꯊꯥꯡ ꯇꯔꯦꯠ ꯃꯊꯧ ꯇꯥꯕꯒꯤ ꯃꯍꯨꯠꯇ꯫ ꯀꯔꯝꯕ ꯗꯖꯟ ꯊꯥꯗꯣꯛꯀꯗꯒꯦ ꯍꯣꯡꯗꯣꯛꯂꯤꯕ ꯁꯤꯁ꯭ꯇꯦꯝꯁꯤꯡꯅ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯠꯇ ꯍꯣꯡꯗꯣꯛꯇꯦ, ꯃꯔꯃꯗꯤ ꯁ꯭ꯄꯤꯟꯁꯤꯡ ꯑꯁꯤ ꯃꯔꯤ ꯂꯩꯅꯗꯦ꯫
ꯆꯛꯔꯗ
ꯗꯖꯟ ꯑꯃꯒꯤ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ ꯑꯁꯤ ꯆꯛꯔꯒꯤ ꯃꯄꯥꯟꯊꯣꯡꯗ ꯆꯦꯟꯊꯔꯛꯂꯤ; ꯑꯍꯥꯅꯕ ꯗꯖꯟꯅ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ꯒꯤ ꯄꯣꯀꯦꯠꯁꯤꯡꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯂꯧꯏ, ꯃꯈꯣꯌ ꯑꯁꯤ ꯆꯛꯔ ꯄꯨꯝꯕꯗ ꯆꯦꯟꯊꯔꯛꯂꯕ ꯃꯐꯃꯁꯤꯡꯗ ꯂꯩ꯫ ꯗꯖꯟ ꯑꯁꯤ ꯍꯛꯆꯥꯡ ꯂꯩꯕ ꯁꯦꯛꯇꯔꯆꯛꯔꯁꯦꯛꯇꯔꯆꯛꯔꯗ ꯃꯔꯛ ꯂꯩꯇꯅ ꯃꯈꯥ ꯆꯠꯅꯅ ꯂꯩꯕ ꯄꯣꯀꯦꯠꯁꯤꯡꯒꯤ ꯁꯔꯨꯛ, ꯂꯦꯑꯥꯎꯠꯇ ꯂꯩꯕ ꯀꯥꯡꯂꯨꯞ ꯑꯃꯗꯒꯤ ꯇꯣꯉꯥꯟꯅ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯠꯇ ꯂꯩꯇꯕ ꯂꯦꯑꯥꯎꯠꯀꯤ ꯕꯦꯠꯅꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯕꯥꯏꯌꯥꯁ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯃꯁꯤ ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯁꯤꯖꯤꯟꯅꯗꯦ꯫
ꯋꯥꯍꯪꯁꯤꯡ
ꯅꯠꯇꯦ꯫ ꯑꯃꯃꯃꯅ 37 ꯗꯒꯤ 12 ꯅꯤ꯫ ꯑꯅꯤꯁꯨꯕ ꯗꯖꯟꯗ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯌꯥꯝꯅ ꯕꯦꯠ ꯊꯝꯕ ꯃꯁꯤꯡ 17 ꯌꯥꯎꯏ, ꯃꯁꯤꯅ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯠꯇ ꯍꯣꯡꯗꯣꯛꯇꯦ꯫
ꯌꯥꯏ, ꯑꯃꯁꯨꯡ ꯁ꯭ꯄꯤꯟ 37 ꯒꯤ ꯃꯅꯨꯡꯗꯒꯤ 36 ꯗ ꯅꯍꯥꯛꯅ ꯑꯃꯥ ꯃꯥꯏꯄꯥꯛꯀꯅꯤ ꯑꯃꯁꯨꯡ ꯑꯅꯤ ꯃꯥꯏꯊꯤꯕ ꯐꯪꯒꯅꯤ, ꯑꯃꯁꯨꯡ ꯖꯤꯔꯣꯗ ꯑꯍꯨꯃꯃꯛ ꯃꯥꯏꯊꯤꯕ ꯐꯪꯒꯅꯤ꯫
ꯑꯅꯤꯃꯛꯅ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ ꯀꯨꯞꯏ꯫ ꯄꯦꯑꯥꯎꯠꯀꯤ ꯅꯤꯌꯝꯅ ꯀꯨꯞꯄ ꯃꯁꯤꯡ ꯈꯛꯇ ꯃꯁꯤꯡ ꯊꯤꯜꯂꯤ꯫
ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

ꯁ꯭ꯄꯤꯟꯁꯤꯡꯒꯤ 64.9% ꯃꯥꯏꯄꯥꯛꯏ꯫ ꯁꯦꯜꯒꯤ 2.70% ꯃꯥꯡꯏ꯫
ꯍꯧꯔꯛꯐꯃꯁꯤꯡ
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.