ꯔꯨꯂꯦꯠ ꯇꯤꯌꯦꯌꯔ ꯗꯨ ꯁꯤꯂꯦꯟꯗ꯭ꯔ
“ꯆꯛꯔꯒꯤ ꯁꯔꯨꯛ ꯑꯍꯨꯝ ꯊꯣꯀꯄꯒꯤ ꯑꯃ”: ꯔꯨꯂꯦꯠꯀꯤ ꯇꯤꯌꯦꯌꯔ ꯕꯦꯠꯅ ꯖꯤꯔꯣꯒꯤ ꯃꯥꯌꯣꯛ ꯅꯥꯏꯅꯕ ꯄꯣꯀꯦꯠ ꯇꯔꯥꯅꯤꯊꯣꯏ ꯀꯨꯞꯏ꯫

ꯁ꯭ꯞꯂꯤꯠ ꯇꯔꯨꯛ, ꯆꯤꯞ ꯇꯔꯨꯛ, ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ: ꯆꯛꯔꯗ 27 ꯗꯒꯤ 33 ꯐꯥꯑꯣꯕ꯫ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ 32.43%, ꯀꯔꯝꯕ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯗꯁꯨ ꯅꯦꯠ +12 ꯌꯨꯅꯤꯠ꯫
ꯁ꯭ꯞꯂꯤꯠꯁꯤꯡ
5-8, 10-11, 13-16, 23-24, 27-30, 33-36꯫ ꯆꯤꯞꯁꯦꯜꯆꯤꯞꯂꯦꯞꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯃꯜ ꯇꯥꯛꯄ ꯇꯣꯀꯟ, ꯕꯦꯠ ꯊꯝꯅꯕ ꯂꯦꯑꯥꯎꯠꯇ ꯊꯝꯃꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯆꯦꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯇꯔꯨꯛ, ꯑꯃꯃꯃ 17 ꯗꯒꯤ 1 ꯄꯤꯕ ꯁ꯭ꯞꯂꯤꯠꯕꯦꯠꯁ꯭ꯞꯂꯤꯠꯌꯨꯝꯂꯣꯟꯅꯕ ꯃꯁꯤꯡ ꯑꯅꯤ, 17:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →꯫ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ ꯑꯁꯤ ꯆꯛꯔꯗ 27 ꯗꯒꯤ 33 ꯐꯥꯑꯣꯕ ꯈꯥꯌꯗꯣꯛꯇꯅ ꯆꯠꯂꯤ: 27 13 36 11 30 8 23 10 5 24 16 33꯫ “ꯇꯤꯌꯦꯌꯔ” ꯍꯥꯌꯅ ꯂꯥꯑꯣꯊꯣꯀꯏ (ꯇꯤꯌꯦꯌꯔ ꯗꯨ ꯁꯤꯂꯦꯟꯗ꯭ꯔꯐ꯭ꯔꯦꯟꯆ · ꯁꯦꯛꯇꯔꯇꯤꯌꯦꯌꯔ ꯗꯨ ꯁꯤꯂꯦꯟꯗ꯭ꯔ“ꯆꯛꯔꯒꯤ ꯁꯔꯨꯛ ꯑꯍꯨꯃꯒꯤ ꯑꯃꯥ”: ꯖꯤꯔꯣꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯂꯩꯕ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ, ꯆꯛꯔꯗ 27 ꯗꯒꯤ 33 ꯐꯥꯑꯣꯕ, ꯁ꯭ꯞꯂꯤꯠ ꯇꯔꯨꯛꯅ ꯕꯦꯠ ꯊꯝꯃꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, ꯖꯔꯃꯟ ꯀꯦꯁꯤꯅꯣꯁꯤꯡꯗ ꯃꯇꯝ ꯈꯔꯗ ꯑꯍꯥꯅꯕ ꯁ꯭ꯞꯂꯤꯠꯀꯤ ꯃꯃꯤꯡꯗ “ꯁꯤꯔꯤꯖ 5/8”)꯫
ꯄꯦꯑꯥꯎꯠ ꯑꯃꯁꯨꯡ ꯐꯪꯒꯗꯕ ꯃꯃꯜ
ꯀꯔꯝꯕ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯅꯁꯨ ꯁ꯭ꯞꯂꯤꯠ ꯑꯃꯗ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 17 ꯄꯤ ꯑꯃꯁꯨꯡ ꯑꯇꯣꯞꯄ ꯃꯉꯥ ꯃꯥꯡꯏ: ꯌꯨꯅꯤꯠ 6 ꯊꯝꯂꯕꯗ ꯅꯦꯠ +12꯫ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 12/37꯫ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯒꯤ EV: (12/37)(12) − (25/37)(6) = (144 − 150)/37 = −6/37, ꯃꯁꯤ ꯌꯨꯅꯤꯠ ꯇꯔꯨꯛꯀꯤ 2.70% ꯅꯤ꯫ ꯗꯖꯟꯕꯦꯠꯗꯖꯟ1–12, 13–24 ꯅꯠꯔꯒ 25–36, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯒꯥ ꯀꯨꯞꯄ ꯃꯥꯟꯅꯩ, ꯂꯦꯑꯥꯎꯠꯈꯨꯠꯂꯥꯏꯂꯦꯑꯥꯎꯠꯇꯦꯕꯜꯗ ꯏꯔꯕ ꯕꯦꯠ ꯊꯝꯕꯒꯤ ꯒ꯭ꯔꯤꯗ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯇꯦꯕꯜ, ꯐꯦꯜꯠ, ꯀ꯭ꯂꯣꯊ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯇ ꯅꯠꯇꯅ ꯆꯛꯔꯗ, ꯑꯃꯁꯨꯡ ꯄꯦꯑꯥꯎꯠꯁꯦꯜꯄꯦꯑꯥꯎꯠꯃꯥꯏꯄꯥꯛꯄ ꯕꯦꯠ ꯑꯃꯅ ꯍꯜꯂꯛꯄ ꯁꯦꯜ, ꯍꯜꯂꯀꯄ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯊꯛꯇ “X ꯗꯒꯤ 1” ꯍꯥꯌꯅ ꯍꯥꯌꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯥꯟꯅꯩ: ꯃꯥꯏꯄꯥꯛꯄ ꯈꯨꯗꯤꯡꯗ ꯑꯗꯨꯃꯛ ꯄꯤ꯫
ꯇꯤꯌꯦꯌꯔ ꯑꯃꯁꯨꯡ ꯗꯖꯟ
ꯑꯅꯤꯃꯛꯅ 32.43% ꯗ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ ꯀꯨꯞꯏ꯫ $30 ꯒꯤ ꯗꯖꯟ ꯑꯃꯅ ꯃꯥꯏꯄꯥꯛꯂꯕꯗ +$60 ꯄꯤ, $5 ꯒꯤ ꯁ꯭ꯞꯂꯤꯠ ꯇꯔꯨꯛꯀꯨꯝ ꯆꯞ ꯃꯥꯟꯅꯅ꯫ ꯄꯦꯑꯥꯎꯠ ꯑꯃꯁꯨꯡ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯗ ꯃꯈꯣꯌ ꯕꯦꯠ ꯑꯃꯈꯛꯇꯅꯤ; ꯀꯔꯝꯕ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏꯅꯣ ꯑꯃꯁꯨꯡ ꯃꯁꯤꯡꯁꯤꯡ ꯑꯗꯨꯅ ꯁꯔꯨꯛ ꯑꯃꯥ ꯁꯦꯝꯕꯔꯥ ꯍꯥꯌꯕꯗ ꯈꯛꯇ ꯈꯦꯠꯅꯩ꯫ ꯕꯥꯏꯌꯥꯁ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯒꯤꯗꯃꯛ ꯃꯗꯨ ꯄꯨꯝꯅꯃꯛꯅꯤ; ꯁꯤꯁ꯭ꯇꯦꯝ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯒꯤꯗꯃꯛ ꯀꯔꯤꯁꯨ ꯅꯠꯇꯦ꯫
ꯀꯔꯤꯒꯤ ꯖꯤꯔꯣꯒꯤ ꯃꯥꯌꯣꯛ ꯅꯥꯏꯅꯕꯒꯦ
ꯐ꯭ꯔꯦꯟꯆ ꯁꯦꯛꯇꯔꯆꯛꯔꯁꯦꯛꯇꯔꯆꯛꯔꯗ ꯃꯔꯛ ꯂꯩꯇꯅ ꯃꯈꯥ ꯆꯠꯅꯅ ꯂꯩꯕ ꯄꯣꯀꯦꯠꯁꯤꯡꯒꯤ ꯁꯔꯨꯛ, ꯂꯦꯑꯥꯎꯠꯇ ꯂꯩꯕ ꯀꯥꯡꯂꯨꯞ ꯑꯃꯗꯒꯤ ꯇꯣꯉꯥꯟꯅ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯕꯦꯠꯁꯤꯡꯅ ꯆꯛꯔ ꯑꯗꯨ ꯈꯥꯌꯗꯣꯛꯂꯤ: ꯚꯣꯌꯥꯖꯦꯟ ꯗꯨ ꯖꯦꯔꯣꯐ꯭ꯔꯦꯟꯆ · ꯁꯦꯛꯇꯔꯚꯣꯌꯥꯖꯦꯟ ꯗꯨ ꯖꯦꯔꯣ“ꯖꯤꯔꯣꯒꯤ ꯌꯨꯝꯂꯣꯟꯅꯕꯁꯤꯡ”: ꯆꯛꯔꯗ 22 ꯗꯒꯤ 25 ꯐꯥꯑꯣꯕ ꯃꯁꯤꯡ ꯇꯔꯥꯇꯔꯦꯠ, ꯆꯤꯞ ꯃꯥꯄꯟꯅ ꯕꯦꯠ ꯊꯝꯃꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯅ ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯒꯤ ꯃꯅꯥꯛꯀꯤ ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 17 ꯂꯧꯏ, ꯇꯤꯌꯦꯌꯔꯅ ꯃꯥꯌꯣꯛ ꯅꯥꯏꯅꯕ 12, ꯑꯣꯔꯐꯦꯂꯦꯟꯐ꯭ꯔꯦꯟꯆ · ꯁꯦꯛꯇꯔꯑꯣꯔꯐꯦꯂꯦꯟ“ꯃꯆꯥ ꯅꯨꯄꯥꯡꯕꯁꯤꯡ”: ꯚꯣꯌꯥꯖꯦꯟ ꯑꯃꯁꯨꯡ ꯇꯤꯌꯦꯌꯔꯅ ꯀꯨꯞꯇꯨꯅ ꯂꯩꯔꯤꯕ ꯃꯁꯤꯡ ꯅꯤꯄꯥꯟ: 17, 34, 6 ꯑꯃꯁꯨꯡ 1, 20, 14, 31, 9꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯅ ꯑꯄꯤꯛꯄ ꯁꯔꯨꯛ ꯑꯅꯤꯗ ꯂꯦꯃꯍꯧꯔꯤꯕ 8꯫ ꯄꯨꯟꯅꯥ ꯃꯈꯣꯌꯅ 37 ꯄꯨꯝꯅꯃꯛ ꯑꯃꯨꯛꯇ ꯀꯨꯞꯏ꯫ ꯑꯍꯨꯝ ꯑꯁꯤ ꯃꯣꯟꯇꯦ ꯀꯥꯔꯂꯣꯗ ꯃꯇꯧ ꯑꯣꯏꯅ ꯁꯦꯃꯈꯤ ꯑꯃꯁꯨꯡ ꯂꯥꯏꯕ ꯇꯦꯕꯜ ꯈꯨꯗꯤꯡꯒꯤ ꯔꯦꯁꯇ꯭ꯔꯦꯛꯇꯦꯕꯜꯔꯦꯁꯇ꯭ꯔꯦꯛꯂꯥꯏꯕ ꯑꯃꯁꯨꯡ ꯏꯂꯦꯛꯠꯔꯣꯅꯤꯛ ꯂꯦꯑꯥꯎꯠꯁꯤꯡꯗ ꯃꯁꯤꯡꯁꯤꯡ ꯆꯛꯔꯒꯤ ꯃꯊꯪ ꯃꯇꯨꯡ ꯏꯟꯅ ꯎꯠꯄ ꯑꯣꯚꯦꯜ ꯃꯑꯣꯡꯒꯤ ꯁꯔꯨꯛ, ꯌꯨꯝꯂꯣꯟꯅꯕ ꯑꯃꯁꯨꯡ ꯁꯦꯛꯇꯔ ꯕꯦꯠꯁꯤꯡ ꯇꯦꯞ ꯑꯃꯈꯛꯇꯅ ꯊꯝꯅꯕ ꯁꯤꯖꯤꯟꯅꯩ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯇ ꯏꯔꯤ꯫
ꯇꯦꯕꯜꯗ
ꯍꯛꯆꯥꯡ ꯂꯩꯕ ꯗꯤꯂꯔ ꯑꯃꯅ ꯆꯤꯞ ꯇꯔꯨꯛ ꯆꯦꯛꯀꯟꯗ ꯈꯔꯗ ꯊꯝꯃꯤ ꯑꯃꯁꯨꯡ ꯀꯣꯜ ꯑꯗꯨ ꯍꯟꯅꯥ ꯍꯥꯌꯔꯀꯏ (ꯑꯃꯃꯃꯗ ꯌꯨꯅꯤꯠ ꯃꯉꯥꯒꯤꯗꯃꯛ “ꯇꯤꯌꯦꯌꯔ, ꯁꯦꯉ꯭ꯛ ꯄꯤꯌꯦꯁ”)꯫ ꯑꯣꯅꯂꯥꯏꯟꯗ, ꯔꯦꯁꯇ꯭ꯔꯦꯛ ꯕꯇꯟꯗ ꯇꯦꯞ ꯑꯃꯈꯛꯅ ꯇꯔꯨꯛꯃꯛ ꯊꯝꯃꯤ꯫ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯦꯝꯕ ꯉꯝꯈꯩ ꯑꯁꯤ ꯀꯣꯜ ꯑꯗꯨꯒꯤ ꯄꯨꯝꯅꯃꯛꯇ ꯆꯠꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ $5 ꯒꯤ ꯃꯅꯨꯡꯒꯤ ꯉꯝꯈꯩ ꯑꯁꯤ $1 ꯒꯤ ꯆꯤꯞ ꯇꯔꯨꯛꯅ ꯃꯄꯨꯡ ꯐꯥꯍꯜꯂꯤ꯫
ꯋꯥꯍꯪꯁꯤꯡ
ꯌꯥꯎꯗꯦ꯫ ꯃꯁꯤ ꯖꯤꯔꯣꯗꯒꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯂꯥꯞꯄ ꯆꯛꯔꯒꯤ ꯁꯔꯨꯛ ꯑꯍꯨꯝ ꯊꯣꯀꯄꯒꯤ ꯑꯃꯅꯤ꯫
ꯁ꯭ꯞꯂꯤꯠ ꯇꯔꯨꯛ ꯑꯗꯨ ꯅꯍꯥꯛꯅ ꯃꯁꯥꯅ ꯄꯥꯝꯕ ꯑꯣꯖꯟꯗ ꯊꯝꯕ ꯌꯥꯏ; ꯀꯣꯜ ꯕꯦꯠꯇꯦꯕꯜꯀꯣꯜ ꯕꯦꯠꯈꯨꯠꯅ ꯊꯝꯗꯅ ꯗꯤꯂꯔꯗ ꯂꯥꯑꯣꯊꯣꯛꯄ ꯕꯦꯠ, ꯌꯥꯝꯅ ꯚꯣꯌꯥꯖꯦꯟ ꯅꯠꯔꯒ ꯇꯤꯌꯦꯌꯔꯒꯨꯝꯕ ꯆꯛꯔꯒꯤ ꯁꯦꯛꯇꯔ ꯕꯦꯠ ꯑꯃꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: “ꯂꯥꯑꯣꯊꯣꯛꯄ ꯕꯦꯠ”꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨꯗꯤ ꯃꯥꯟꯅꯕ ꯆꯤꯞ ꯇꯔꯨꯛꯅꯤ꯫
ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

ꯄꯣꯀꯦꯠ ꯇꯔꯥꯅꯤꯊꯣꯏ, ꯆꯤꯞ ꯇꯔꯨꯛ, ꯆꯛꯔꯒꯤ ꯁꯔꯨꯛ ꯑꯍꯨꯝ ꯊꯣꯀꯄꯒꯤ ꯑꯃ꯫
ꯍꯧꯔꯛꯐꯃꯁꯤꯡ
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Wykes, A. The Complete Illustrated Guide to Gambling.