ꯔꯨꯂꯦꯠ ꯗꯖꯟ ꯊꯧꯔꯥꯡ ꯑꯃꯁꯨꯡ ꯀꯂꯝꯁꯤꯡ
ꯔꯨꯂꯦꯠ ꯗꯖꯟ ꯊꯧꯔꯥꯡ ꯑꯃꯅ ꯗꯖꯟ ꯑꯅꯤ ꯅꯠꯔꯒ ꯀꯂꯝ ꯑꯅꯤꯗ ꯑꯃꯨꯛꯇ ꯕꯦꯠ ꯊꯝꯃꯤ, ꯃꯁꯤꯡ 37 ꯒꯤ ꯃꯅꯨꯡꯗꯒꯤ 24 ꯀꯨꯞꯏ꯫
ꯁ꯭ꯄꯤꯟꯁꯤꯡꯒꯤ 64.9% ꯗ ꯅꯦꯠ +1 ꯌꯨꯅꯤꯠ ꯃꯥꯏꯄꯥꯛꯏ; ꯑꯇꯣꯞꯄ 35.1% ꯗ ꯌꯨꯅꯤꯠ 2 ꯃꯥꯡꯏ꯫ ꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯦꯊꯃꯦꯇꯤꯛꯁꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯇꯝ ꯁꯥꯡꯅ ꯌꯦꯡꯂꯕꯗ ꯕꯦꯠ ꯑꯃꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩ꯫ ꯃꯔꯨꯑꯣꯏꯕ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →: ꯊꯝꯂꯕ ꯌꯨꯅꯤꯠ ꯑꯅꯤꯒꯤ −2.70%꯫
ꯗꯖꯟ ꯑꯅꯤꯒꯤ ꯔꯨꯂꯦꯠ ꯊꯧꯔꯥꯡꯒꯤ ꯍꯤꯁꯥꯕ
ꯗꯖꯟꯕꯦꯠꯗꯖꯟ1–12, 13–24 ꯅꯠꯔꯒ 25–36, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯅꯤꯒꯤ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯥ꯫ ꯀꯅꯥꯒꯨꯝꯕ ꯑꯃꯗ ꯊꯣꯛꯂꯕꯗ 2 ꯄꯤ ꯑꯃꯁꯨꯡ ꯑꯇꯣꯞꯄ ꯑꯗꯨ ꯃꯥꯡꯏ: +1꯫ ꯊꯣꯛꯇ꯭ꯔꯕꯗ (ꯑꯍꯨꯃꯁꯨꯕ ꯗꯖꯟ ꯅꯠꯔꯒ ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →) ꯑꯅꯤꯃꯛ ꯃꯥꯡꯏ: −2꯫ (24 × 1 − 13 × 2)/37 = (24 − 26)/37 = ꯊꯝꯂꯕ ꯌꯨꯅꯤꯠ ꯑꯅꯤꯗ −2/37 = ꯌꯨꯅꯤꯠ ꯈꯨꯗꯤꯡꯗ −1/37꯫ ꯑꯇꯣꯞꯄ ꯄꯨꯝꯅꯃꯛꯀꯨꯝꯅ ꯑꯦꯖ ꯑꯗꯨꯃꯛ, ꯃꯑꯣꯡ ꯈꯦꯠꯅꯩ: ꯑꯍꯨꯃꯗ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯅꯤ ꯔꯣꯝ, ꯈꯨꯗꯤꯡꯃꯛ ꯃꯥꯏꯊꯤꯕ ꯁ꯭ꯄꯤꯟ ꯑꯃꯒꯤ ꯁꯔꯨꯛ ꯑꯅꯤꯗ ꯑꯃꯒꯤ ꯃꯃꯜ꯫
ꯀꯔꯤꯒꯤ ꯃꯥꯏꯄꯥꯛꯂꯤꯕꯒꯨꯝ ꯐꯥꯑꯣꯕꯅꯣ
ꯁ꯭ꯄꯤꯟꯁꯤꯡꯒꯤ 65% ꯃꯥꯏꯄꯥꯛꯄ ꯑꯁꯤ, ꯃꯁꯤꯡ 25 ꯒꯤ ꯖꯦꯃꯁ ꯕꯣꯟꯗ ꯁꯟꯗꯣꯛꯄ ꯅꯠꯇꯕꯗꯤ, ꯃꯇꯝ ꯄꯨꯝꯕꯒꯤ ꯕꯦꯠꯁꯤꯡꯅ ꯄꯤꯕ ꯉꯝꯕ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯕ ꯊꯣꯛꯄꯒꯤ ꯔꯦꯠꯅꯤ꯫ ꯗꯖꯟ ꯑꯅꯤꯗ ꯕꯦꯠ ꯊꯝꯕꯒꯤ ꯁꯦꯁꯟ ꯑꯃꯥ ꯁꯦꯡꯂꯣꯡꯒꯤ ꯌꯥꯁꯤꯡꯒꯨꯝꯕ ꯁꯥꯡꯂꯕ ꯇꯞꯄ ꯃꯑꯣꯡ ꯑꯃꯅꯤ: ꯑꯃꯥ ꯀꯥꯏ, ꯑꯃꯥ ꯀꯥꯏ, ꯑꯅꯤ ꯇꯥꯏ, ꯑꯃꯥ ꯀꯥꯏ꯫ ꯑꯦꯚꯔꯦꯖ ꯊꯦꯡꯅꯕ ꯑꯁꯤ ꯇꯔꯅꯑꯣꯚꯔꯒꯤꯁꯦꯜꯇꯔꯅꯑꯣꯚꯔꯁꯦꯁꯟ ꯅꯠꯔꯒ ꯃꯇꯝ ꯑꯃꯒꯤ ꯃꯅꯨꯡꯗ ꯕꯦꯠ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ, ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯝꯂꯕ ꯃꯥꯏꯄꯥꯛꯇꯨꯅ ꯐꯪꯂꯕ ꯁꯦꯜꯁꯨ ꯌꯥꯎꯅ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯍꯦꯟꯗꯜ, ꯑꯦꯛꯁꯟ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → −2.70% ꯅꯤ, ꯑꯃꯁꯨꯡ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯌꯨꯅꯤꯠ ꯑꯅꯤ ꯊꯝꯕꯅ, ꯇꯔꯅꯑꯣꯚꯔ ꯑꯁꯤ ꯗꯖꯟ ꯑꯃꯈꯛꯀꯤꯗꯒꯤ ꯑꯅꯤ ꯊꯥꯛ ꯑꯣꯏ꯫
- p10 −$500
- p25 −$500
- ꯃꯤꯗꯤꯌꯥꯟ −$360
- p75 +$0
- p90 +$280
ꯗꯖꯟꯁꯤꯡꯗ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ
ꯃꯥꯏꯊꯤꯕꯒꯤ ꯃꯇꯨꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯅꯤ ꯊꯥꯛ ꯇꯧꯕꯅ 2 ꯗꯒꯤ 1 ꯒꯤ ꯕꯦꯠꯇ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯇ ꯇꯧꯕꯒꯨꯝꯅ ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯐꯪꯍꯟꯗꯦ꯫ ꯅꯍꯥꯛꯅ ꯌꯨꯅꯤꯠ 2 ꯃꯥꯡꯈꯤ (ꯗꯖꯟ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯑꯃꯥ), 2 ꯑꯃꯁꯨꯡ 2 ꯑꯣꯏꯅ ꯑꯅꯤ ꯊꯥꯛ ꯇꯧꯈꯤ, ꯑꯃꯁꯨꯡ ꯃꯥꯏꯄꯥꯛꯈꯤ ꯍꯥꯌꯔꯁꯤ: ꯅꯍꯥꯛꯅ 4 ꯐꯪꯏ ꯑꯃꯁꯨꯡ ꯑꯇꯣꯞꯄ ꯗꯖꯟꯗ 2 ꯃꯥꯡꯏ, ꯅꯦꯠ +2, ꯃꯁꯤꯅ ꯃꯃꯥꯡꯒꯤ ꯃꯥꯡꯈꯤꯕ ꯁꯦꯜ ꯑꯗꯨꯈꯛ ꯁꯣꯟꯊꯍꯜꯂꯤ, ꯍꯦꯟꯅꯥ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯠꯇ ꯂꯩꯇꯦ꯫ ꯃꯥꯏꯊꯤꯕ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯃꯇꯨꯡꯗ ꯅꯦꯠ +1 ꯐꯪꯅꯕꯒꯤꯗꯃꯛ ꯑꯅꯤ ꯊꯥꯛꯇꯒꯤ ꯍꯦꯟꯅꯥ ꯇꯧꯒꯗꯕꯅꯤ, ꯑꯃꯁꯨꯡ ꯗꯖꯟꯒꯤ ꯃꯇꯝ ꯄꯨꯝꯕꯒꯤ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟꯊꯧꯔꯥꯡꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟꯃꯃꯥꯡꯒꯤ ꯃꯍꯩꯁꯤꯡꯒꯤ ꯃꯈꯥꯗ ꯊꯝꯂꯕ ꯁꯦꯜ ꯍꯣꯡꯍꯟꯕ ꯅꯤꯌꯝ ꯀꯔꯤꯒꯨꯝꯕ꯫ ꯅꯦꯒꯦꯇꯤꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡꯅ ꯃꯥꯏꯊꯤꯔꯕꯥ ꯃꯇꯨꯡꯗ ꯍꯦꯅꯒꯠꯍꯜꯂꯤ, ꯄꯣꯖꯤꯇꯤꯕꯁꯤꯡꯅ ꯃꯥꯏꯄꯥꯛꯂꯕꯥ ꯃꯇꯨꯡꯗ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯑꯍꯨꯝ ꯊꯥꯛ ꯇꯧꯕꯅꯤ: 1, 3, 9, 27, 81꯫ ꯑꯍꯧꯕ $5 ꯗꯒꯤ $500 ꯒꯤ ꯉꯝꯈꯩ ꯑꯗꯨ ꯃꯥꯏꯊꯤꯕ ꯃꯉꯥꯒꯤ ꯃꯇꯨꯡꯗ ꯌꯧꯏ; ꯍꯣꯠꯅꯕ ꯈꯨꯗꯤꯡꯗ (13/37)⁵ ≈ 0.5%, ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡꯗ ꯍꯣꯠꯅꯕ ꯀꯌꯥ ꯂꯩ꯫
ꯍꯣꯟꯊꯣꯛꯄ ꯑꯃꯁꯨꯡ “ꯇꯨꯝꯂꯤꯕ” ꯗꯖꯟꯁꯤꯡ
ꯌꯣꯜꯂꯤꯕ ꯁꯤꯁ꯭ꯇꯦꯝ ꯀꯌꯥꯅ ꯀꯔꯝꯕ ꯗꯖꯟ ꯊꯥꯗꯣꯛꯀꯗꯒꯦ ꯍꯥꯌꯕꯗ ꯍꯣꯟꯊꯣꯀꯏ, ꯃꯇꯝ ꯌꯥꯝꯅꯥ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯛꯅ ꯊꯣꯀꯈꯤꯕ ꯅꯠꯔꯒ ꯃꯇꯝ ꯈꯔꯥ ꯊꯣꯀꯈꯤꯗꯕ ꯑꯗꯨ꯫ ꯁ꯭ꯄꯤꯟꯁꯤꯡ ꯃꯔꯤ ꯂꯩꯅꯗꯦ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯀꯔꯝꯕ ꯃꯁꯤꯡ 13 ꯀꯨꯞꯇꯅ ꯊꯃꯒꯗꯒꯦ ꯍꯥꯌꯕ ꯈꯅꯕꯅ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯠꯇꯗ ꯐꯟꯗꯦ꯫ ꯁꯤꯁ꯭ꯇꯦꯝꯁꯤꯡ ꯑꯁꯤ ꯃꯈꯣꯌ ꯃꯁꯥꯒꯥ ꯑꯃꯁꯨꯡ ꯀꯨꯞꯇꯕ ꯗꯖꯟ ꯑꯗꯨ ꯔꯦꯟꯗꯝ ꯑꯣꯏꯅ ꯈꯅꯕꯒꯥ ꯆꯞ ꯃꯥꯟꯅꯩ꯫
ꯔꯨꯂꯦꯠ ꯀꯂꯝ ꯊꯧꯔꯥꯡ
ꯃꯊꯛꯇ ꯂꯩꯕ ꯄꯨꯝꯅꯃꯛ ꯃꯁꯤꯡ 24 ꯀꯨꯞꯄ ꯀꯂꯝꯕꯦꯠꯀꯂꯝꯂꯦꯑꯥꯎꯠꯀꯤ ꯊꯣꯡꯅꯥꯡꯒꯤ ꯀꯂꯝ ꯑꯃꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯅꯤꯗ, ꯅꯠꯔꯒ ꯃꯁꯤꯡ 20 ꯀꯨꯞꯄ ꯗꯖꯟ ꯑꯃꯥ ꯑꯃꯁꯨꯡ ꯀꯂꯝ ꯑꯃꯗ (ꯃꯁꯤꯡ ꯃꯔꯤ ꯑꯅꯤ ꯊꯥꯛ ꯃꯁꯤꯡ ꯊꯤꯔꯕ) ꯆꯠꯂꯤ꯫ ꯕꯦꯠ ꯕꯤꯜꯗꯔ ꯈꯨꯠꯂꯥꯏ ꯑꯗꯨꯅ ꯀꯔꯤꯒꯨꯝꯕ ꯄꯨꯟꯁꯤꯟꯕ ꯑꯃꯒꯤ ꯆꯞꯆꯥꯕ ꯗꯤꯁ꯭ꯇ꯭ꯔꯤꯕ꯭ꯌꯨꯁꯟ ꯄꯤ꯫
ꯍꯦꯟꯅꯥ ꯇꯞꯄ ꯑꯅꯤ ꯊꯥꯛ ꯇꯧꯕ
ꯂꯥꯁ ꯚꯦꯒꯥꯁꯇ ꯌꯣꯜꯂꯤꯕ ꯄꯦꯝꯐ꯭ꯂꯦꯠ ꯑꯃꯥ, Famous Las Vegas Gambling Systems, ꯅ ꯀꯂꯝ ꯑꯃꯒꯤꯗꯃꯛ ꯍꯦꯟꯅꯥ ꯇꯞꯄ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ ꯑꯃꯥ ꯄꯤ: ꯌꯨꯅꯤꯠ 1 ꯊꯝꯕ, ꯃꯥꯏꯊꯤꯕꯒꯤ ꯃꯇꯨꯡꯗ 1 ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯝꯕ, ꯑꯃꯁꯨꯡ ꯃꯈꯥ ꯆꯠꯅꯕ ꯃꯥꯏꯊꯤꯕ ꯑꯅꯤꯒꯤ ꯃꯇꯨꯡꯗ ꯈꯛꯇ ꯑꯅꯤ ꯊꯥꯛ ꯇꯧꯕ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯊꯝꯂꯕ ꯁꯦꯜꯁꯤꯡ 1, 1, 2, 2, 4, 4, 8, 8 ꯑꯣꯏꯅ ꯆꯠꯂꯤ (Bollman, 2024)꯫ ꯊꯝꯂꯕ ꯁꯦꯜꯁꯤꯡ ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯒꯤꯊꯧꯔꯥꯡꯃꯥꯔꯇꯤꯟꯒꯦꯜꯃꯥꯏꯊꯤꯕ ꯈꯨꯗꯤꯡꯒꯤ ꯃꯇꯨꯡꯗ ꯕꯦꯠ ꯑꯗꯨ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯟꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ꯫ ꯃꯁꯤꯅ ꯀꯔꯤ ꯇꯧꯕꯒꯦ ꯑꯃꯁꯨꯡ ꯀꯔꯤ ꯇꯧꯗꯕꯒꯦ ꯍꯥꯌꯕ ꯊꯧꯔꯥꯡꯒꯤ ꯁꯦꯛꯁꯅꯗ ꯌꯦꯡꯕꯤꯌꯨ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯁꯔꯨꯛ ꯑꯅꯤꯗ ꯑꯃꯒꯤ ꯊꯨꯅ ꯍꯦꯅꯒꯠꯂꯤ, ꯑꯃꯁꯨꯡ ꯃꯃꯜ ꯑꯗꯨꯗꯤ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯅ ꯃꯥꯡꯈꯤꯕ ꯁꯦꯜꯁꯤꯡ ꯃꯇꯝ ꯄꯨꯝꯕꯗ ꯁꯣꯟꯊꯍꯜꯂꯣꯏ: ꯄꯦꯌꯔ ꯑꯃꯒꯤ ꯑꯅꯤꯁꯨꯕ ꯕꯦꯠꯇ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯅ ꯅꯍꯥꯛꯄꯨ ꯆꯞ ꯃꯥꯟꯅꯕ ꯅꯠꯔꯒ ꯃꯥꯡꯂꯕ ꯑꯣꯏꯅ ꯊꯃꯕ ꯌꯥꯏ꯫ ꯃꯈꯥ ꯆꯠꯅꯕ ꯊꯣꯛꯇꯕ ꯇꯔꯥꯅ ꯌꯨꯅꯤꯠ 62 ꯃꯥꯡꯍꯜꯂꯤ ꯑꯃꯁꯨꯡ ꯍꯣꯠꯅꯕ 50 ꯗ ꯑꯃꯨꯛ ꯔꯣꯝ ꯊꯣꯀꯏ, ꯃꯔꯃꯗꯤ ꯀꯂꯝ ꯑꯃꯅ 37 ꯗ 25 ꯊꯣꯀꯄ ꯉꯃꯗꯦ꯫ ꯊꯝꯂꯕ ꯌꯨꯅꯤꯠ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯍꯧꯖꯤꯀꯁꯨ 2.70% ꯌꯥꯎꯏ꯫
ꯋꯥꯍꯪꯁꯤꯡ
ꯊꯣꯛꯄꯒꯤ ꯔꯦꯠ ꯍꯦꯟꯅꯥ ꯋꯥꯡꯏ, ꯃꯥꯡꯈꯤꯕ ꯁꯦꯜꯁꯤꯡ ꯍꯦꯟꯅꯥ ꯆꯥꯎꯏ, ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯆꯞ ꯃꯥꯟꯅꯩ꯫ ꯊꯝꯂꯕ ꯄꯨꯝꯅꯃꯛ ꯆꯞ ꯃꯥꯟꯅꯕꯗ ꯑꯉꯥꯡꯕꯒꯤꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯚꯦꯌꯔꯤꯌꯦꯟꯁꯃꯦꯊꯃꯦꯇꯤꯛꯁꯚꯦꯌꯔꯤꯌꯦꯟꯁꯃꯍꯩꯁꯤꯡ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯒꯤ ꯑꯀꯣꯌꯕꯗ ꯀꯌꯥ ꯁꯟꯗꯣꯛꯅ ꯂꯩꯕꯒꯦ ꯍꯥꯌꯕꯒꯤ ꯆꯥꯡ꯫ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯇ ꯋꯥꯡꯏ, ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡꯗ ꯅꯦꯝꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯍꯦꯟꯅꯥ ꯅꯦꯝꯃꯤ꯫
ꯖꯤꯔꯣꯗ ꯆꯤꯞꯁꯦꯜꯆꯤꯞꯂꯦꯞꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯃꯜ ꯇꯥꯛꯄ ꯇꯣꯀꯟ, ꯕꯦꯠ ꯊꯝꯅꯕ ꯂꯦꯑꯥꯎꯠꯇ ꯊꯝꯃꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯆꯦꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯥ ꯍꯥꯄꯆꯤꯜꯂꯕꯗ ꯅꯍꯥꯛꯅ ꯃꯁꯤꯡ 25 ꯀꯨꯞꯏ; ꯃꯗꯨꯗꯒꯤ ꯖꯤꯔꯣꯅ −2 ꯒꯤ ꯃꯍꯨꯠꯇ 35 − 2 = +33 ꯄꯤ꯫ ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯑꯁꯤ ꯌꯨꯅꯤꯠ ꯑꯍꯨꯃꯗ −3/37 ꯑꯣꯏ: ꯌꯨꯅꯤꯠ ꯈꯨꯗꯤꯡꯗ ꯍꯣꯡꯗꯦ꯫
ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯥ ꯁꯥꯟꯅꯕ
ꯃꯁꯤꯁꯤꯡ ꯑꯍꯥꯅꯕꯗ ꯅꯍꯥꯛ ꯃꯁꯥꯃꯛꯅ ꯍꯣꯠꯅꯕꯤꯌꯨ꯫ ꯄꯥꯎꯈꯨꯝ ꯈꯨꯗꯤꯡꯃꯛ ꯊꯨꯡꯗꯨꯅ ꯊꯝꯂꯤ; ꯁꯦꯝ ꯁꯥꯔꯕ ꯃꯇꯃꯗ ꯍꯥꯡꯗꯣꯛꯄꯤꯌꯨ꯫
ꯂꯥꯏꯔꯤꯛ ꯑꯄꯤꯛꯄ ꯑꯗꯨꯒꯤ ꯀꯂꯝꯕꯦꯠꯀꯂꯝꯂꯦꯑꯥꯎꯠꯀꯤ ꯊꯣꯡꯅꯥꯡꯒꯤ ꯀꯂꯝ ꯑꯃꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯁꯤꯁ꯭ꯇꯦꯝꯅ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 1, 1, 2, 2, 4, 4, 8, 8 ꯊꯝꯏ, ꯃꯈꯥ ꯆꯠꯅꯅ ꯃꯥꯏꯊꯤꯕ ꯑꯅꯤꯒꯤ ꯃꯇꯨꯡꯗꯈꯛ ꯑꯃꯨꯛ ꯑꯅꯤ ꯇꯧꯏ, ꯑꯃꯁꯨꯡ ꯑꯍꯥꯅꯕ ꯃꯥꯏꯄꯥꯛꯄꯗ ꯂꯦꯞꯏ꯫ ꯀꯂꯝ ꯑꯃꯅ 2 ꯗꯒꯤ 1 ꯄꯤ꯫ ꯑꯍꯥꯅꯕ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯗꯨ ꯕꯦꯠ 1, 2, 3 … 8 ꯗ ꯂꯥꯛꯂꯕꯗꯤ ꯅꯍꯥꯛ ꯀꯌꯥ ꯀꯥꯟꯅꯒꯅꯤ ꯅꯠꯔꯒꯥ ꯃꯥꯡꯒꯅꯤ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯕꯦꯠ 1, 3, 5 ꯅꯠꯔꯒꯥ 7 ꯗ ꯃꯥꯏꯄꯥꯛꯂꯕꯗꯤ ꯌꯨꯅꯤꯠ 2 ꯀꯥꯟꯅꯩ꯫ ꯕꯦꯠ 2, 4, 6 ꯅꯠꯔꯒꯥ 8 ꯗ ꯃꯥꯏꯄꯥꯛꯂꯕꯗꯤ ꯌꯨꯅꯤꯠ +1, 0, −2 ꯑꯃꯁꯨꯡ −6: ꯃꯇꯝ ꯄꯨꯝꯕꯒꯤ +2 ꯗꯒꯤ ꯍꯟꯊꯩ, ꯑꯃꯁꯨꯡ ꯕꯦꯠ 6 ꯗꯒꯤ ꯍꯧꯔꯒꯥ ꯃꯥꯡꯏ꯫
ꯊꯝꯂꯕ ꯁꯦꯜ s ꯗ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯅ 2s ꯄꯤ; ꯃꯗꯨꯒꯤ ꯃꯃꯥꯡꯗ ꯃꯥꯡꯈꯤꯕ ꯄꯨꯝꯅꯃꯛ ꯂꯧꯊꯣꯀꯄꯤꯌꯨ꯫
ꯕꯦꯠ 1 (ꯊꯝꯂꯕ 1): +2꯫ ꯕꯦꯠ 2 (ꯊꯝꯂꯕ 1, ꯃꯃꯥꯡꯗ 1 ꯃꯥꯡꯈꯤ): 2 − 1 = +1꯫ ꯕꯦꯠ 3 (ꯊꯝꯂꯕ 2, 2 ꯃꯥꯡꯈꯤ): 4 − 2 = +2꯫ ꯕꯦꯠ 4 (ꯊꯝꯂꯕ 2, 4 ꯃꯥꯡꯈꯤ): 4 − 4 = 0꯫ ꯕꯦꯠ 5 (ꯊꯝꯂꯕ 4, 6 ꯃꯥꯡꯈꯤ): 8 − 6 = +2꯫ ꯕꯦꯠ 6 (ꯊꯝꯂꯕ 4, 10 ꯃꯥꯡꯈꯤ): 8 − 10 = −2꯫ ꯕꯦꯠ 7 (ꯊꯝꯂꯕ 8, 14 ꯃꯥꯡꯈꯤ): 16 − 14 = +2꯫ ꯕꯦꯠ 8 (ꯊꯝꯂꯕ 8, 22 ꯃꯥꯡꯈꯤ): 16 − 22 = −6꯫
ꯄꯦꯌꯔ ꯈꯨꯗꯤꯡꯒꯤ ꯑꯍꯥꯅꯕ ꯊꯝꯂꯕ ꯁꯦꯜꯅ ꯃꯇꯝ ꯄꯨꯝꯅꯃꯛꯇ ꯅꯦꯠ +2 ꯄꯤ; ꯑꯅꯤꯁꯨꯕꯅ +1, 0, −2, −6, −14 ꯑꯁꯤꯅꯆꯤꯡꯕ ꯄꯤ, ꯑꯃꯨꯛ ꯈꯨꯗꯤꯡꯗ ꯍꯦꯟꯅ ꯐꯠꯏ꯫ ꯃꯁꯤ ꯍꯦꯟꯅ ꯂꯦꯡꯕ ꯋꯥꯡꯈꯠꯄꯒꯤ ꯃꯃꯜꯅꯤ꯫ ꯀꯂꯝ ꯑꯃꯅ 37 ꯗ ꯑꯃꯨꯛ 25 ꯌꯥꯃꯗꯦ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯥ ꯆꯠꯅꯅ ꯌꯥꯃꯗꯕ ꯇꯔꯥ, ꯌꯨꯅꯤꯠ 62 ꯃꯥꯡꯕ, ꯍꯣꯠꯅꯕ 50 ꯗ ꯑꯃꯨꯛ ꯈꯔ ꯂꯥꯀꯏ꯫
ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ
ꯗꯖꯟ ꯑꯅꯤ: ꯊꯣꯛꯄꯒꯤ ꯔꯦꯠ 65%, ꯃꯃꯜ 2.70%꯫
ꯍꯧꯔꯛꯐꯃꯁꯤꯡ
- RouletteDoc꯫ ꯔꯨꯂꯦꯠ ꯊꯧꯔꯥꯡꯁꯤꯡꯒꯤ ꯄꯨꯝꯅꯃꯛ ꯌꯦꯡꯕ꯫
- Roulette77꯫ ꯔꯨꯂꯦꯠ ꯊꯧꯔꯥꯡꯁꯤꯡꯒꯤ ꯄꯨꯝꯅꯃꯛ ꯌꯦꯡꯕ꯫
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed.