ꯍꯦꯟꯅꯥ · ꯄꯥꯅꯕꯥ ꯄꯔꯤꯡ · ꯃꯤꯅꯤꯠ 8

ꯔꯨꯂꯦꯠꯀꯤ ꯂꯥꯏꯔꯤꯀꯁꯤꯡ: ꯄꯥꯅꯕꯥ ꯄꯔꯤꯡ

ꯁꯥꯏꯠ ꯑꯁꯤꯅ ꯌꯨꯝꯐꯝ ꯑꯣꯏꯅ ꯂꯧꯔꯤꯕ ꯔꯨꯂꯦꯠꯀꯤ ꯂꯥꯏꯔꯤꯀꯁꯤꯡ ꯑꯃꯁꯨꯡ ꯄꯦꯄꯔꯁꯤꯡ, ꯃꯁꯤꯡ ꯀꯨꯟꯅꯤꯊꯣꯏ, ꯐꯪꯒꯗꯕ ꯃꯃꯂꯒꯤ ꯃꯇꯥꯡꯗ 1657 ꯒꯤ ꯂꯥꯏꯔꯤꯛ ꯑꯃꯗꯒꯤ 2025 ꯒꯤ ꯇꯦꯛꯁ꯭ꯠꯕꯨꯛ ꯑꯃꯐꯥꯑꯣꯕ, ꯃꯈꯣꯌ ꯈꯨꯗꯤꯡ ꯀꯔꯤꯒꯤ ꯃꯔꯨꯑꯣꯏꯕꯒꯦ ꯍꯥꯌꯕꯒꯤ ꯋꯥꯍꯩ ꯄꯔꯦꯡ ꯑꯃꯒꯥ ꯂꯣꯌꯅꯅ꯫

ꯊꯨꯅ ꯄꯥꯎꯈꯨꯝ

ꯃꯦꯊꯃꯦꯇꯤꯛꯁ (ꯍꯣꯏꯒꯦꯟꯁ, ꯕꯔꯅꯨꯂꯤ, ꯍꯥꯂꯃꯣꯁ, ꯐꯦꯂꯔ, ꯊꯣꯔꯞ, ꯑꯦꯄꯁ꯭ꯇꯥꯏꯟ, ꯏꯊꯤꯌꯔ, ꯑꯃꯁꯨꯡ ꯕꯣꯂꯃꯦꯟ, ꯇꯦꯂꯔ ꯑꯃꯁꯨꯡ ꯍꯨꯅꯥꯆꯦꯛꯀꯤ ꯅꯧꯕ ꯇꯦꯛꯁ꯭ꯠꯕꯨꯀꯁꯤꯡ), ꯄꯨꯋꯥꯔꯤ (ꯂꯥꯕ꯭ꯂꯦ, ꯕꯥꯔꯅꯍꯥꯔꯠ, ꯁ꯭ꯋꯥꯔꯠꯖ, ꯀꯦꯚꯅꯥꯒ, ꯃꯥꯔꯀꯁ, ꯒꯣꯜꯗꯃꯦꯟ), ꯐꯤꯖꯤꯛꯁ (ꯕꯦꯁ, ꯁ꯭ꯃꯣꯜ ꯑꯃꯁꯨꯡ ꯇ꯭ꯁꯦ) ꯑꯃꯁꯨꯡ ꯃꯈꯣꯌ ꯄꯨꯝꯅꯃꯛꯇꯒꯤ ꯍꯦꯟꯅꯥ ꯐꯕ ꯅꯣꯚꯦꯜ ꯑꯃꯈꯛ (ꯗꯣꯁ꯭ꯇꯣꯌꯦꯚꯁ꯭ꯀꯤ)꯫ ꯁꯥꯏꯠ ꯑꯁꯤꯗ ꯂꯩꯕ ꯄꯨꯝꯅꯃꯛ ꯂꯥꯏꯔꯤꯛ ꯊꯝꯃꯣꯛ ꯑꯁꯤꯗ ꯌꯨꯝꯐꯝ ꯑꯣꯏꯔꯤ꯫

ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯑꯔꯤꯕ
ꯍꯣꯏꯒꯦꯟꯁ, 1657
ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯑꯅꯧꯕ
ꯍꯨꯅꯥꯆꯦꯛ, 2025
ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯕ ꯂꯥꯏꯔꯤꯛ ꯑꯃꯈꯛ
ꯏꯊꯤꯌꯔ, 2010
ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯕ ꯅꯣꯚꯦꯜ
ꯗ ꯒꯦꯝꯕ꯭ꯂꯔ, 1866

ꯃꯦꯊꯃꯦꯇꯤꯛꯁ

ꯂꯥꯏꯔꯤꯛꯆꯍꯤꯀꯔꯤꯒꯤ ꯄꯥꯒꯗꯒꯦ
Huygens, De Ratiociniis in Ludo Aleae1657ꯐꯪꯒꯗꯕ ꯃꯃꯂꯒꯤ ꯃꯇꯥꯡꯗ ꯑꯍꯥꯅꯕ ꯐꯣꯡꯈꯤꯕ ꯂꯥꯏꯔꯤꯛ; EV ꯀꯗꯥꯏꯗꯒꯤ ꯂꯥꯀꯈꯤꯕꯅꯣ
Bernoulli, Ars Conjectandi1713ꯑꯆꯧꯕ ꯃꯁꯤꯡꯒꯤ ꯅꯤꯌꯝ, ꯁꯤꯁ꯭ꯇꯦꯝꯁꯤꯡꯅ ꯑꯔꯥꯟꯕ ꯈꯟꯅꯔꯤꯕ
Halmos, “Invariants of certain stochastic transformations”1939ꯀꯔꯤꯒꯨꯝꯕ ꯕꯦꯇꯤꯡ ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯃꯠꯇꯅ ꯐꯪꯒꯗꯕ ꯃꯍꯩ ꯍꯣꯡꯗꯣꯛꯄ ꯉꯃꯗꯕꯒꯤ ꯑꯍꯥꯅꯕ ꯄꯨꯝꯅꯃꯀꯄ ꯄ꯭ꯔꯨꯐ
Feller, An Introduction to Probability Theory, vol. 11968ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯂꯣꯏꯁꯤꯟꯕ, ꯔꯦꯟꯗꯝ ꯋꯥꯛ, ꯁ꯭ꯇ꯭ꯔꯤꯛꯁꯤꯡ; ꯃꯍꯧꯁꯥꯒꯤ ꯔꯦꯐꯔꯦꯟꯁ
Thorp, “Optimal gambling systems for favorable games”1969ꯕꯦꯇꯤꯡ ꯁꯤꯁ꯭ꯇꯦꯝꯁꯤꯡꯅ ꯀꯗꯥꯏꯗ ꯃꯇꯦꯡ ꯄꯥꯡꯕ ꯉꯃꯒꯅꯤ (ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯐꯕ ꯒꯦꯝ ꯑꯃꯗ ꯈꯛꯇ) ꯑꯃꯁꯨꯡ ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯃꯠꯇꯅ ꯃꯥꯏꯄꯥꯀꯍꯟꯕ ꯉꯃꯗꯕ ꯃꯍꯩ ꯑꯗꯨꯒꯤ ꯃꯇꯨꯡꯗ ꯂꯩꯕ ꯐꯤꯚꯃꯁꯤꯡ
Thorp, The Mathematics of Gambling1984ꯔꯨꯂꯦꯠ ꯀꯝꯄ꯭ꯌꯨꯇꯔ ꯑꯗꯨ ꯁꯦꯃꯈꯤꯕ ꯃꯤꯑꯣꯏ ꯃꯁꯥꯃꯛꯅ ꯍꯥꯌꯔꯤꯕ, ꯑꯦꯖ ꯑꯃꯗ ꯀꯌꯥ ꯕꯦꯠ ꯊꯝꯒꯗꯒꯦ ꯍꯥꯌꯕꯒꯤ ꯃꯁꯤꯡ ꯊꯤꯕꯒꯥ ꯂꯣꯌꯅꯅ
Epstein, The Theory of Gambling and Statistical Logic2013 (ꯑꯦꯗꯤꯁꯟ 2)ꯀꯦꯁꯤꯅꯣꯒꯤ ꯒꯦꯝ ꯈꯨꯗꯤꯡ ꯌꯦꯡꯁꯤꯟꯈꯤꯕ; ꯃꯈꯣꯌꯒꯤ ꯃꯔꯛꯇ ꯔꯨꯂꯦꯠ
Ethier, The Doctrine of Chances2010ꯐꯣꯡꯈꯤꯕ ꯂꯥꯏꯔꯤꯀꯁꯤꯡꯒꯤ ꯃꯅꯨꯡꯗ ꯔꯨꯂꯦꯠꯀꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯃꯄꯨꯡ ꯐꯥꯕ ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯤ ꯊꯤꯖꯤꯅꯕ
Bollman, Mathematics of the Big Four Casino Table Games2021ꯁꯥꯏꯗ ꯕꯦꯠꯁꯤꯡ, ꯃꯍꯧꯁꯥꯒꯤ ꯅꯠꯇꯕ ꯆꯛꯔꯁꯤꯡ ꯑꯃꯁꯨꯡ ꯀꯥꯔꯗ ꯔꯨꯂꯦꯠ ꯑꯃꯃꯃꯛ ꯃꯃꯜ ꯊꯤꯕ, ꯁꯃꯁ꯭ꯌꯥꯁꯤꯡꯒꯥ ꯂꯣꯌꯅꯅ
Taylor, Games, Gambling, and Probability2021 (ꯑꯦꯗꯤꯁꯟ 2)ꯁ꯭ꯇ꯭ꯔꯤꯛꯁꯤꯡ, ꯀꯦꯂꯤ ꯕꯦꯇꯤꯡ ꯑꯃꯁꯨꯡ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯂꯣꯏꯁꯤꯟꯕ ꯀꯣꯔꯁ ꯑꯃꯒꯨꯝꯅ ꯁꯦꯃꯈꯤꯕ
Bollman, Basic Gambling Mathematics2024 (ꯑꯦꯗꯤꯁꯟ 2)ꯀꯦꯁꯤꯅꯣꯒꯤ ꯄ꯭ꯔꯣꯃꯣꯁꯅꯁꯤꯡ ꯑꯃꯁꯨꯡ ꯔꯤꯕꯦꯠꯁꯤꯡ, ꯑꯃꯁꯨꯡ ꯃꯍꯩ ꯕꯣꯔꯗ ꯑꯃꯅ ꯀꯦꯁꯤꯅꯣꯒꯤꯗꯃꯛ ꯃꯁꯥꯒꯤ ꯃꯃꯜ ꯀꯌꯥ ꯊꯨꯅ ꯍꯟꯅ ꯐꯪꯍꯜꯂꯤꯕꯒꯦ
Hunacek, Quantitative Literacy Through Games and Gambling2025ꯂꯥꯏꯕ ꯑꯍꯥꯅꯕ ꯀꯣꯔꯁ ꯑꯃꯥ; ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯑꯗꯨꯃꯛ ꯂꯩ ꯍꯥꯌꯕ ꯃꯁꯤꯒꯤ ꯋꯥꯐꯝ ꯑꯗꯨ ꯌꯦꯡꯕꯤꯌꯨ, ꯃꯁꯤꯡ ꯃꯉꯥꯒꯤ ꯕꯦꯠꯅ ꯃꯗꯨ ꯊꯨꯒꯥꯏ

ꯄꯨꯋꯥꯔꯤ

ꯂꯥꯏꯔꯤꯛꯆꯍꯤꯀꯔꯤꯒꯤ ꯄꯥꯒꯗꯒꯦ
Lablée, La Roulette, ou le Jour1801ꯒꯦꯝ ꯑꯁꯤꯒꯤ ꯑꯍꯥꯅꯕ ꯃꯄꯨꯡ ꯐꯥꯕ ꯐꯣꯡꯗꯣꯀꯄ, ꯅꯣꯚꯦꯜ ꯑꯃꯗ
Barnhart, Beating the Wheel1992ꯕꯥꯏꯌꯥꯁ ꯁꯤꯖꯤꯟꯅꯗꯨꯅ ꯁꯥꯟꯅꯕꯒꯤ ꯄꯨꯋꯥꯔꯤ: ꯖꯦꯒꯔ, ꯄꯦꯂꯥꯌꯣꯁꯤꯡꯒꯤ ꯃꯃꯥꯡꯗ ꯂꯩꯔꯝꯕꯁꯤꯡ, ꯃꯑꯣꯡꯁꯤꯡ
Schwartz, Roll the Bones2006ꯖꯨꯌꯥꯒꯤ ꯄꯨꯝꯅꯃꯛꯀꯤ ꯄꯨꯋꯥꯔꯤ; ꯃꯗꯨꯗ ꯔꯨꯂꯦꯠꯀꯤ ꯃꯐꯝ
Kavanagh, Dice, Cards, Wheels2005ꯐ꯭ꯔꯥꯟꯁꯀꯤ ꯖꯨꯌꯥꯒꯤ ꯂꯝꯕꯤ; ꯄꯦꯂꯦ-ꯔꯣꯌꯥꯜ ꯑꯃꯁꯨꯡ ꯁ꯭ꯄꯥꯁꯤꯡ
Marcus, American Roulette2003ꯄꯥꯁ꯭ꯠ-ꯄꯣꯁ꯭ꯇꯤꯡ, ꯃꯁꯤ ꯇꯧꯔꯝꯕꯁꯤꯡꯒꯤ ꯃꯔꯛꯇ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯃꯃꯤꯡ ꯂꯩꯕ ꯃꯤꯑꯣꯏ ꯑꯗꯨꯅ ꯃꯅꯨꯡꯗꯒꯤ ꯐꯣꯡꯗꯣꯀꯄ
Goldman, Great Gambling Scams2007ꯅꯤꯁꯇ ꯂꯤ, ꯃꯥꯔꯀꯁ ꯑꯃꯁꯨꯡ ꯔꯤꯠꯖ ꯍꯟꯅ ꯍꯥꯌꯔꯤꯕ; ꯄꯨꯛꯅꯤꯡ ꯆꯤꯡꯁꯤꯅꯕ, ꯑꯗꯨꯕꯨ ꯐꯦꯛꯇ ꯀꯌꯥꯗ ꯑꯔꯥꯟꯕ (ꯔꯨꯂꯦꯠꯇ ꯃꯤꯅꯝꯕ ꯌꯦꯡꯕꯤꯌꯨ)

ꯐꯤꯖꯤꯛꯁ ꯑꯃꯁꯨꯡ ꯑꯦꯗꯚꯥꯟꯇꯦꯖ ꯄ꯭ꯂꯦ

ꯂꯥꯏꯔꯤꯛꯆꯍꯤꯀꯔꯤꯒꯤ ꯄꯥꯒꯗꯒꯦ
Bass, The Eudaemonic Pie1985ꯈꯣꯡꯎꯞꯇ ꯂꯣꯠꯄ ꯀꯝꯄ꯭ꯌꯨꯇꯔꯒꯤ ꯋꯥꯔꯤ; ꯔꯨꯂꯦꯠꯀꯤ ꯐꯤꯖꯤꯛꯁꯀꯤ ꯃꯇꯥꯡꯗ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯕ ꯃꯤꯌꯥꯝꯅ ꯄꯥꯕ ꯂꯥꯏꯔꯤꯛ
Small & Tse, “Predicting the outcome of roulette”2012ꯃꯍꯩ ꯂꯥꯎꯊꯣꯀꯄꯒꯤ ꯐꯤꯖꯤꯛꯁ, ꯆꯥꯡ ꯊꯤꯗꯨꯅ; ꯑꯦꯖ ꯑꯃꯒꯤꯗꯃꯛ ꯀꯔꯤ ꯃꯊꯧ ꯇꯥꯕꯒꯦ
Pearson, “On the criterion…”1900ꯀꯥꯏ-ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯇꯦꯁ꯭ꯠ, ꯔꯨꯂꯦꯠ ꯁ꯭ꯄꯤꯟꯁꯤꯡꯗ ꯎꯠꯈꯤꯕ

ꯔꯨꯂꯦꯠ ꯆꯛꯔꯒꯤ ꯐꯤꯖꯤꯛꯁ

ꯅꯣꯚꯦꯜ

ꯗꯣꯁ꯭ꯇꯣꯌꯦꯚꯁ꯭ꯀꯤ (Dostoevsky), The Gambler (1866)꯫ ꯄꯕ꯭ꯂꯤꯁꯔ ꯑꯃꯒꯤ ꯀꯟꯠꯔꯥꯛꯀꯤ ꯃꯇꯝ ꯉꯝꯈꯩ ꯑꯗꯨ ꯐꯪꯅꯕ ꯅꯨꯃꯤꯠ 26 ꯗ ꯏꯈꯤꯕ, ꯔꯨꯂꯦꯠꯀꯤ ꯃꯔꯃꯗ ꯀꯔꯖ ꯀꯌꯥ ꯊꯨꯡꯂꯕ ꯏꯕꯥ ꯑꯃꯅ; ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯑꯔꯥꯟꯕ ꯋꯥꯈꯜ, ꯁꯤꯁ꯭ꯇꯦꯝ, ꯂꯦꯞꯄ ꯉꯃꯗꯕ ꯑꯃꯁꯨꯡ ꯁ꯭ꯄꯥ ꯀꯦꯁꯤꯅꯣ ꯃꯅꯨꯡꯗꯒꯤ꯫ ꯃꯊꯛꯇ ꯂꯩꯕ ꯔꯨꯂꯦꯠ ꯂꯥꯏꯔꯤꯛ ꯑꯃꯠꯇꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯊꯨꯕ ꯑꯃꯁꯨꯡ ꯃꯈꯣꯌ ꯌꯥꯝꯅ ꯆꯥꯎꯕꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯑꯆꯨꯝꯕ꯫

ꯕꯥꯗ ꯍꯣꯝꯕꯔꯒ ꯑꯃꯁꯨꯡ ꯁ꯭ꯄꯥ ꯀꯦꯁꯤꯅꯣꯁꯤꯡꯗꯣꯁ꯭ꯇꯣꯌꯦꯚꯁ꯭ꯀꯤꯒꯤ ꯔꯨꯂꯦꯇꯦꯟꯕꯔꯒ

ꯄꯥꯟꯗꯝ ꯈꯨꯗꯤꯡꯒꯤꯗꯃꯛ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯕ ꯔꯨꯂꯦꯠ ꯂꯥꯏꯔꯤꯀꯁꯤꯡ

ꯃꯁꯤꯡ ꯊꯤꯕꯒꯤꯗꯃꯛ, ꯏꯊꯤꯌꯔ ꯑꯃꯁꯨꯡ ꯃꯗꯨꯒꯤ ꯃꯇꯨꯡꯗ ꯐꯦꯂꯔ꯫ ꯋꯥꯔꯤꯁꯤꯡꯒꯤꯗꯃꯛ, ꯕꯥꯔꯅꯍꯥꯔꯠ ꯑꯃꯁꯨꯡ ꯕꯦꯁ꯫ ꯃꯤꯁꯤꯡꯅ ꯃꯗꯨꯃꯛ ꯑꯣꯏꯔꯕꯁꯨ ꯀꯔꯤꯒꯤ ꯁꯥꯟꯅꯕꯒꯦ ꯍꯥꯌꯕꯒꯤꯗꯃꯛ, ꯗꯣꯁ꯭ꯇꯣꯌꯦꯚꯁ꯭ꯀꯤ꯫ ꯁꯤꯁ꯭ꯇꯦꯝꯒꯤ ꯌꯦꯛꯅꯕ ꯈꯨꯗꯤꯡ ꯂꯣꯏꯁꯤꯜꯂꯤꯕ ꯄ꯭ꯔꯨꯐꯀꯤꯗꯃꯛ, ꯍꯥꯂꯃꯣꯁ, ꯑꯃꯁꯨꯡ ꯃꯍꯩ ꯑꯗꯨꯃꯛ ꯂꯥꯏꯕ ꯋꯥꯍꯩꯗ ꯄꯥꯅꯕꯒꯤꯗꯃꯛ, ꯊꯣꯔꯄꯀꯤ 1984 ꯒꯤ ꯂꯥꯏꯔꯤꯛ꯫ ꯁꯃꯁ꯭ꯌꯥꯁꯤꯡꯒꯤꯗꯃꯛ, ꯇꯦꯂꯔ ꯅꯠꯔꯒꯥ ꯕꯣꯂꯃꯦꯟ꯫ ꯁꯥꯏꯠ ꯑꯁꯤꯒꯤ ꯑꯥꯔꯇꯤꯀꯜ ꯈꯨꯗꯤꯡꯒꯤ ꯁꯣꯔꯁꯁꯤꯡꯒꯤ ꯕꯀꯁꯅ ꯂꯥꯏꯔꯤꯛ ꯊꯝꯃꯣꯛ ꯑꯁꯤꯗꯒꯤ ꯂꯧꯏ꯫

ꯋꯥꯍꯪꯁꯤꯡ

ꯐꯕ ꯔꯨꯂꯦꯠ ꯊꯧꯔꯥꯡ ꯂꯥꯏꯔꯤꯀꯁꯤꯡ ꯂꯩꯕꯔꯥ?

ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯃꯥ ꯌꯣꯟꯕ ꯑꯃꯠꯇ ꯐꯕ ꯂꯩꯇꯦ꯫ ꯊꯣꯔꯄꯀꯤ 1984 ꯒꯤ ꯂꯥꯏꯔꯤꯛꯇ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯤ ꯃꯥꯏꯊꯤꯕꯒꯦ ꯍꯥꯌꯕꯒꯤ ꯊꯨꯕ ꯆꯦꯞꯇꯔ ꯑꯃꯥ ꯂꯩ; ꯑꯦꯄꯁ꯭ꯇꯥꯏꯟ ꯑꯃꯁꯨꯡ ꯏꯊꯤꯌꯔꯅ ꯃꯈꯣꯌ ꯈꯨꯗꯤꯡꯒꯤ ꯃꯑꯣꯡ ꯌꯥꯎꯍꯜꯂꯤ꯫

ꯄꯤꯌꯔꯁꯟ ꯅꯠꯔꯒꯥ ꯍꯣꯏꯒꯦꯟꯁ ꯀꯗꯥꯏꯗ ꯄꯥꯕ ꯌꯥꯒꯅꯤ?

ꯑꯅꯤꯃꯛ ꯀꯣꯄꯤꯔꯥꯏꯠꯇꯒꯤ ꯊꯥꯗꯣꯀꯈ꯭ꯔꯦ ꯑꯃꯁꯨꯡ ꯑꯣꯅꯂꯥꯏꯟꯗ ꯂꯩ꯫ ꯄꯤꯌꯔꯁꯟ ꯑꯀꯅꯕꯅ ꯊꯨꯡꯏ; ꯍꯣꯏꯒꯦꯟꯁ ꯊꯨꯏ ꯑꯃꯁꯨꯡ ꯍꯟꯗꯣꯛꯂꯕꯗ ꯉꯛꯅꯤꯡꯉꯥꯏ ꯑꯣꯏꯅ ꯄꯥꯕ ꯂꯥꯏ꯫

ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

ꯁꯥꯏꯠ ꯑꯁꯤꯗ ꯂꯩꯕ ꯄꯨꯝꯅꯃꯛ ꯂꯥꯏꯔꯤꯛ ꯊꯝꯃꯣꯛ ꯑꯁꯤꯒꯤ ꯐꯨꯠꯅꯣꯠꯅꯤ꯫

ꯁꯥꯏꯠ ꯑꯁꯤꯗ ꯂꯩꯕ ꯄꯨꯝꯅꯃꯛ ꯂꯥꯏꯔꯤꯛ ꯊꯝꯃꯣꯛ ꯑꯁꯤꯒꯤ ꯐꯨꯠꯅꯣꯠꯅꯤ꯫

ꯍꯧꯔꯛꯐꯃꯁꯤꯡ

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010꯫ ꯆꯦꯞꯇꯔ 13, ꯔꯨꯂꯦꯠ꯫
  2. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, ꯑꯦꯗꯤꯁꯟ 3, 1968꯫ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯂꯣꯏꯁꯤꯟꯕ, ꯆꯦꯞꯇꯔ XIV꯫
  3. Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.” Duke Mathematical Journal 5(2), 1939꯫
  4. Thorp, E. O. “Optimal gambling systems for favorable games.” Review of the International Statistical Institute 37(3), 1969꯫
  5. Thorp, E. O. The Mathematics of Gambling. Gambling Times / Lyle Stuart, 1984꯫
  6. Bass, T. A. The Eudaemonic Pie. Houghton Mifflin, 1985꯫
  7. Barnhart, R. T. Beating the Wheel. Lyle Stuart, 1992꯫
  8. Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette. CRC Press, 2021꯫ ꯆꯦꯞꯇꯔ 2, ꯔꯨꯂꯦꯠ꯫
  9. Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed. CRC Press, 2024꯫
  10. Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021꯫
  11. Hunacek, M. Quantitative Literacy Through Games and Gambling. Chapman & Hall/CRC, 2025꯫
  12. Marcus, R. American Roulette: How I Turned the Odds Upside Down. St. Martin’s Press, 2003꯫
  13. Goldman, N. Great Gambling Scams. John Blake, 2007꯫
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