ᐃᓚᒋᐊᖅᑕᐅᔪᑦ · ᐅᖃᓕᒫᒐᒃᓴᑦ · 8 ᒥᓂᑦ

ᕉᓚᑦ ᐅᖃᓕᒫᒐᐃᑦ: ᐅᖃᓕᒫᒐᒃᓴᑦ

ᕉᓚᑦ ᐅᖃᓕᒫᒐᐃᑦ ᑎᑎᕋᖅᓯᒪᔪᓪᓗ ᑕᒫᓂ ᑐᙵᕕᒋᔭᐅᔪᑦ, ᒪᕐᕉᒃ ᖁᓕᑦ ᒪᕐᕉᒡᓗ, 1657-ᒥ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓᓂᒃ ᑎᑎᕋᖅᓯᒪᔪᒥᑦ 2025-ᒥ ᐃᓕᓐᓂᐊᕈᑎᒧᑦ, ᐊᑕᐅᓯᐊᓗᐊᑦ ᓱᖕᒪᑦ ᐱᒻᒪᕆᐅᓂᖏᓐᓂᒃ ᐅᖃᐅᓯᕐᒥᒃ ᐊᑕᐅᓯᕐᒥᒃ.

ᓇᐃᑦᑐᖅ ᑭᐅᔾᔪᑎ

ᓈᓴᐃᓂᖅ (ᕼᐊᐃᒍᓐᔅ (Huygens), ᐳᐊᓄᓕ (Bernoulli), ᕼᐊᓪᒧᔅ (Halmos), ᕙᓚ (Feller), ᑐᐊᑉ (Thorp), ᐃᑉᔅᑕᐃᓐ (Epstein), ᐃᑎᐊ (Ethier), ᐅᓪᓗᒥᓗ ᐃᓕᓐᓂᐊᕈᑏᑦ ᐳᓪᒪᓐ (Bollman), ᑕᐃᓚ (Taylor) ᕼᐅᓈᓯᒃ (Hunacek)-ᓗ), ᐱᐅᓯᑐᖃᖅ (ᓚᐳᓚ (Lablée), ᐹᓐᕼᐋᑦ (Barnhart), ᓲᑦᔅ (Schwartz), ᑲᕙᓇ (Kavanagh), ᒫᑲᔅ (Marcus), ᒎᓪᒪᓐ (Goldman)), ᐊᐅᓚᓂᖅ (ᐸᔅ (Bass), ᓯᒪᓪ & ᓯ (Small & Tse)) ᐊᑕᐅᓯᕐᓗ ᐅᓂᒃᑳᖅ ᑕᒪᐃᓐᓂᑦ ᐱᐅᓂᖅᓴᖅ (ᑕᔅᑐᐃᐅᕝᔅᑭ (Dostoevsky)). ᑕᒪᒃᑯᐊ ᑕᒫᓂ ᑐᙵᕕᖃᖅᑐᑦ ᑕᒪᒃᑯᓂᖓ ᐅᖃᓕᒫᒐᓂᒃ.

ᐃᑐᓪᓕᖅᐹᖅ
Huygens, 1657
ᓄᑖᓛᖅ
Hunacek, 2025
ᐱᐅᓛᖅ ᐅᖃᓕᒫᒐᖅ
Ethier, 2010
ᐱᐅᓛᖅ ᐅᓂᒃᑳᖅ
ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᖅᑎ (The Gambler), 1866

ᓈᓴᐃᓂᖅ

ᑎᑎᕋᖅᓯᒪᔪᖅᐊᕐᕌᒍᓱᖕᒪᑦ ᐅᖃᓕᒫᕐᓗᒍ
Huygens, De Ratiociniis in Ludo Aleae1657ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓ ᓯᕗᓪᓕᖅᐹᒥ ᓴᖅᑭᑕᐅᓯᒪᔪᖅ; EV ᓇᑭᙶᕐᒪᖔᑦ
Bernoulli, Ars Conjectandi1713ᐊᒥᓱᑦ ᓈᓴᐅᑏᑦ ᒪᓕᒐᖓ, ᐸᕐᓇᐅᑏᑦ ᑐᑭᓯᓗᐊᖅᑕᖓ
Halmos, “Invariants of certain stochastic transformations”1939ᓯᕗᓪᓕᖅᐹᖅ ᓇᓗᓇᐃᖅᓯᓂᖅ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᕐᒧᑦ ᐸᕐᓇᐅᑎ ᓇᓕᐊᑐᐃᓐᓇᖅ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᔪᒐᐅᑎ ᐊᓯᑦᑐᖅᑎᑦᑐᓐᓇᙱᓐᓂᖓᓂᒃ
Feller, An Introduction to Probability Theory, vol. 11968ᐱᙳᐊᖅᑎᐅᑉ ᐃᓘᓐᓇᖏᓐᓂᒃ ᐊᓯᐅᔾᔨᓂᖓ, ᓇᓚᐅᑦᑕᐃᓐᓇᖅ ᐃᖏᕐᕋᓂᖅ, ᑐᓪᓕᖅᑐᑦ; ᑐᙵᕕᐅᒐᔪᒃᑐᖅ
Thorp, “Optimal gambling systems for favorable games”1969ᐱᙳᐊᕈᑎᓕᐅᕐᓂᕐᒧᑦ ᐸᕐᓇᐅᑏᑦ ᖃᖓ ᐃᑲᔪᖅᑐᐃᔪᓐᓇᕐᒪᖔᑕ (ᐱᙳᐊᖅᑎ ᐱᐅᓂᖅᓴᐅᓂᖃᖅᑎᓪᓗᒍ ᑭᓯᐊᓂ) ᐸᕐᓇᐅᑎ ᐱᓕᕆᐊᖑᙱᓐᓂᖓᑕᓗ ᑐᙵᕕᖏᑦ
Thorp, The Mathematics of Gambling1984ᕉᓚᑦ ᖃᕆᑕᐅᔭᖓ ᓴᓇᔨᐅᑉ ᐅᓂᒃᑳᖅᑕᖓ, ᐱᐅᓂᖅᓴᐅᓂᖃᖅᑎᓪᓗᒍ ᖃᓄᐃᓪᓗᐊᖅ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᐊᕐᒪᖔᑦ ᓈᓴᐃᓂᖓᓗ
Epstein, The Theory of Gambling and Statistical Logic2013 (2-ᖓ ᓴᖅᑭᑕᐅᓂᖓ)ᑳᓯᓅᑉ ᐱᙳᐊᕐᓂᖏᑦ ᑕᒪᐃᓐᓂ ᖃᐅᔨᓴᖅᑕᐅᓯᒪᔪᑦ; ᕉᓚᑦ ᐊᓯᖏᓐᓂ ᐊᑐᕐᓂᖓ
Ethier, The Doctrine of Chances2010ᕉᓚᑦᒧᑦ ᓈᓴᐃᓂᒃᑯᑦ ᑎᑎᕋᖅᓯᒪᔪᑦ ᐃᓘᓐᓇᖅᐸᓪᓚᐅᓛᖅ
Bollman, Mathematics of the Big Four Casino Table Games2021ᓴᓂᐊᓄᑦ ᐱᙳᐊᕈᑏᑦ, ᐊᔾᔨᒋᙱᑦᑐᑦ ᐊᒃᓴᓗᐊᐃᑦ ᑳᑦᑎᑦᑐᑦ ᕉᓚᓪᓗ ᐊᑕᐅᓯᐊᓗᐊᑦ ᐊᑭᖏᑦ ᓈᓴᖅᑕᐅᓯᒪᔪᑦ, ᐃᓕᓐᓂᐊᕈᑏᓪᓗ
Taylor, Games, Gambling, and Probability2021 (2-ᖓ ᓴᖅᑭᑕᐅᓂᖓ)ᑐᓪᓕᖅᑐᑦ, ᑲᐃᓕ (Kelly) ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ ᐱᙳᐊᖅᑎᐅᑉ ᐃᓘᓐᓇᖏᓐᓂᒃ ᐊᓯᐅᔾᔨᓂᖓᓗ ᐃᓕᓐᓂᐊᕈᑎᑐᑦ
Bollman, Basic Gambling Mathematics2024 (2-ᖓ ᓴᖅᑭᑕᐅᓂᖓ)ᑳᓯᓅᑉ ᓂᐅᕕᖅᑎᑦᓯᓇᓱᒃᑐᖏᑦ ᐅᑎᖅᑎᑕᐅᔪᑦ ᑮᓇᐅᔭᓪᓗ, ᐊᔪᒐᐅᑎᑦ ᓇᓗᓇᐃᖅᑯᑎᖏᓪᓗ ᑳᓯᓄᒧᑦ ᖃᓄᖅ ᓱᒃᑲᐃᑦᑐᒥᒃ ᐊᑭᖏᓐᓂᒃ ᐅᑎᖅᑎᑦᓯᕙᒻᒪᖔᑕ
Hunacek, Quantitative Literacy Through Games and Gambling2025ᐊᔪᕐᓇᙱᑦᑐᖅ ᓯᕗᓪᓕᖅᐹᖅ ᐃᓕᓐᓂᐊᕈᑎ; ᐅᖃᐅᓯᖓ ᖃᐅᔨᓴᕐᓗᒍ ᐱᙳᐊᕈᑏᑦ ᑕᒪᐃᓐᓂ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓ ᐊᔾᔨᒌᒃᑐᖅ, ᑕᓪᓕᒪᓄᑦ ᐱᙳᐊᕈᑎ ᓱᓕᙱᓐᓂᖓᓂᒃ ᑕᑯᑎᑦᑎᔪᖅ

ᐱᐅᓯᑐᖃᖅ

ᑎᑎᕋᖅᓯᒪᔪᖅᐊᕐᕌᒍᓱᖕᒪᑦ ᐅᖃᓕᒫᕐᓗᒍ
Lablée, La Roulette, ou le Jour1801ᐱᙳᐊᕐᓂᐅᑉ ᓯᕗᓪᓕᖅᐹᖅ ᓇᓗᓇᐃᖅᓯᓂᖓ ᐃᓘᓐᓇᖅ, ᐅᓂᒃᑳᒥ
Barnhart, Beating the Wheel1992ᓴᖑᓯᒪᔪᓂᒃ ᐊᒃᓴᓗᐊᓂᒃ ᐱᙳᐊᕐᓂᐅᑉ ᐱᐅᓯᑐᖃᖓ: ᔮᒡᒐ, ᐱᓚᔪᑦ (Pelayo) ᓯᕗᓕᖏᑦ, ᐱᓕᕆᓯᒪᓂᖏᑦ
Schwartz, Roll the Bones2006ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᕐᓂᐅᑉ ᐱᐅᓯᑐᖃᖓ; ᕉᓚᑦ ᑕᐃᑲᓂ ᐃᓂᖓ
Kavanagh, Dice, Cards, Wheels2005ᕖᓇᓯ ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᕐᓂᐅᑉ ᐃᓕᖁᓯᖓ; ᐹᓚᐃ-ᕉᔭᓪ (Palais-Royal) ᐅᓇᕐᓯᓂᖅᑐᖅ ᐃᒪᐅᑉ ᓄᓇᓖᓪᓗ
Marcus, American Roulette2003ᐊᔪᒐᐅᑎ ᓴᖅᑭᑎᓪᓗᒍ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ ᐃᓗᐊᓂᑦ ᓇᓗᓇᐃᖅᓯᔭᐅᓯᒪᔪᖅ ᐃᓕᓴᕆᔭᐅᓂᖅᐹᒥᑦ ᑕᐃᒪᐃᓕᐅᖅᑎᒥᑦ
Goldman, Great Gambling Scams2007ᓕ (Leigh) ᓃᔅᒥ (Nice), ᒫᑲᔅ ᕆᑦᔅᒥᓗ (Ritz) ᐅᓂᒃᑳᖅᑕᐅᑲᓐᓂᖅᑐᑦ; ᐅᓂᒃᑳᑦᑎᐊᖅ, ᐊᒥᓱᓂᒡᓗ ᓱᓕᙱᑦᑐᓂᒃ ᐃᓗᓕᖃᖅᑐᖅ (ᑕᑯᓗᒍ ᕉᓚᑦᒥ ᑕᒡᓚᕐᓂᖅ)

ᐊᐅᓚᓂᖅ ᐱᐅᓂᖅᓴᐅᓂᕐᒥᒡᓗ ᕿᓂᕐᓂᖅ

ᑎᑎᕋᖅᓯᒪᔪᖅᐊᕐᕌᒍᓱᖕᒪᑦ ᐅᖃᓕᒫᕐᓗᒍ
Bass, The Eudaemonic Pie1985ᐱᓪᓗᒃᑯᑦ ᖃᕆᑕᐅᔭᐅᑉ ᐅᓂᒃᑳᖓ; ᕉᓚᑦ ᐊᐅᓚᓂᖓᓄᑦ ᐱᐅᓛᖅ ᐃᓄᓐᓄᑦ ᐅᖃᓕᒫᒐᖅ
Small & Tse, “Predicting the outcome of roulette”2012ᓯᕗᓂᒃᓴᒥ ᖃᐅᔨᓂᐅᑉ ᐊᐅᓚᓂᖓ, ᐊᒃᓱᕈᕐᓇᖅᑐᒥᒃ ᓈᓴᐅᑕᐅᓯᒪᔪᖅ; ᐱᐅᓂᖅᓴᐅᓂᖅ ᓱᓇᒥᒃ ᐱᒋᐊᖃᕐᒪᖔᑦ
Pearson, “On the criterion…”1900ᑲᐃ-ᔅᑯᐃᐅ ᖃᐅᔨᓴᕈᑎ, ᕉᓚᑦ ᑲᐃᕙᕐᓃᓐᓂ ᑕᑯᑎᑦᑕᐅᓯᒪᔪᖅ

ᕉᓚᑦ ᐊᒃᓴᓗᐊᖓᑕ ᐊᐅᓚᓂᖓ

ᐅᓂᒃᑳᖅ

ᑕᔅᑐᐃᐅᕝᔅᑭ (Dostoevsky), ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᖅᑎ (The Gambler, 1866). ᑎᑎᕋᖅᑕᐅᓯᒪᔪᖅ 26 ᐅᓪᓗᓂ ᓴᖅᑭᑎᑦᑎᔨᐅᑉ ᐊᖏᖃᑎᒌᒍᑎᖓᑕ ᑭᒡᓕᖓ ᑎᑭᑦᑎᓇᓱᒡᓗᒍ, ᑎᑎᕋᖅᑎᒥᑦ ᕉᓚᑦᒥ ᐊᑭᓕᒃᓴᖃᓪᓚᕆᒃᑐᒥᑦ; ᐱᙳᐊᖅᑎᐅᑉ ᐃᓱᒪᒋᓗᐊᖅᑕᖓ, ᐸᕐᓇᐅᑎ, ᓄᖅᑲᖅᑐᓐᓇᙱᓐᓂᖅ ᐅᓇᕐᓯᓂᖅᑐᖅ ᐃᒪᐅᑉ ᓄᓇᓕᖓᓂ ᑳᓯᓄᓗ ᐃᓗᐊᓂᑦ. ᓇᐃᓂᖅᓴᐅᔪᖅ ᕉᓚᑦ ᐅᖃᓕᒫᒐᐃᑦ ᖁᓛᓃᑦᑐᑦ ᑕᒪᐃᓐᓂᑦ, ᓱᓕᓂᖅᓴᐅᓪᓗᓂᓗ ᐊᒥᓲᓂᖏᓐᓂᑦ.

ᐹᑦ ᕼᐊᒻᐳᕐᒡ ᐃᒥᖅᑕᕐᕕᓪᓗ ᑳᓯᓅᑦᑕᔅᑐᔪᐃᕝᔅᑭᐅᑉ ᕉᓚᑦᑕᓐᐳᕐᒡ

ᕉᓚᑦ ᐅᖃᓕᒫᒐᐃᑦ ᐱᐅᓛᑦ ᑐᕌᒐᖅ ᒪᓕᒡᓗᒍ

ᓈᓴᐃᓂᕐᒧᑦ, ᐃᑎᐊ (Ethier) ᑕᐃᒪ ᕙᓚ (Feller). ᐅᓂᒃᑳᓄᑦ, ᐹᓐᕼᐋᑦ (Barnhart) ᐸᔅ (Bass)-ᓗ. ᓱᖕᒪᑦ ᐃᓄᐃᑦ ᐱᙳᐊᖅᑐᐃᓐᓇᕐᒪᖔᑕ, ᑕᔅᑐᐃᐅᕝᔅᑭ. ᓇᓗᓇᐃᖅᓯᓂᕐᒧᑦ ᐸᕐᓇᐅᑏᑦ ᐱᔾᔪᑎᒋᓪᓗᒋᑦ ᐊᐱᕆᓂᖅ ᑕᒪᐃᓐᓂ ᐃᓱᓕᑦᑎᔪᒧᑦ, ᕼᐊᓪᒧᔅ (Halmos), ᐊᔾᔨᒋᔭᖓᓄᓪᓗ ᐊᔪᕐᓇᙱᑦᑐᓂᒃ ᐅᖃᐅᓰᑦ, ᑐᐊᑉ (Thorp) 1984-ᒥ ᐅᖃᓕᒫᒐᖓ. ᐃᓕᓐᓂᐊᕈᑏᓄᑦ, ᑕᐃᓚ (Taylor) ᐅᕝᕙᓘᓐᓃᑦ ᐳᓪᒪᓐ (Bollman). ᐱᕝᕕᒋᔭᐅᔪᑦ ᑎᑎᕋᖅᓯᒪᔪᓂ ᑕᒪᐃᓐᓂ ᑕᒫᓂ ᑕᒪᒃᑯᓂᖓ ᐅᖃᓕᒫᒐᓂᑦ ᐱᔭᐅᔪᑦ.

ᐊᐱᖅᑯᑏᑦ

ᕉᓚᑦ ᐸᕐᓇᐅᑎᖏᓐᓄᑦ ᐱᐅᔪᓂᒃ ᐅᖃᓕᒫᒐᖃᖅᐸ?

ᐸᕐᓇᐅᑎᒥᒃ ᓂᐅᕕᖅᑎᑦᓯᔪᓂᒃ ᐱᑕᖃᙱᑦᑐᖅ. ᑐᐊᑉ 1984-ᒥ ᐅᖃᓕᒫᒐᖓ ᓇᐃᑦᑐᒥᒃ ᐃᓚᖃᖅᑐᖅ ᓱᖕᒪᑦ ᐱᓕᕆᐊᖑᙱᒻᒪᖔᑕ; ᐃᑉᔅᑕᐃᓐ ᐃᑎᐊᓗ ᐊᑕᐅᓯᐊᓗᐊᑕ ᐊᐅᓚᓂᖏᓐᓂᒃ ᓇᓗᓇᐃᖅᓯᔪᒃ.

ᐱᐊᓴᓐ (Pearson) ᕼᐊᐃᒍᓐᔅ (Huygens)-ᓗ ᓇᐅᑦᑕ ᐅᖃᓕᒫᕐᓂᐊᖅᐱᒃᑭᒃ?

ᒪᕐᕉᒃ ᓴᓇᔨᖏᑕ ᐱᖃᑦᑕᕐᓂᖏᑦ ᓄᖅᑲᖅᓯᒪᔪᑦ ᖃᕆᑕᐅᔭᒃᑯᓪᓗ ᐱᔭᐅᔪᓐᓇᖅᑐᒃ. ᐱᐊᓴᓐ ᐊᔪᕐᓇᖅᑐᖅ; ᕼᐊᐃᒍᓐᔅ ᓇᐃᑦᑐᖅ ᐅᖃᓕᒫᕆᐊᒃᓴᐅᓪᓗᓂᓗ ᐅᖃᐅᓯᐅᑉ ᐊᓯᐊᓄᑦ ᓄᐊᑦᓯᒪᔪᖅ.

ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ

ᑕᒪᒃᑯᐊ ᑕᒫᓂ ᑕᒪᒃᑯᓂᖓ ᐅᖃᓕᒫᒐᓂᒃ ᑐᙵᕕᖃᖅᑐᑦ.

ᑕᒪᒃᑯᐊ ᑕᒫᓂ ᑕᒪᒃᑯᓂᖓ ᐅᖃᓕᒫᒐᓂᒃ ᑐᙵᕕᖃᖅᑐᑦ.

ᐱᕝᕕᒋᔭᐅᔪᑦ

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. ᐃᓚᖓ 13, ᕉᓚᑦ.
  2. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3rd ed., 1968. ᐱᙳᐊᖅᑎᐅᑉ ᐃᓘᓐᓇᖏᓐᓂᒃ ᐊᓯᐅᔾᔨᓂᖓ, ᐃᓚᖓ 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. ᐃᓚᖓ 2, ᕉᓚᑦ.
  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.
ᐅᕙᑦᑎᓐᓂᒃᐱᕝᕕᒋᔭᐅᔪᑦᐱᐅᓯᑐᖃᖅ ᐃᓕᖁᓯᕐᓗᕉᓚᑦ ᐅᓂᒃᑳᓂᐱᐅᓯᑐᖃᖅ ᐃᓕᖁᓯᕐᓗᕉᓚᑦᒥ ᐸᕐᓇᐅᑏᑦ ᐱᐅᓯᑐᖃᖏᑦᐱᐅᓯᑐᖃᖅ ᐃᓕᖁᓯᕐᓗᔫᑎᒪᓐᔅ
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