ᕉᓚᑦᒥ ᐸᕐᓇᐅᑏᑦ ᐱᐅᓯᑐᖃᖏᑦ
ᐊᕐᕌᒍᐃᑦ ᒪᕐᕉᒃ ᕼᐊᓐᑐᕆᑦ ᐃᓄᐃᑦ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᑕ ᐊᓯᑦᑐᖅᑎᑕᐅᓂᖓᓄᑦ ᒪᓕᒐᓂᒃ ᑎᑎᕋᖅᐸᒃᑐᑦ.
ᒫᑎᓐᒐᐃᓪ 18-ᖓᓂ ᐊᕐᕌᒍᐃᑦ ᑕᑕᑎᒐᖏᓐᓂ ᐱᒋᐊᖅᑐᖅ; ᑕᓚᒻᐱᐅᕐ ᐊᑎᖃᖅᑐᖅ ᓈᓴᐃᓂᓕᕆᔨᒥᒃ ᓇᒡᓗᒋᙱᑦᑐᒥᒃ; ᓚᐳᓯᐊᕐ ᕖᑐᕆᐊ ᐱᓂᕐᓗᓕᖓᓂ ᒐᕙᒪᓕᕆᔨᐅᑉ ᐱᙳᐊᕐᓂᕆᐊᖓ. ᑕᐃᑦᓱᒪᓂ ᐊᑕᐅᓯᕐᒥᒃ ᐱᓕᕆᐊᖃᑦᑎᐊᓚᐅᙱᑦᑐᑦ.
ᒫᑎᓐᒐᐃᓪ
ᐊᑎᖓ ᐳᕌᕙᓐᓴᓪ ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᖅᑏᑦ ᐅᖃᐅᓯᖏᓐᓂᑦ ᐱᕝᕕᖃᖅᑐᖅ (à la martegalo, “ᒫᑎᒡ ᐃᓄᖏᑦ ᐱᐅᓯᖏᑎᑐᑦ”, ᐃᓱᒪᑦᓴᐃᓐᓇᕆᐊᖃᖅᑐᑦ ᑐᓴᐅᒪᔭᐅᔪᑦ) ᒪᕐᕉᕆᐊᖅᓗᒍ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᕐᒧᑦ, ᕖᓇᓯ ᐅᖃᐅᓰᑦ ᓇᓗᓇᐃᖅᓯᒪᔪᓂ 1760-ᖏᓐᓂᑦ ᑎᑎᕋᖅᓯᒪᔪᖅ. ᑖᑉ (Thorp, 1984), American Heritage Dictionary ᒪᓕᒡᓗᒍ, ᐊᐃᑉᐱᐊᓂᒃ ᐅᓂᒃᑲᐅᓯᑐᖃᒥᒃ ᐅᖃᐅᓯᖃᖅᑐᖅ: ᒫᑎᒡ ᐃᓄᖏᑦ ᐱᐅᓯᖏᑦ ᐊᔾᔨᒋᙱᑦᑐᑦ ᐃᑦᑕᕐᓂᓴᖅᑕᐅᔪᑦ, ᐃᓚᖓᓂ ᖃᕐᓕᒥᓂᒃ ᑐᓄᐊᒍᑦ ᖃᖏᓴᐅᔾᔨᓂᖏᑦ, ᑕᐃᒪᓐᓇᓗ ᐅᖃᐅᓯᖅ “ᐃᑦᑕᕐᓇᖅᑐᒃᑯᑦ” ᑐᑭᖃᓕᖅᑐᖅ. 18-ᖓᓂ ᐊᕐᕌᒍᐃᑦ ᑕᑕᑎᒐᖏᓐᓂ ᐸᐃᕆᔅᒥ ᖃᐅᔨᒪᔭᐅᓕᖅᓯᒪᔪᖅ ᐊᑦᑕᓇᖅᑐᒥᒃ ᐅᓂᒃᑳᑐᑦ: ᑳᓴᓄᕙ (Casanova) ᐅᓂᒃᑳᖅᑐᖅ 1750-ᖏᓐᓂ ᕙᓂᔅᒥ ᕙᐊᕈᒥ ᒪᕐᕉᕆᐊᖅᓗᒍ ᐱᙳᐊᕈᑎᓕᐅᖅᑐᓂ ᐊᒥᓱᓂᒃ ᑮᓇᐅᔭᓂᒃ ᐊᓯᐅᔾᔨᓯᒪᓂᖓᓂᒃ. ᓱᒻᒪᑦ ᐊᔪᕐᓂᖓᓂᒃ ᓈᓴᐃᓂᖅ, ᐱᙳᐊᕐᕕᐅᑉ ᑭᒡᓕᖓᐱᙳᐊᕐᕕᒃᐱᙳᐊᕐᕕᐅᑉ ᑭᒡᓕᖓᐱᙳᐊᕈᑎ ᒥᑭᓛᖅ ᐊᖏᓛᕐᓗ ᐊᖏᖅᑕᐅᔪᑦ. ᐊᖏᓛᖅ ᒪᕐᕉᕆᐊᖅᑎᑦᓯᔪᑦ ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᐅᔪᑦ ᓄᖅᑲᖅᑎᑦᑕᖏᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᑭᒡᓕᖃᖅᑐᓪᓗ ᐱᙳᐊᕈᑎᒃᓴᐃᑦᑮᓇᐅᔭᖅᐱᙳᐊᕈᑎᒃᓴᐃᑦᑮᓇᐅᔭᑦ ᐃᓘᓐᓇᖏᑦ ᐱᙳᐊᕐᓂᕐᒧᑦ ᐊᕕᒃᓯᒪᔭᐅᔪᑦ. ᐱᙳᐊᕈᑎᒃᓴᓂᒃ ᐊᐅᓚᑦᓯᓂᖅ ᑐᑭᖃᖅᑐᖅ ᖃᔅᓯᑦ ᐱᙳᐊᕈᑎ ᐊᑐᓂ ᐱᙳᐊᖅᑕᐅᓂᖓᓂᓗ ᐊᑐᓂ ᐊᓯᐅᔪᓐᓇᖅᑕᐅᓂᐊᕐᒪᖔᑕ ᐃᓱᒪᓕᐅᕐᓂᕐᒥᒃ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →, 1770-ᖏᓐᓄᑦ ᑐᑭᓯᐅᒪᔭᐅᓕᖅᓯᒪᔪᖅ. ᐱᔪᓐᓇᕐᓂᐅᑉᓈᓴᐃᓂᖅᐱᔪᓐᓇᕐᓂᖅᐱᓐᓂᐅᑉ ᐱᔪᓐᓇᕐᓂᖓ, 0-ᒥᑦ 1-ᒧᑦ ᐅᕝᕙᓘᓐᓃᑦ 0%-ᒥᑦ 100%-ᒧᑦ. ᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ: 1/37 = 2.70%.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐃᓱᒪᓕᐅᕈᓯᖓᓂ “ᒫᑎᓐᒐᐃᓪᐸᕐᓇᐅᑎᒫᑎᓐᒐᐃᓪᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᖅ ᐊᓯᐅᔾᔨᓂᖅ ᑕᒪᐃᓐᓂ ᐱᙳᐊᕈᑎ ᒪᕐᕉᕆᐊᖅᑐᖅ. ᐸᕐᓇᐅᑏᑦ ᐃᓚᖓᓂ ᑕᑯᓗᒍ ᖃᓄᐃᓕᐅᕐᓂᖓ ᖃᓄᐃᓕᐅᙱᓐᓂᖓᓗ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →” 1930-ᖏᓐᓂ ᐃᓕᓐᓂᐊᖅᑐᓄᑦ ᐅᖃᐅᓯᐅᓕᖅᑐᖅ ᓈᒻᒪᒃᑐᒧᑦ ᐱᙳᐊᕐᓂᕐᒧᑦᓈᓴᐃᓂᖅᓈᒻᒪᒃᑐᖅ ᐱᙳᐊᕐᓂᖅᐱᙳᐊᕐᓂᖅ ᓇᓕᐊᑐᐃᓐᓇᖅ ᐱᐅᓂᖅᓴᐅᓂᖃᙱᑦᑐᖅ: ᐱᙳᐊᕈᑎ ᑕᒪᐃᓐᓂ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓ ᓯᕉ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →, ᑕᐃᒪᐃᓐᓇᐅᙱᑦᑐᖅ ᐊᑕᐅᓯᐅᔪᖅ ᕉᓚᑦᒥ ᒫᑎᓐᒐᐃᓪ.
ᑕᓚᒻᐱᐅᕐ
ᔮᓐ ᓚ ᕌᓐ ᑕᓚᒻᐱᐅᕐ (Jean le Rond d’Alembert) Encyclopédie-ᒥ (1754) ᐅᖃᖅᑐᖅ ᑮᓇᐅᔭᐅᑉ ᓯᓚᑖᓂ ᑐᓪᓕᖅᑐᑦ ᑭᖑᓂᖓᓂ ᑐᓄᐊ ᐱᔪᓐᓇᓂᖅᓴᐅᓕᖅᑐᖅ, ᐱᙳᐊᖅᑎᐅᑉ ᐃᓱᒪᒋᓗᐊᖅᑕᖓᓂᒃ ᓯᕗᓪᓕᐅᔪᖅ ᐅᖃᐅᓯᖃᕐᓂᖅ ᓈᓴᐃᓂᓕᕆᔨᒥᑦ ᑐᓴᐅᒪᔭᐅᔪᒥᑦ. ᐱᙳᐊᕈᑎᓕᐅᕐᓂᕐᒧᑦ ᐸᕐᓇᐅᑎ, ᐊᓯᐅᔾᔨᓂᐅᑉ ᑭᖑᓂᖓᓂ ᐊᑕᐅᓯᕐᒥᒃ ᐊᑦᔨᐅᑎᒥᒃᑮᓇᐅᔭᖅᐊᑦᔨᐅᑎᐸᕐᓇᐅᑎᐅᑉ ᐅᕝᕙᓘᓐᓃᑦ ᐱᙳᐊᖅᑎᐅᑉ ᑐᙵᕕᒋᔭᖓ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ. ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᐅᔪᑦ ᐊᑦᔨᐅᑎᓄᑦ ᓇᓗᓇᐃᖅᑕᐅᕙᒃᑐᑦ, ᑕᐃᒪ ᓇᓕᐊᓂᑐᐃᓐᓇᖅ ᐱᙳᐊᕐᕕᒻᒥ ᐊᑐᕈᓐᓇᖁᓪᓗᒋᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐃᓚᒋᐊᖅᓯᓂᖅ ᐊᔪᒐᕐᓂᐅᑉ ᑭᖑᓂᖓᓂᓗ ᐊᑕᐅᓯᕐᒥᒃ ᐲᖅᓯᓂᖅ, ᐊᑎᖓᓂᒃ ᐊᑎᖅᑖᖅᑎᑕᐅᔪᖅ ᑭᖑᓂᐊᒍᑦ ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᖅᑎᓂᑦ ᐅᑦᑕᖃᑎᖃᖅᑐᓂᑦ. ᐅᐊᑦᑕ ᐊᑑᑎᔪᖃᖅᑐᓂ ᐅᖃᓚᐅᙱᑦᑐᖅ, ᐃᓱᒪᑦᑎᐊᖅᑎᓪᓗᓂᓗ ᐊᖏᓚᐅᙱᓐᓇᔭᖅᑐᖅ.
ᓚᐳᓯᐊᕐ
ᕼᐃᓐᕆ ᓚᐳᓯᐊᕐᐸᕐᓇᐅᑎᓚᐳᓯᐊᕐᐲᖅᓯᓂᕐᒧᑦ ᐸᕐᓇᐅᑎ: ᓈᓴᐅᑏᑦ ᑐᑭᓕᐊᖓᓂᒃ ᑎᑎᕋᕐᓗᑎᑦ, ᐃᓱᖏᒃ ᒪᕐᕉᒃ ᑲᑎᓪᓗᒋᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓗᑎᑦ, ᐊᔪᒐᖅᑲᓂ ᐲᖅᓯᓗᒋᒃ, ᐊᓯᐅᔾᔨᒐᓂ ᐊᓯᐅᔾᔨᓯᒪᔭᕐᓂᒃ ᐃᓚᒋᐊᕐᓗᒍ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → (Henry Labouchère, 1831–1912), ᑐᓴᒐᒃᓴᓕᕆᔨ, ᑕᑯᓐᓇᑦᓴᓕᕆᕝᕕᒻᒥᒃ ᓇᖏᖅᑐᖅ ᓕᐳᕈᓪ MP-ᓗ, 1870-ᖏᓐᓂ ᓚᓐᑕᓐᒥ ᐃᓄᓕᒫᓂ ᐲᖅᓯᓂᕐᒧᑦ ᐸᕐᓇᐅᑎᒥᒃ ᑐᓴᐅᒪᔭᐅᓕᖅᑎᑦᓯᔪᖅ, ᐅᖃᐅᓯᐅᔪᖅᓗ ᒪᓐᑎ ᑳᓗᒥ ᐊᑐᖅᓯᒪᓂᖓᓂᒃ. ᐸᕐᓇᐅᑎ, ᓈᓴᐅᑏᑦ ᑐᓪᓕᐊᓂᖏᓐᓂᒃ ᑎᑎᕋᕐᓂᖅ ᐃᓱᖏᓪᓗ ᑲᑎᑦᑐᒋᑦ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ, ᐅᐊᑦᑕ ᓯᕗᓂᐊᓂ ᐊᑐᖅᑕᐅᓯᒪᓕᖅᑐᖅ. ᐊᑎᖓ ᐊᑐᐃᓐᓇᐅᓕᖅᑐᖅ ᐊᓯᖏᓐᓂᒃ ᐱᔾᔪᑎᖃᖅᓗᓂ ᑐᓴᐅᒪᔭᐅᒻᒪᑦ, ᐸᕐᓇᐅᑎᓗ ᐱᓕᕆᑦᑎᐊᖅᐸᒃᑐᖅ ᐊᒥᖅᑯᓗᐃᓐᓇᖅ ᐊᔾᔨᖃᖅᑐᒥᒃ ᐱᐅᓯᖃᕐᒪᑦ, ᑕᐃᒪᓐᓇᓗ ᓂᕆᓂᐊᕐᓂᕐᒥ ᐅᖃᓪᓚᒃᑳᕆᔭᐅᕙᒃᑐᖅ.
ᑳᓴᓄᕙ ᕙᐊᕈᒥ ᒪᕐᕉᕆᐊᖅᓗᒍ ᐱᙳᐊᕈᑎᓕᐅᖅᑐᓂ ᐊᓯᐅᔾᔨᔪᖅ. ᒫᑎᓐᒐᐃᓪ ᐃᑦᑐᕆᓕᖅᓯᒪᔪᖅ.
ᑕᓚᒻᐱᐅᕐ ᐃᓱᒪᒋᓗᐊᖅᑕᒥᓂᒃ ᓴᖅᑭᑦᑎᔪᖅ, ᑭᖑᓂᐊᒍᑦ ᐸᕐᓇᐅᑎᒥᒃ ᐊᑎᖓᓄᑦ ᐊᑎᖅᑖᖅᑐᒥᒃ.
“ᒫᑎᓐᒐᐃᓪ” ᕖᓇᓯ ᐅᖃᐅᓰᑦ ᓇᓗᓇᐃᖅᓯᒪᔪᓄᑦ ᐃᓕᔭᐅᔪᖅ ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᖅᑏᑦ ᐅᖃᐅᓯᖓᑎᑐᑦ.
ᓚᐳᓯᐊᕐ ᓚᓐᑕᓐᒥ ᐲᖅᓯᓂᕐᒧᑦ ᐸᕐᓇᐅᑎᒥᒃ ᑐᓴᐅᒪᔭᐅᓕᖅᑎᑦᓯᔪᖅ.
ᕕᐳᓈᑦᓯ ᐸᕈᓕᓗ ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓃᑦ ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᕐᓂᕐᒧᑦ ᐃᓕᓐᓂᐊᕈᑎᓂ ᓴᖅᑭᖅᑐᑦ.
ᐊᒃᓴᓗᐊᑉ ᐋᖅᑭᒃᓯᒪᓂᖓᓂᒃ ᑐᙵᕕᓕᒃ “ᐊᒃᓴᓗᐊᑉ ᐃᓚᖓᓄᑦ” ᐸᕐᓇᐅᑏᑦ ᑎᑎᖅᑲᒃᑯᑦ ᓂᐅᕕᖅᑕᐅᔪᑦ.
ᕼᐊᓪᒨᔅ (Halmos), ᑐᐹᑉ (Doob) ᐃᓕᓐᓂᐊᖅᑎᖓ, ᓇᓗᓇᐃᖅᓯᔪᖅ ᐸᕐᓇᐅᑎ ᓇᓪᓕᐊᑐᐃᓐᓇᖅ ᐊᓯᐅᔾᔨᑎᑦᓯᔪᒥᒃ ᐱᙳᐊᕐᓂᕐᒥᒃ ᐱᐅᓯᑦᑎᐊᖅᑐᒧᑦ ᐊᓯᑦᑐᖅᓯᔪᓐᓇᙱᓐᓂᖓᓂᒃ.
ᖃᕆᑕᐅᔭᐃᑦ ᐸᕐᓇᐅᑏᑦ ᑕᒪᐃᓐᓂᒃ ᐊᔾᔨᐅᖅᓯᔪᑦ. ᑕᒪᕐᒥᒃ ᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᓐᓂᑦ −1/37 ᑕᑯᔅᓴᐅᑎᑦᓯᔪᑦ.
ᐸᕐᓇᐅᑏᑦ ᐊᔾᔨᖏᑦ ᐃᓂᑦᑎᐊᕐᓂᒃᑯᑦ ᓂᐅᕕᖅᑕᐅᔪᑦ ᐊᔾᔨᒋᔭᖏᓐᓂᒃ ᐊᔪᕐᓂᖃᖅᑐᑦ, ᑖᓐᓇ ᐃᑦᑕᕐᓂᓴᓕᕆᕝᕕᒻᒥ ᖃᕆᑕᐅᔭᒃᑯᑦ ᑕᑯᓐᓇᐅᑎᒥ ᐊᔾᔨᐅᖅᑕᐅᔪᑦ.
20-ᖓ ᑕᑕᑎᒐᖅ
ᕕᐳᓈᑦᓯᐸᕐᓇᐅᑎᕕᐳᓈᑦᓯᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᖅ ᓈᓴᐅᑏᑦ 1, 1, 2, 3, 5, 8, 13… ᑐᓪᓕᐊᓂᖏᓐᓂᒃ ᒪᓕᒃᑐᖅ: ᐊᓯᐅᔾᔨᓂᖅ ᑭᖑᓂᖓᓂ ᐊᑕᐅᓯᕐᒥᒃ ᓯᕗᒧᑦ, ᐊᔪᒐᕐᓂᖅ ᑭᖑᓂᖓᓂ ᒪᕐᕉᓂᒃ ᑐᓄᒧᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐸᕈᓕᐸᕐᓇᐅᑎᐸᕈᓕᐱᐅᔪᖅ ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᖅ: ᐊᔪᒐᕐᓂᖅ ᑭᖑᓂᖓᓂ ᒪᕐᕉᕆᐊᖅᓗᒍ, ᐊᓯᐅᔾᔨᓂᖅ ᑭᖑᓂᖓᓂ ᐅᕝᕙᓘᓐᓃᑦ ᐱᖓᓱᑦ ᐊᔪᒐᕐᓃᑦ ᑐᓪᓕᖅᑐᑦ ᑭᖑᓂᖏᓐᓂ ᐱᒋᐊᖅᑭᓪᓗᒍ. ᐊᓯᐊᓂ ᐊᑎᖓ: ᐅᑎᖅᑕᖅ ᒫᑎᓐᒐᐃᓪ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →-ᓗ ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᕐᓂᕐᒧᑦ ᐃᓕᓐᓂᐊᕈᑎᓄᑦ 1900 ᖃᓂᒋᔮᓂ ᐃᓕᔭᐅᔪᑦ. ᑕᑕᑎᒐᐅᑉ ᑕᑦᑎᓂᖓᓂ ᑎᑎᖅᑲᒃᑯᑦ ᓂᐅᕕᖅᑕᐅᔪᑦ ᐸᕐᓇᐅᑏᑦ ᓴᖅᑭᖅᑐᑦ, ᑕᒪᕐᒥᒃ ᓂᐅᕕᖅᑐᐃᓂᑦ ᓴᓚᒃᓴᐅᓂᕐᒥᒃ ᐅᖃᐅᓯᖃᖅᑐᑦ ᑮᓇᐅᔭᓂᒃ ᐅᑎᖅᑎᑦᓯᓂᐊᕐᓂᕐᒥᓪᓗ ᐊᖏᖅᑐᑦ, ᓯᕗᓪᓕᖅᐹᓪᓗ ᖃᕆᑕᐅᔭᒃᑯᑦ ᐊᔾᔨᐅᖅᑕᐅᓃᑦ, ᓈᓴᐃᓂᐅᑉ ᐅᖃᐅᓯᕆᓕᖅᓯᒪᔭᖓᓂᒃ ᑕᑯᔅᓴᐅᑎᑦᓯᔪᑦ. ᐸᕐᓇᐅᑎ ᓇᓪᓕᐊᑐᐃᓐᓇᖅ ᐱᓕᕆᑦᑎᐊᕈᓐᓇᙱᓐᓂᖓᓄᑦ ᓇᓗᓇᐃᖅᓯᒪᐅᑎ ᐊᑐᐃᓐᓇᐅᓕᖅᓯᒪᔪᖅ: ᔪᓯᕝ ᑐᐹᑉ (Joseph Doob, 1936) ᐹᓪ ᕼᐊᓪᒨᔅᓗ (Paul Halmos, 1939) ᓇᓗᓇᐃᖅᓯᔪᑦ ᒪᓕᒐᖅ ᓇᓪᓕᐊᑐᐃᓐᓇᖅ ᖃᖓ ᖃᓄᐃᓪᓗ ᐊᒥᓲᑎᒋᓗᒍ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᕐᒧᑦ ᓈᒻᒪᒃᑐᒥ ᐅᕝᕙᓘᓐᓃᑦ ᐊᓯᐅᔾᔨᑎᑦᓯᔪᒥ ᐱᙳᐊᕐᓂᕐᒥ ᓂᕆᐅᒋᔭᐅᔪᒥᒃ ᐊᓯᑦᑐᖅᓯᔪᓐᓇᙱᓐᓂᖓᓂᒃ, ᑖᑉ 1969-ᒥ ᖃᐅᔨᓴᕐᓂᖓᓂ ᑖᒃᑯᐊ ᐱᔾᔪᑎᑦ ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᖅᑏᑦ ᑕᑯᕙᒃᑕᖏᑎᑐᑦ ᓇᓗᓇᐃᖅᑕᐅᔪᑦ. ᑕᐃᑦᓱᒪᙵᑦ ᐸᕐᓇᐅᑏᑦ ᐊᓯᑦᑐᓚᐅᙱᑦᑐᑦ; ᓂᐅᕕᖅᑎᑦᓯᓇᓱᐊᕈᑏᑦ ᑕᑕᑦᑕᐅᔪᓂᑦ ᑕᑯᓐᓇᑦᓴᓄᑦ ᓅᑦᑐᑦ.
ᓱᒻᒪᑦ ᐊᑐᖅᑕᐅᑐᐃᓐᓇᖅᐸᑦ
ᐸᕐᓇᐅᑎ ᐱᙳᐊᖅᑎᒧᑦ ᐱᓕᕆᐊᒃᓴᒥᒃ ᐅᓂᒃᑳᒃᓴᒥᓪᓗ ᑐᓂᓯᔪᖅ. ᐱᙳᐊᖅᑕᐅᓂᖏᑦ ᐅᓄᖅᓯᓂᖏᑦ ᐸᕐᓇᐅᑏᓂ ᐅᓄᖅᓯᓂᖏᓐᓂ ᒥᑭᔪᒥᒃ ᐊᔪᒐᕐᓂᕐᒥᒃ ᐃᓱᓕᕙᒃᑐᑦ, ᑕᐃᒪᐃᑦᑐᖅ ᐅᓂᒃᑳᑦᑎᐊᕙᐅᓂᖅᓴᐅᔪᖅ ᓈᓴᐃᓂᕐᒥᑦ. ᐊᓯᐅᔾᔨᓂᕐᒥᒃ ᐃᓱᓕᔪᑦ ᐱᙳᐊᖅᑕᐅᓂᖏᑦ ᐊᒥᖅᑯᓂᖅᓴᐅᔪᑦ ᐃᖃᐅᒪᔭᐅᓪᓗᑎᒡᓗ ᐊᔪᕐᓂᐅᓪᓗᑎᒃ. ᓂᐅᕕᖅᑎᑦᓯᓇᓱᐊᕈᑏᑦ ᐱᔪᓐᓇᕐᓂᖏᓐᓂᒃ ᓴᒡᓗᔭᕆᐊᖃᙱᑦᑐᑦ; ᐊᔪᒐᕐᓂᕐᒥᒃ ᐃᓱᓕᔪᒥᒃ ᐱᙳᐊᖅᑕᐅᓂᖓᓂᒃ ᑕᑯᔅᓴᐅᑎᑦᓯᔭᕆᐊᖃᖅᑐᐃᓐᓇᖅᑐᑦ, ᐅᓄᖅᑐᑦᓗ. ᐊᖏᙱᓐᓂᕐᒧᑦ ᐃᓱᒪᓕᐅᕈᓯᖅ, ᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᓐᓂᑦᑮᓇᐅᔭᖅᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᑦᐱᙳᐊᖅᑕᐅᓂᖓᓂ ᐅᕝᕙᓘᓐᓃᑦ ᐱᕕᒃᓴᕐᒥ ᐱᙳᐊᕈᑎᒋᔭᐅᔪᑦ ᑲᑎᓪᓗᒋᑦ, ᐊᔪᒐᐅᑎᑦ ᐱᙳᐊᕈᑎᒋᖃᑦᑕᖅᑕᐅᔪᑦ ᐃᓚᓗᒋᑦ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᕼᐋᓐᑐᓪ, ᐋᒃᓴᓐ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → 2.70%, 1843-ᒥᑦ ᐊᑐᐃᓐᓇᐅᓯᒪᔪᖅ, ᑭᓯᐊᓂ ᖃᖓᓕᒫᖅ ᐅᓐᓄᐊᖅ ᐊᔪᒐᕐᓂᖃᑦᑎᐊᖅᑐᖅ ᑕᒪᑐᒥᖓ ᐅᑉᐱᕈᓱᒃᑕᐅᓂᖅᓴᐅᔪᖅ.
ᓂᐅᕕᖅᑕᐅᔪᑦ ᐸᕐᓇᐅᑏᑦ
20-ᖓᓂ ᐊᕐᕌᒍᐃᑦ ᑕᑕᑎᒐᖏᓐᓂ ᓂᐅᕕᕐᓂᖅ ᓇᒻᒥᓂᖅ ᐸᕐᓇᐅᑎᓂᒃ ᐃᓚᒋᐊᖅᓯᔪᖅ, ᑕᒪᕐᒥᒃ ᐊᓯᐅᔾᔨᑎᑦᓯᔪᓄᑦ ᐱᙳᐊᕈᑏᑦ ᐊᔾᔨᖏᑕ ᓄᑖᖅ ᐋᖅᑭᒃᓯᒪᓂᖏᑦ. Phase One ᓂᐅᕕᖅᑕᐅᔪᖅ $25-ᒧᑦ ᓂᐅᕕᖅᑎᐅᓪᓗ ᐊᔪᒐᕐᓂᖏᓐᓂᑦ 10%-ᒧᑦ, Phase Two-ᓗ ᐊᖏᖅᑕᐅᔪᖅ $500 ᐊᑭᓕᖅᑕᐅᑦᓯᐊᕐᒪᑦ, “Inner Circle”-ᓗ $5,000-ᒧᑦ. ᐊᑕᐅᓯᕐᒥᒃ ᓈᓴᐃᓂᕐᒥᒃ ᐊᓯᑦᑐᖅᓯᙱᑦᑐᑦ: ᐱᙳᐊᕈᑏᑦ ᑐᓪᓕᐊᓂᖏᑕ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓᓈᓴᐃᓂᖅᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓᐱᙳᐊᕈᑎ ᐊᑐᓂ ᐊᑯᓂᐅᓂᖅᓴᒥ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ ᐱᓐᓂᖓ. ᐃᐅᕌᐸ ᐱᙳᐊᕈᑎ ᑕᒪᐃᓐᓂ −1/37 ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᓂᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᑐᓂ ᓂᕆᐅᒋᔭᐅᔪᑦ ᐊᑭᖏᑦ ᑲᑎᑦᑐᒋᑦ.
ᐸᕐᓇᐅᑎᐅᙱᑦᑐᖅ ᐊᑕᐅᓯᖅ
ᓄᖅᑲᕐᓂᕐᒧᑦ ᒪᓕᒐᐃᑦ: ᓯᕗᓂᐊᓂ ᖃᓄᖅ ᐊᒥᓲᑎᒋᓗᒍ ᐊᓯᐅᔾᔨᓂᐊᕐᒪᖔᖕᓂ ᐊᔪᒐᕐᓂᐊᕐᒪᖔᖕᓂᓗ ᐃᓱᒪᓕᐅᕐᓂᖅ ᐊᓂᓪᓗᓂᓗ. ᐸᕐᓇᐅᑎᐅᑉ ᐃᓚᖓᑎᑐᑦ ᓂᐅᕕᖅᑕᐅᒐᔪᒃᑐᑦ, ᐊᑕᐅᓯᐅᔪᖅᓗ ᐃᓚᖓ ᓴᓇᔪᓐᓇᖅᑐᖅ, ᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᓐᓂᒃ ᒥᑭᓕᖅᑎᑦᓯᒻᒪᑕ. ᐃᓄᒻᒥᒃ ᐊᑎᖃᖅᑐᒥᒃ ᐊᑎᖃᙱᑦᑐᑦ, ᑕᐃᒪᐃᑦᑐᖅ ᓈᒻᒪᒃᑐᖅ.
ᐊᐱᖅᑯᑏᑦ
ᒫᑎᓐᒐᐃᓪ, ᐊᕐᕌᒍᐃᑦ ᕼᐊᓐᑐᕆᑦ ᐅᕝᕙᓘᓐᓃᑦ ᐅᓄᕐᓂᖅᓴᐃᑦ ᓯᕗᓪᓕᐅᓪᓗᓂ. ᐊᓯᐅᔾᔨᓂᐅᑉ ᑭᖑᓂᖓᓂ ᒪᕐᕉᕆᐊᖅᓗᒍ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ ᐃᓄᓕᒫᑦ ᓯᕗᓪᓕᖅᐹᒥᒃ ᐃᓱᒪᒋᔭᖓ.
ᑕᓚᒻᐱᐅᕐ ᖃᓂᒡᓕᓛᖑᔪᖅ, ᐱᕙᓪᓕᐊᔾᔪᑎᒋᙱᑕᖓ. ᐸᓯᑲᓪ, ᕙᕐᒫ, ᕼᐊᐃᒡᔅ, ᐸᕐᓄᓕ ᓚᐸᓚᔅᓗ (Laplace) ᑕᒪᕐᒥᒃ ᓇᓗᓇᐃᖅᓯᔪᑦ ᓱᒻᒪᑦ ᐊᔪᕐᒪᖔᑕ.
ᐱᙳᐊᖅᑕᐅᓂᖏᑦ ᐅᓄᖅᓯᓂᖏᑦ ᐊᔪᒐᕐᓂᕐᒥᒃ ᐃᓱᓕᒻᒪᑕ, ᐊᔪᒐᕐᓂᕐᒥᒃ ᐃᓱᓕᔪᒥᒃ ᐱᙳᐊᖅᑕᐅᓂᖓᓂᒃ ᑕᑯᓐᓇᑦᓴᓕᐅᕐᓂᖅ ᐊᑭᑭᑦᑐᖅ.
ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ
ᐊᕐᕌᒍᐃᑦ ᒪᕐᕉᒃ ᕼᐊᓐᑐᕆᑦ ᐊᑎᖏᑦ. ᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ.
ᐱᕝᕕᒋᔭᐅᔪᑦ
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- d’Alembert, J. “Croix ou pile.”
- Schwartz, D. G. Roll the Bones: The History of Gambling.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.