ᑭᓕ ᓈᓴᐅᑎᓕᐅᕈᑎ ᕉᓚᓪᓗ
ᑭᓕ ᓈᓴᐅᑎᓕᐅᕈᑎᖓᑕ ᐅᖃᐅᑎᔭᖓ ᐱᙳᐊᖅᑎ ᐱᐅᓂᖅᓴᐅᓂᖃᖅᑐᖅ ᖃᓄᐃᓪᓗ ᐊᒥᓱᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕆᐊᖃᕐᒪᖔᑦ. ᕉᓚᑦᒥ ᑭᐅᔾᔪᑎᖓ ᓇᓗᓇᙱᑦᑐᖅ: ᓱᓇᓕᒫᓐᓂᒃ.
ᑭᓕ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ = ᐱᐅᓂᖅᓴᐅᓂᖅ / ᐊᑭᓕᐅᑎ. ᐱᐅᓂᖅᓴᐅᓂᖅ ᓯᕉᐅᑉ ᐊᑖᓃᑉᐸᑦ, ᓈᓴᐅᑎᓕᐅᕈᑎ ᓯᕉᐅᑉ ᐊᑖᓃᑦᑐᒥᒃ ᐃᓚᒋᔭᐅᔪᒥᒃ ᑐᓂᓯᔪᖅ: ᐱᙳᐊᕈᑎᓕᐅᖁᔨᙱᑦᑐᖅ. ᑭᓯᐊᓂ ᓱᓕ ᐃᑲᔪᖅᑐᖅ ᑐᑭᓯᓇᓱᒃᑐᓄᑦ ᓱᒻᒪᑦ ᓴᖑᓯᒪᔪᓂᒃ ᐊᒃᓴᓗᐊᓂᒃ ᐱᙳᐊᖅᑏᑦ ᐱᙳᐊᕈᑏᑦ ᐊᖏᓂᖏᓐᓂᒃ ᐃᒪᓐᓇ ᓇᓚᐅᑦᑖᖅᓯᒪᒻᒪᑕ, ᓱᒻᒪᓗ ᐊᓯᖏᑦ ᐃᓘᓐᓇᑎᒃ ᑮᓇᐅᔭᒃᓴᐅᑉ ᐸᕐᓇᐅᑎᖓᑎᒍᑦ ᓇᓚᐅᑦᑖᕆᐊᖃᕐᒪᑕ.
ᓈᓴᐅᑎᓕᐅᕈᑎ
ᔮᓐ ᑭᓕ (John Kelly) (1956) ᐊᐱᖅᓱᖅᓯᒪᔪᖅ ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᖅᑎ ᐱᐅᓂᖅᓴᐅᓂᖃᖅᑐᖅ ᓇᓗᓇᙱᑦᑐᒥᒃ ᖃᓄᖅ ᐊᖏᑎᒋᔪᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕆᐊᖃᕐᒪᖔᑦ ᐱᙳᐊᕈᑎᒃᓴᖏᑦᑮᓇᐅᔭᖅᐱᙳᐊᕈᑎᒃᓴᐃᑦᑮᓇᐅᔭᑦ ᐃᓘᓐᓇᖏᑦ ᐱᙳᐊᕐᓂᕐᒧᑦ ᐊᕕᒃᓯᒪᔭᐅᔪᑦ. ᐱᙳᐊᕈᑎᒃᓴᓂᒃ ᐊᐅᓚᑦᓯᓂᖅ ᑐᑭᖃᖅᑐᖅ ᖃᔅᓯᑦ ᐱᙳᐊᕈᑎ ᐊᑐᓂ ᐱᙳᐊᖅᑕᐅᓂᖓᓂᓗ ᐊᑐᓂ ᐊᓯᐅᔪᓐᓇᖅᑕᐅᓂᐊᕐᒪᖔᑕ ᐃᓱᒪᓕᐅᕐᓂᕐᒥᒃ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᑯᓂᐅᓂᖅᓴᒥ ᐊᖏᒡᓕᒋᐊᑦᑎᐊᕐᓂᐊᖅᑎᓪᓗᒋᑦ. ᑭᐅᔾᔪᑎᖓ: ᐱᙳᐊᕈᑎ b:1 ᐊᑭᓕᐅᑎᓕᒃ, ᐊᔪᒐᕐᓂᕐᒧᑦ ᐱᔪᓐᓇᕐᓂᖓᓈᓴᐃᓂᖅᐱᔪᓐᓇᕐᓂᖅᐱᓐᓂᐅᑉ ᐱᔪᓐᓇᕐᓂᖓ, 0-ᒥᑦ 1-ᒧᑦ ᐅᕝᕙᓘᓐᓃᑦ 0%-ᒥᑦ 100%-ᒧᑦ. ᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ: 1/37 = 2.70%.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → p, ᐊᓯᐅᔾᔨᓂᕐᒧᓪᓗ ᐱᔪᓐᓇᕐᓂᖓ q = 1 − p, ᐱᙳᐊᕈᑎᒃᓴᓂᑦ ᐃᓚᒋᔭᐅᔪᖅ f* = (bp − q) / b ᐃᓕᔭᐅᒋᐊᖃᖅᑐᖅ. f* ᓯᕉᐅᑉ ᐅᖓᑖᓃᑉᐸᑦ, ᑕᒪᓐᓇ ᐃᓚᒋᔭᐅᔪᖅ ᐱᙳᐊᕈᑎᐅᓗᓂ; ᓯᕉᐅᑉᐸᑦ ᐅᕝᕙᓘᓐᓃᑦ ᐊᑖᓃᑉᐸᑦ, ᐱᙳᐊᕈᑎᓕᐅᕐᓇᓂ. ᑭᓕ ᐱᓕᕆᓚᐅᖅᓯᒪᔪᖅ Bell Labs-ᒥ, ᑎᑎᕋᖅᓯᒪᔭᖓᓗ, “A new interpretation of information rate”, ᐊᐱᖅᑯᑎ ᐃᓕᓚᐅᖅᑕᖓ ᐸᓐ ᓴᓐᓇᓐ (Claude Shannon) ᑐᓴᒐᒃᓴᓕᕆᓂᕐᒧᑦ ᐃᓱᒪᓕᐅᕐᓂᖓᓄᑦ: ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᖅᑎ ᐅᖃᐅᔾᔪᐃᓂᒃ ᓈᒻᒪᙱᑦᑐᑎᒍᑦ ᐅᖃᓘᑎᒃᑯᑦ ᑐᓴᖅᑐᖅ, ᓈᒻᒪᒃᑐᓂᒃ ᐊᑭᓕᐅᑎᓕᓐᓂ, ᐱᙳᐊᕈᑎᒃᓴᖏᑦ ᐊᖏᒡᓕᒋᐊᖅᑎᑦᓯᔪᓐᓇᖅᑐᖅ ᐅᖃᓘᑎᑉ ᑐᓴᒐᒃᓴᓂᒃ ᐊᐅᓚᑦᓯᓂᖓᑐᑦ ᐊᖏᓛᒥᒃ. 1961-ᒥ ᓕᐅ ᐳᕋᐃᒪᓐ (Leo Breiman) ᓱᓕᔪᒥᒃ ᑕᑯᑎᑦᓯᓚᐅᖅᑐᖅ ᑭᓕ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖓ, ᐊᑯᓂᐅᓂᖅᓴᒥ, ᐸᕐᓇᐅᑏᑦ ᐊᔾᔨᒋᙱᑦᑐᑦ ᐃᓘᓐᓇᑎᒃ ᐱᐅᓂᖅᓴᐅᓂᐊᕐᒪᑦ, ᑎᑭᐅᒪᔭᕆᔭᐅᔪᒥᒡᓗ ᓱᒃᑲᓛᒥᒃ ᑎᑭᑦᑎᓂᐊᕐᒪᑦ.
ᑭᓕ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖓ ᕉᓚᑦᒥ
ᐊᐅᐸᓗᒃᑐᒧᑦᐱᙳᐊᕈᑎᐊᐅᐸᓗᒃᑐᖅᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎ 18 ᐊᐅᐸᓗᒃᑐᓄᑦ ᓈᓴᐅᑎᓄᑦ. ᕖᓇᓯᑐᑦ: ᕈᔾ (rouge).ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →: b = 1, p = 18/37, q = 19/37; f* = (18/37 − 19/37)/1 = −1/37. ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᒧᑦᐱᙳᐊᕈᑎᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ, ᐊᑭᓕᐅᑎ 35:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →: b = 35, p = 1/37, q = 36/37; f* = (35/37 − 36/37)/35 = −1/1295. ᐱᙳᐊᕈᑏᑦ ᐃᓘᓐᓇᑎᒃ ᓯᕉᐅᑉ ᐊᑖᓃᑦᑐᒥᒃ ᑭᓕ ᐃᓚᒋᔭᐅᔪᒥᒃ ᑐᓂᓯᔪᑦ, ᐱᙳᐊᕈᑏᑦ ᐃᓘᓐᓇᑎᒃ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓ ᓯᕉᐅᑉ ᐊᑖᓃᒻᒪᑦ; ᐊᖏᒡᓕᒋᐊᑦᑎᐊᕐᓂᕐᒧᑦ ᐱᐅᓛᖅ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ ᓯᕉ. ᑭᓕ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖓ ᕉᓚᑦᒥ ᐅᖃᐅᓯᐅᔪᖅ ᑳᓯᓅᑉ ᐃᓚᖓᓄᑦ ᒪᑉᐱᒐᐅᑉ ᐅᖃᐅᓯᖓᓂᒃ: ᐱᙳᐊᕈᑎ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓ ᓯᕉᐅᑉ ᐊᑖᓃᑦᑐᖅ ᐱᙳᐊᕈᑎᒃᓴᓂᒃ ᐊᖏᒡᓕᒋᐊᖅᑎᑦᓯᔪᓐᓇᙱᑦᑐᖅ ᖃᓄᐃᑦᑐᒥᒃ ᐊᖏᑎᒋᑉᐸᑦ.
ᑭᓕ ᓇᐅᓂ ᐊᑐᓚᐅᖅᓯᒪᕙ
ᓴᖑᓯᒪᔪᓂᒃ ᐊᒃᓴᓗᐊᓂᒃ ᐱᙳᐊᖅᑏᑦ ᐱᐅᓂᖅᓴᐅᓂᖃᓚᐅᖅᑐᑦ, ᐊᐱᖅᑯᑎᖃᓚᐅᖅᑐᓪᓗ ᐱᙳᐊᕈᑏᑦ ᐊᖏᓂᖏᓐᓂᒃ. ᔮᒐ (Jagger), ᒑᓯᐊ-ᐱᓚᔪᐃᑦ (García-Pelayo) ᔪᑎᒧᓐᐃᓪᓗ (Eudaemons) ᐃᓘᓐᓇᑎᒃ ᓇᓚᐅᑦᑖᕆᐊᖃᓚᐅᖅᑐᑦ ᖃᓄᐃᓪᓗ ᐊᒥᓱᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕆᐊᖃᕐᒪᖔᑕ ᓇᓚᐅᑦᑖᖅᓯᒪᔭᖏᑦ ᐱᐅᓂᖅᓴᐅᓂᖏᓐᓄᑦ. ᒥᑭᓗᐊᖅᑐᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ ᐱᐅᓂᖅᓴᐅᓂᖅ ᐊᓯᐅᑎᑦᑎᔪᖅ, ᐊᖏᓗᐊᖅᑐᓂᒡᓗ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᔪᓐᓇᖅᑎᑦᑎᔪᖅ ᐱᐅᓂᖅᓴᐅᓂᖅ ᓴᖅᑭᑎᓐᓇᒍ. ᐃᓂᒧᑦᐊᑐᖅᑕᐅᔪᑦᐃᓂᑲᐃᕙᖅᑐᒥ 37 ᓈᓴᐅᑎᓕᑦ ᐃᓂᑦ ᐊᑕᐅᓯᖓ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐃᓂᒋᐊᖅ, ᖃᓪᓗᐊᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → 30-ᓂ 1-ᖑᓗᓂ ᓴᖅᑭᕙᒃᑐᒧᑦ, ᑭᓕ ᐅᖃᖅᑐᖅ ᑲᐃᕙᕐᓂᕐᒧᑦ ᐊᑐᓂ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ 0.57%-ᖓᓂᒃ ᑕᒪᑐᒧᖓ ᓈᓴᐅᑎᒧᑦ: $10,000-ᓂᒃ ᐱᑕᖃᖅᑎᓪᓗᑎᑦ, ᖃᓂᒋᔭᖓ $57 ᑲᐃᕙᕐᓂᕐᒧᑦ, ᐊᖏᒡᓕᒋᐊᕐᓂᖅ ᐊᑐᖅᑕᐅᒐᔪᒃᑐᖅ ᖃᓂᒋᔭᖓ 0.054% ᑲᐃᕙᕐᓂᕐᒧᑦ, ᐅᕝᕙᓘᓐᓃᑦ ×1.7 1,000 ᑲᐃᕙᕐᓂᓂ. ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ ᑮᓇᐅᔭᒃᓴᕐᓂᖅ ᒪᕐᕉᕆᐊᖅᓗᒍ, 0.11% ᑲᐃᕙᕐᓂᕐᒧᑦ, ᑭᓯᐊᓂ ᑭᓕ ᑕᒃᑯᒥᓇᖅᑐᖅ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐊᑐᖅᑕᐅᒐᔪᒃᑐᓄᑦ, ᐊᔾᔨᒌᒃᑎᑕᐅᔪᒧᑦ ᐊᓯᐊᒍᑦ; ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ ᐊᖏᓕᖅᑎᑕᐅᕙᒃᑐᖅ ᐊᒥᓲᙱᑦᑐᓂᒃ ᐱᔪᓐᓇᕐᓂᒃᑯᑦ ᐱᐅᔪᓂᒃ ᐱᙳᐊᖅᑕᐅᓂᖏᓐᓄᑦ. ᑭᓕ ᓇᑉᐸᖓ ᐊᑐᖅᑕᐅᒐᔪᒃᑐᖅ, ᐱᐅᓂᖅᓴᐅᓂᐅᑉ ᓇᓚᐅᑦᑖᖅᑕᐅᓂᖓ ᐊᑦᑕᓇᖅᑐᖃᕐᒪᑦ.
ᐊᑐᖅᑕᐅᒐᔪᒃᑐᖅ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᓗ
ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐊᑐᖅᑕᐅᒐᔪᒃᑐᑦ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᓪᓗ ᐊᑯᓐᓂᖏᑦ ᐊᖏᔪᖅ. ᐃᓂ 25-ᓂ 1-ᖑᓗᓂ ᓴᖅᑭᕙᒃᑐᖅ ᐃᓱᒪᒋᓗᒍ, ᐱᐅᓂᖅᓴᐅᓂᖅ 44%, ᑑᕐᐲ (Thorp) ᐅᖃᐅᓯᖓ ᓴᓇᔭᖓᓄᑦ. ᑭᓕ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ 1.26%-ᖓᓂᒃ ᑕᐃᑲᓂ ᐱᙳᐊᕈᑎᓕᐅᖅᑎᑦᓯᔪᖅ. 1,000 ᑲᐃᕙᕐᓃᑦ ᑭᖑᓪᓗᒋᑦ, ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐊᑐᖅᑕᐅᒐᔪᒃᑐᑦ ᖃᓂᒋᔭᖓ 11.5-ᕆᐊᖅᓗᒍ ᐊᖏᒡᓕᒋᐊᖅᓯᒪᔪᑦ, ᐊᔾᔨᒌᒃᑎᑕᐅᔪᓕ, ᐊᒥᓲᙱᑦᑐᓂᒃ ᐱᔪᓐᓇᕐᓂᒃᑯᑦ ᐱᐅᓪᓚᕆᒃᑐᓂᒃ ᐱᙳᐊᖅᑕᐅᓂᖏᓐᓄᑦ ᐊᖏᓕᖅᑎᑕᐅᓪᓗᓂ, ᖃᓂᒋᔭᖓ 249-ᕆᐊᖅᓗᒍ ᐊᖏᒡᓕᒋᐊᖅᓯᒪᔪᖅ. ᑭᓕ ᐅᖓᑖᓄᑦ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᒥᒃ ᐊᖏᓕᖅᑎᑦᓯᔪᖅ ᐊᑐᖅᑕᐅᒐᔪᒃᑐᒥᒡᓗ ᒥᑭᓕᖅᑎᑦᓯᓪᓗᓂ: ᑭᓕ ᐱᙳᐊᕈᑎᖓᓂᒃ ᒪᕐᕉᕆᐊᖅᓗᒍ ᐱᙳᐊᕈᑎᓕᐅᖅᐸᑦ, ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐊᑐᖅᑕᐅᒐᔪᒃᑐᑦ ᒪᕐᕉᕆᐊᖅᓗᒍ ᑐᐊᖅ ᐊᖏᒡᓕᒋᐊᖅᑐᑦ, ᒪᕐᕉᕆᐊᖅᓗᒍ ᓇᑉᐸᖓᓗ ᐱᙳᐊᕈᑎᓕᐅᖅᐸᑦ ᒥᑭᓕᖅᑐᑦ, ᐱᙳᐊᕈᑏᑦ ᐃᓘᓐᓇᑎᒃ ᓱᓕ 44% ᐱᐅᓂᖅᓴᐅᓂᖃᖅᑎᓪᓗᒋᑦ. ᒥᑭᓂᖅᓴᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ ᐊᑭᑭᑦᑐᖅ: ᓇᑉᐸᖓ ᐊᖏᒡᓕᒋᐊᕐᓂᐅᑉ ᓯᑕᒪᐅᓂᖏᓐᓂ ᐱᖓᓱᓂᒃ ᐃᓚᖏᓐᓂᒃ ᐱᑕᖃᖅᑎᑦᓯᔪᖅ.
ᐱᐅᓂᖅᓴᐅᓂᖅ ᓇᓚᐅᑦᑖᖅᑕᐅᑐᐃᓐᓇᕐᓂᕐᒥ
ᑭᓕ ᐃᓱᒪᔪᖅ ᐱᐅᓂᖅᓴᐅᓂᖅ ᓇᓗᓇᙱᓐᓂᐊᕐᒪᑦ. ᐱᙳᐊᕐᕕᒻᒥ ᓇᓚᐅᑦᑖᖅᑕᐅᔪᖅ ᑐᐊᖅ, ᓇᓚᐅᑦᑖᖅᑕᐅᓂᖓᓗ ᐊᑐᖅᑕᐅᒐᔪᒃᑐᖅ ᐊᖏᓗᐊᖅᑐᖅ. ᐃᑉᔅᑕᐃᓐ (Epstein) ᐆᑦᑐᕋᐅᑎᖓ, ᑑᕐᐲ 44%-ᖓᓄᑦ ᓴᓇᔭᐅᓯᒪᔪᖅ, ᓈᓴᐅᑎ 49-ᓂ ᓴᖅᑭᓯᒪᔪᖅ 1,225 ᑲᐃᕙᕐᓂᓂ ᒪᕐᕉᒃ ᓯᕉᐊᒃᓴᓗᐊᖅᓯᕉᐊᑕᐅᓯᖅ ᐅᔾᔪᐊᕌᔭᒃ ᐃᓂ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᖕᓄᑦ, ᑕᓴᓐᓄᑦ ᓇᑉᐸᖅᑐᓄᓪᓘᓐᓃᑦ ᐱᙳᐊᕈᑏᑦ ᐃᓚᐅᑎᙱᑕᖓ; ᑳᓯᓅᑉ ᐃᓚᖓᑕ ᐱᓇᓪᓗᑎᖓ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐊᑕᐅᓯᖅ ᓯᕉ, 0.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᒃᓴᓗᐊᖓᓂ: 25-ᓂ 1, ᐱᐅᓂᖅᓴᐅᓂᖅ 44%, ᑭᓕ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ 1.26%. ᑭᓯᐊᓂ ᓈᒻᒪᒃᑐᖅ ᒪᕐᕉᒃ ᓯᕉ ᐊᒃᓴᓗᐊᖅ 38-ᓂᒃ ᓈᓴᐅᑎᖃᖅᑐᖅ, ᓴᖅᑭᓛᖑᔪᓗ 1,225 ᑲᐃᕙᕐᓂᓂ 49-ᓂᒃ ᐅᕝᕙᓘᓐᓃᑦ ᐅᖓᑖᓄᑦ ᑎᑭᑦᑎᕙᒃᑐᖅ ᖃᓂᒋᔭᖓ ᐊᕐᕕᓂᓖᑦ ᐱᖓᓱᓂ ᐊᑕᐅᓯᐊᖅ. ᓴᖅᑭᓛᖑᔪᖅ ᓈᓴᐅᑎ ᑎᑎᕋᖅᓯᒪᔪᓂ ᐱᔪᓐᓇᕐᓂᒃᑯᑦ ᐃᑲᔪᖅᑕᐅᓛᖑᔪᖅ, ᑕᐃᒪ ᓴᖑᓯᒪᓪᓚᕆᒃᑐᖅ ᐃᓂ ᐊᓪᓛᑦ ᑎᑎᕋᖅᓯᒪᔪᓂ ᐱᐅᓂᖅᓴᐅᔮᖅᑐᖅ ᓱᓕᔪᒥᑦ: ᐊᔪᒐᖅᑐᐅᑉ ᐊᓯᐅᔾᔨᓂᖓ (winner’s curse). ᑕᒪᓐᓇ ᐃᓂ ᓱᓕᓪᓚᕆᒃᑐᒥᒃ ᓴᖑᓯᒪᙱᑉᐸᑦ, ᑭᓕ ᐱᙳᐊᕈᑎᖓ ᐱᙳᐊᕈᑎᑐᐃᓐᓇᐅᔪᖅ ᐊᔾᔨᒌᒃᑎᓪᓗᒋᑦ 5.26%-ᒥᒃ ᐊᓯᐅᔾᔨᔪᖅ. ᑭᐅᔾᔪᑏᑦ ᐊᑐᖅᑕᐅᒐᔪᒃᑐᑦ: ᑭᓕ ᐃᓚᒋᔭᖓᓂᒃ ᑐᐊᖅ ᐱᙳᐊᕈᑎᓕᐅᕐᓗᑎᑦ, ᓈᓴᐃᓗᑎᑦᓗ ᐱᐅᓂᖅᓴᐅᓂᖅ ᓄᑖᓂ ᑎᑎᕋᖅᓯᒪᔪᓂ ᓴᖅᑭᑎᓐᓇᒍ (ᑕᑯᓗᒍ ᕉᓚᑦ ᐊᒃᓴᓗᐊᖓᑕ ᓴᖑᓯᒪᓂᖓᓂᒃ ᖃᓄᖅ ᖃᐅᔨᔪᓐᓇᖅᐱᑦ).
ᐃᓄᐃᑦ ᐱᐅᓂᖅᓴᐅᓂᖃᖅᑐᑦ
ᐱᐅᓂᖅᓴᐅᓂᖅ ᖃᐅᔨᒪᓂᐊᖅ ᐊᑐᑦᑎᐊᕐᓂᕐᒥᑦ ᐊᔾᔨᒋᙱᑦᑐᖅ. ᕼᐊᒐᓂ ᑐᐃᓗ (Haghani and Dewey) (2016) 61-ᓄᑦ ᐃᓄᖕᓄᑦ $25-ᒥᒃ ᐊᑐᓂ ᑐᓂᓯᓚᐅᖅᑐᒃ, ᐃᑲᕐᕋᐅᑉ ᓇᑉᐸᖓᓂ ᐱᙳᐊᕈᑎᓕᐅᖁᓪᓗᒋᑦ ᑮᓇᐅᔭᕐᒥᒃ ᐅᖃᐅᑎᔭᐅᓯᒪᔪᒥᒃ ᑭᓈᖓ 60%-ᖓᓂ ᖁᓛᓄᑦ ᓴᖅᑭᕙᓐᓂᖓᓂᒃ, ᐊᔪᒐᕐᓂᖅ $250-ᒥᑦ ᐅᖓᑖᓄᑦ ᐊᔪᓐᓇᖅᑐᖅ (ᐱᙳᐊᖅᑏᑦ ᑭᒡᓕᖓ ᖃᐅᔨᓚᐅᖅᑐᑦ ᑎᑭᑦᑐᒋᑦ ᑐᐊᖅ). ᑭᓕ ᐅᖃᖅᑐᖅ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ 20%-ᖓᓂᒃ ᑭᓈᖓᓄᑦ ᐱᙳᐊᕈᑎᓕᐅᕐᓗᑎᑦ ᑕᒪᐃᓐᓂ, ᑎᑎᕋᖅᑎᒃᓗ ᓇᓚᐅᑦᑖᖅᑐᒃ 10–20% ᐊᓯᑦᑐᐃᓐᓇᙱᑦᑐᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ ᑭᒡᓕᖓᓄᑦ ᑎᑭᑦᑎᓂᐊᕐᒪᑦ ᖃᓂᒋᔭᖓ 95%-ᖓᓂ. ᐱᙳᐊᖅᑏᑦ 21%-ᖏᑦ ᑐᐊᖅ ᑎᑭᑦᑐᑦ. 28% ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᔾᔨᔪᑦ, 61-ᓂᑦ 18 ᐃᓘᓐᓇᑎᒃ ᐊᑕᐅᓯᕐᒥ ᒥᖕᒋᕆᐊᖅᑎᑦᓯᓂᕐᒥ ᐱᙳᐊᕈᑎᓕᐅᖅᑐᑦ, ᐱᖓᓱᓂ ᐊᑕᐅᓯᐊ ᖃᓂᒋᔭᖓ $25 ᐱᒋᐊᕐᕕᖏᑦ ᐊᑖᓃᑦᑐᑦ ᐱᔭᕇᖅᑐᑦ, ᐊᔾᔨᒌᒃᑎᑕᐅᔪᓗ ᐊᑭᓕᐅᑎᑮᓇᐅᔭᖅᐊᑭᓕᐅᑎᐊᔪᒐᖅᑐᖅ ᐱᙳᐊᕈᑎ ᖃᔅᓯᓂᒃ ᐅᑎᖅᑎᑦᓯᒻᒪᖔᑦ, “X 1-ᒧᑦ” ᐅᖃᐅᓯᐅᔪᖅ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ ᐅᑎᖅᑎᑕᐅᔪᖅ ᐃᓚᓇᒍ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → $91. 61-ᓂᑦ ᑕᓪᓕᒪᑦ ᑐᐊᖅ ᑭᓕ ᓈᓴᐅᑎᓕᐅᕈᑎᖓᓂᒃ ᑐᓴᖅᓯᒪᔪᑦ. ᐱᐅᓂᖅᓴᐅᓂᖃᖅᑎᓪᓗᑎᑦ, ᐱᙳᐊᕈᑏᑦ ᐊᖏᓂᖏᑦ ᓇᓚᐅᑦᑖᖅᑐᑦ ᐱᑕᖃᖅᑎᑦᓯᓂᐊᕐᒪᖔᖅᐱᐅᒃ; ᐱᐅᓂᖅᓴᐅᓂᖃᙱᑦᑎᓪᓗᑎᑦ, ᓈᒻᒪᒃᑐᒥᑐᑦ ᐊᒃᓴᓗᐊᕐᒥ, ᐊᖏᓂᖓ ᖃᓄᐃᑦᑐᖅ ᐃᑲᔪᙱᑦᑐᖅ.
ᓱᓇ ᐊᑐᕆᐊᖃᕐᒪᖔᑦ
ᐱᐅᓂᖅᓴᐅᓂᖃᙱᑦᑎᓪᓗᑎᑦ, ᐱᙳᐊᕈᑏᑦ ᐊᖏᓂᖏᑦ ᑮᓇᐅᔭᒃᓴᐅᑉ ᐸᕐᓇᐅᑎᖓᓄᑦ ᐊᐱᖅᑯᑎᐅᔪᑦ, ᐊᖏᒡᓕᒋᐊᕐᓂᕐᒧᑦ ᐊᓯᐊᒍᑦ: ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ = ᑲᐃᕙᕐᓂᕐᒧᑦ ᐊᑐᕈᒪᔭᑎᑦ, ᐃᑲᕐᕋᒧᑦ ᑮᓇᐅᔭᒃᓴᐅᑉ ᐸᕐᓇᐅᑎᖓᓂᑦ ᐱᙳᐊᕐᕕᐅᓪᓗ ᓱᒃᑲᐃᓐᓂᖓᓂᑦ ᓈᓴᐃᓗᒍ (ᐱᙳᐊᕈᑎᒃᓴᓂᒃ ᐊᐅᓚᑦᓯᓂᕐᒧᑦ ᒪᑉᐱᒐᖅ). ᑭᓕ ᐱᙳᐊᖅᑎᓄᑦ ᐊᑐᖅᑕᐅᒐᔪᒃᑐᓄᑦ ᐃᑲᔪᖅᑕᐅᑎᖓ ᑭᐅᔾᔪᑎᖓᑕ ᓇᓗᓇᙱᓐᓂᖓ: ᓯᕉ. ᓯᕉᐅᑉ ᐅᖓᑖᓄᑦ ᐱᙳᐊᕈᑎᓕᐊᕆᔭᑎᑦ ᐃᓘᓐᓇᑎᒃ ᐱᙳᐊᕐᓂᐅᑉ ᐊᑭᖓ, ᐃᓕᖕᓄᑦ ᓇᓚᐅᑦᑖᖅᑕᐅᔪᖅ, ᓈᓴᐅᑎᓕᐅᕈᑎᒧᑦ ᐱᐅᓯᑎᑕᐅᙱᑦᑐᖅ.
ᑭᓕ ᐃᓚᒋᔭᐅᔪᖅ “ᑮᓇᐅᔭᓂᒡᓗ ᐊᐅᓚᑦᓯᓂᖅ”
ᐸᕐᓇᐅᑏᑦ “ᕉᓚᑦᒧᑦ ᑭᓕ”-ᑐᑦ ᓂᐅᕕᖅᑕᐅᔪᑦ, ᐱᙳᐊᕈᑎᒃᓴᓂᑦ ᐊᓯᑦᑐᐃᓐᓇᙱᑦᑐᒥᒃ %-ᖓᓂᒃ ᐱᙳᐊᕈᑎᒧᑦ ᐊᑐᓂ ᐱᙳᐊᕈᑎᓕᐅᖁᔨᔪᑦ, ᐊᔾᔨᒌᒃᑐᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᐅᔪᑦᐸᕐᓇᐅᑎᐊᔾᔨᒌᒃᑐᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅᑲᐃᕙᕐᓂᖅ ᑕᒪᐃᓐᓂ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ. ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᖅ ᑕᒪᐃᑦ ᑕᒪᑐᒧᖓ ᐊᔾᔨᒌᒃᓯᔭᐅᕙᒃᑐᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ ᒥᑭᓕᖅᐸᓪᓕᐊᑎᓪᓗᒍ. ᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᑦᑮᓇᐅᔭᖅᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᑦᐱᙳᐊᖅᑕᐅᓂᖓᓂ ᐅᕝᕙᓘᓐᓃᑦ ᐱᕕᒃᓴᕐᒥ ᐱᙳᐊᕈᑎᒋᔭᐅᔪᑦ ᑲᑎᓪᓗᒋᑦ, ᐊᔪᒐᐅᑎᑦ ᐱᙳᐊᕈᑎᒋᖃᑦᑕᖅᑕᐅᔪᑦ ᐃᓚᓗᒋᑦ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᕼᐋᓐᑐᓪ, ᐋᒃᓴᓐ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → 2.70%-ᖓᓂᒃ ᐊᓯᐅᔾᔨᔪᑦ, ᐱᙳᐊᕈᑎᓗ ᑮᓇᐅᔭᖓ ᐊᓯᐅᔾᔨᑎᓪᓗᑎᑦ ᒥᑭᓕᖅᐸᒻᒪᑦ, ᐃᓘᓐᓇᐃᓪᓗ ᐊᓯᐅᔾᔨᓂᖅ ᐊᑯᓂᐅᓕᖅᑎᑦᓯᔪᑦ, ᐊᑦᑕᓇᙱᓕᖅᑎᑦᓯᙱᑦᑐᑦ. ᑮᓇᐅᔭᒃᓴᐅᑉ ᐸᕐᓇᐅᑎᖓ ᐊᑯᓂᐅᓂᖅᓴᐅᑎᑦᓯᓂᕐᒧᑦ ᐱᐅᔪᖅ; ᑭᓕᐅᙱᑦᑐᖅ, ᑭᓕ ᓄᖅᑲᖁᔨᓂᐊᕐᒪᑦ.
ᓈᓴᐅᑎᓕᐅᕈᑎ
ᐊᐱᖅᑯᑏᑦ
ᐱᐅᓂᖅᓴᐅᓂᖅ ᓈᓴᖅᑕᐅᓯᒪᒃᐸᑦ ᑐᐊᖅ, ᓴᖑᓯᒪᔪᒥᑦ ᐊᒃᓴᓗᐊᕐᒥᑦᖃᐅᔨᓴᕐᕕᒃᓴᖑᓯᒪᔪᖅ ᐊᒃᓴᓗᐊᖅᐊᒃᓴᓗᐊᖅ ᓴᓇᓂᖓᑕ ᐊᑲᐅᙱᓐᓂᖏᑦ ᐃᓂᓂᒃ ᐃᓚᖏᓐᓂᒃ 1/37-ᒥᑦ ᐱᔪᓐᓇᕐᓂᖅᓴᐅᑎᑦᓯᔪᑦ. ᖃᐅᔨᔭᐅᑦᓯᐊᙱᑦᑐᖅ, ᑕᐅᓴᓐ ᐊᒥᓱᑦ ᑲᐃᕙᕐᓃᑦ ᑎᑎᕋᖅᑕᐅᓯᒪᒍᑎᒃ ᖃᐅᔨᔭᐅᔪᓐᓇᖅᑐᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐅᕝᕙᓘᓐᓃᑦ ᐱᕕᒃᓴᓕᕆᐅᑎᒥᑦ. ᓈᒻᒪᒃᑐᒥ ᐊᒃᓴᓗᐊᕐᒥ ᐃᒪᐃᙱᑦᑐᖅ.
ᐱᐅᓂᖅᓴᐅᓂᐅᑉ ᓇᓚᐅᑦᑖᖅᑕᐅᓂᖓ ᑕᒻᒪᖅᑐᖃᕐᒪᑦ, ᐊᖏᓗᐊᖅᑐᓂᒡᓗ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ ᒥᑭᓗᐊᖅᑐᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᕐᒥᑦ ᐊᑭᑦᑐᓂᖅᓴᐅᒻᒪᑦ. ᑭᓕ ᓇᑉᐸᖓ ᐊᖏᒡᓕᒋᐊᕐᓂᐅᑉ ᓯᑕᒪᐅᓂᖏᓐᓂ ᐱᖓᓱᓂᒃ ᑐᓂᓯᔪᖅ, ᐊᔾᔨᒌᙱᓐᓂᐅᑉᓈᓴᐃᓂᖅᐊᔾᔨᒌᙱᓐᓂᖅᐱᓐᓂᐅᔪᑦ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓᑕ ᐊᕙᓗᐊᓂ ᖃᓄᖅ ᓯᐊᒻᒪᒃᓯᒪᓂᖏᓐᓂᒃ ᓈᓴᐅᑎ. ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᒥ ᐊᖏᔪᖅ, ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᖕᓂ ᐱᙳᐊᕈᑏᓐᓂ ᒥᑭᔪᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᓯᑕᒪᐅᓂᖏᓐᓂ ᐊᑕᐅᓯᐊᓂᒃ.
ᐋᒃᑲ. ᑭᓕ ᐊᖏᒡᓕᒋᐊᕐᓂᖅ ᐱᐅᓯᑦᑎᔪᖅ ᐱᐅᓂᖅᓴᐅᓂᖃᖅᑎᓪᓗᑎᑦ. ᐱᙳᐊᕈᑎᒃᓴᓂᒃ ᐊᐅᓚᑦᓯᓂᖅ ᑮᓇᐅᔭᓂᒃ ᐊᑐᕐᓂᖅ ᐊᐅᓚᑦᑎᔪᖅ ᐱᐅᓂᖅᓴᐅᓂᖃᙱᑦᑎᓪᓗᑎᑦ.
ᓈᓴᐃᓂᕐᒥᒃ ᐱᙳᐊᕐᓂᖅ
ᓯᕗᓪᓕᐅᓪᓗᓂ ᐃᓕᖕᓂᒃ ᐆᒃᑐᕐᓗᑎᑦ. ᑭᐅᔾᔪᑏᑦ ᐃᓗᓕᖏᑦ ᒪᑐᔭᐅᓯᒪᔪᑦ; ᐅᐸᒍᓐᓇᕈᕕᑦ ᒪᑐᐃᖅᓯᓗᒍ.
ᑐᐊᑉ ᓵᓄᓐᓗ (Thorp, Shannon) ᓇᓚᐅᑦᑖᕈᑎᖏᑦ ᖃᓂᒋᔭᖓ 44% ᐱᐅᓂᖅᓴᐅᓂᕐᒥᒃ ᑐᓂᓯᔪᑦ. ᐊᑕᐅᓯᕐᒧᑦ ᓈᓴᐅᑎᒧᑦ ᓇᓚᐅᑦᑖᖅᑕᐅᓯᒪᔪᒧᑦ, ᑭᐊᓕ (Kelly) ᐅᖃᖅᑐᖅ ᐱᙳᐊᕈᑎᒃᓴᐃᑦᑮᓇᐅᔭᖅᐱᙳᐊᕈᑎᒃᓴᐃᑦᑮᓇᐅᔭᑦ ᐃᓘᓐᓇᖏᑦ ᐱᙳᐊᕐᓂᕐᒧᑦ ᐊᕕᒃᓯᒪᔭᐅᔪᑦ. ᐱᙳᐊᕈᑎᒃᓴᓂᒃ ᐊᐅᓚᑦᓯᓂᖅ ᑐᑭᖃᖅᑐᖅ ᖃᔅᓯᑦ ᐱᙳᐊᕈᑎ ᐊᑐᓂ ᐱᙳᐊᖅᑕᐅᓂᖓᓂᓗ ᐊᑐᓂ ᐊᓯᐅᔪᓐᓇᖅᑕᐅᓂᐊᕐᒪᖔᑕ ᐃᓱᒪᓕᐅᕐᓂᕐᒥᒃ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → 1.26%-ᖓᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᖁᓪᓗᓂ. ᐊᔾᔨᒋᔭᐅᔪᖅ 44% ᐱᙳᐊᕈᑎᒥ ᐊᑕᐅᓯᕐᒥ ᑕᓪᓕᒪᓄᑦ ᓴᓂᐊᓃᑦᑐᓄᑦ ᓈᓴᐅᑏᓐᓄᑦ ᐊᕕᒃᓯᒪᔪᒥ ᓴᖅᑭᑉᐸᑦ?
ᑭᐅᔾᔪᑎ ᑕᑯᓗᒍ
ᑭᐅᔾᔪᑎ ᑕᐃᑦᓱᒪᓂ ᑭᐊᓕ ᐅᖃᖅᑐᖅ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ 7.1%-ᖏᓐᓂᒃ, ᐱᙳᐊᕈᑎᒃᓴᐃᓪᓗ ᐊᖏᒡᓕᕙᓪᓕᐊᔪᑦ ᐱᖓᓲᔪᖅᑐᕆᐊᖅᓗᒍ ᖃᓂᒋᔭᐅᔪᒥᒃ ᓱᒃᑲᐃᓐᓂᖃᖅᑐᑎᒃ: ᖃᓂᒋᔭᖓ 1.25 ᒥᓕᐊᓐ-ᕆᐊᖅᓗᒍ 1,000 ᐱᙳᐊᕈᑏᓐᓂ, ᖃᓂᒋᔭᖓ 11.5-ᕆᐊᖅᓗᒍ ᐊᑐᓂ.
ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᐱᙳᐊᕈᑎᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ, ᐊᑭᓕᐅᑎ 35:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → 44% ᐱᐅᓂᖅᓴᐅᓂᓕᒃ ᐊᔪᒐᖅᑐᖅ ᐱᔪᓐᓇᕐᓂᓕᒃ 0.04, 36 × 0.04 = 1.44 ᐅᓂᒪᑦ. ᑭᐊᓕᐅᑉ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ ᐱᐅᓂᖅᓴᐅᓂᖅ ᐊᕕᒃᑕᐅᓪᓗᓂ ᐊᑭᓕᐅᑎᒧᑦ: 0.44/35 = 1.26%. ᐊᖏᒡᓕᕙᓪᓕᐊᓂᖓ ᐱᙳᐊᕈᑎᒥ ᑕᒪᐃᓐᓂ 0.04 × ln(1 + 35 × 0.0126) + 0.96 × ln(1 − 0.0126) ≈ 0.00244, ᑕᐃᒪᐃᒻᒪᑦ 1,000 ᐱᙳᐊᕈᑏᑦ ᐱᙳᐊᕈᑎᒃᓴᓂᒃ ᐊᒥᓲᓕᕆᐊᖅᑎᑦᓯᔪᑦ ᖃᓂᒋᔭᖓ e^2.44 ≈ 11.5-ᒧᑦ.
ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ ᐊᑕᐅᓯᖅ ᑕᓪᓕᒪᓄᑦ ᓈᓴᐅᑏᓐᓄᑦ ᐊᕕᒃᓯᒍᕕᐅᒃ, ᐱᙳᐊᕈᑎ ᐊᔪᒐᖅᑐᖅ ᐱᔪᓐᓇᕐᓂᓕᒃ 0.20, ᐊᑭᓕᐅᑎᖃᖅᑐᖅ 36/5, 1-ᒧᑦ ᐱᙳᐊᕈᑎ ᐃᓚᓗᒍ, ᑕᒪᓐᓇ 6.2, 1-ᒧᑦ: 44% ᐱᐅᓂᖅᓴᐅᓂᖅ ᓱᓕ, 0.2 × 7.2 = 1.44 ᐅᓂᒪᑦ. ᑭᐊᓕᐅᑉ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ 0.44/6.2 = 7.10%-ᖑᓕᖅᑐᖅ, ᐊᖏᒡᓕᕙᓪᓕᐊᓂᖓᓗ ᐱᙳᐊᕈᑎᒥ 0.01404, ᖃᓂᒋᔭᖓ 5.75-ᕆᐊᖅᓗᒍ ᐊᒥᓲᓂᖅᓴᐅᓪᓗᓂ. 1,000 ᐱᙳᐊᕈᑏᓐᓂ ᑕᒪᓐᓇ e^14.04, ᖃᓂᒋᔭᖓ 1.25 ᒥᓕᐊᓐ.
ᐱᐅᓂᖅᓴᐅᓂᖅ ᐊᔾᔨᒋᔭᐅᔪᖅ; ᐊᓯᑦᑐᐃᓂᖏᑦ ᒥᑭᓂᖅᓴᐅᔪᑦ. ᐱᙳᐊᕈᑎ ᑕᓪᓕᒪᓄᑦ ᐊᑕᐅᓯᕐᒥ ᐊᔪᒐᖅᑐᖅ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐊᖏᓂᖅᓴᒥᒃ ᐃᓚᖓᓂᒃ ᐱᙳᐊᕈᑎᒋᔪᓐᓇᖅᑐᖅ ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᓂᐊᕐᓂᖏᓐᓂᒃ ᐅᓗᕆᐊᓇᖅᑐᓕᐅᕈᓐᓃᖅᑐᑎᒃ, ᑭᐊᓕᐅᓪᓗ ᐊᖏᒡᓕᕙᓪᓕᐊᓂᖓ ᑕᒪᓐᓇ ᐊᑭᓕᖅᓱᖅᑐᖅ. ᑐᐊᑉ (Thorp, 1984) ᐆᒃᑑᑎᒥᒃ ᐊᑐᖅᑐᖅ ᑕᑯᑎᑦᓯᓇᓱᒃᓗᓂ ᓇᓚᐅᑦᑖᕈᑎᓕᒃ ᐱᙳᐊᖅᑏᑦ ᓱᒻᒪᑦ ᐊᒃᓴᓗᐊᑉ ᐃᓚᖏᓐᓄᑦᐊᒃᓴᓗᐊᖅᐊᒃᓴᓗᐊᑉ ᐃᓚᖓᐊᒃᓴᓗᐊᕐᒥ ᐃᓂᑦ ᓴᓂᓕᐅᑎᒌᒃᑐᑦ ᑲᑎᑦᑐᑦ, ᐱᙳᐊᕈᑎᓕᕆᕝᕕᖕᒥ ᑲᑎᑦᑐᓂᑦ ᐊᔾᔨᒋᙱᑦᑐᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᕈᑎᓕᐅᕐᒪᖔᑕ. ᐱᓕᕆᓂᕐᒥ ᑕᓪᓕᒪᑦ ᓴᓂᐊᓃᑦᑐᑦᐱᙳᐊᕈᑎᓴᓂᐊᓃᑦᑐᑦᓈᓴᐅᑎ ᐊᒃᓴᓗᐊᕐᒥᓗ ᓴᓂᖏᓐᓂ ᒪᕐᕉᓐᓂ ᐃᓂᒃ ᒪᕐᕉᒃ, ᑕᓪᓕᒪᑦ ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑏᑦ ᓯᑉᐳᖏᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᐅᓂᖅᓴᐅᓂᖅ ᒥᑭᓂᖅᓴᒥᒃ ᐱᑕᖃᖅᑐᑦ ᓈᓴᐅᑎ ᐱᐅᓂᖅᐹᖅ ᐊᑕᐅᓯᖅ ᐊᑐᓂ (Advantage Play ᑕᑯᓗᒍ).
ᐱᙳᐊᖅᑎ ᓇᓂᓯᓯᒪᔪᖅ ᒪᕐᕉᖕᓂᒃ ᓴᓂᐊᓃᑦᑐᓂᒃ ᐃᓂᓐᓂᒃᐊᑐᖅᑕᐅᔪᑦᐃᓂᑲᐃᕙᖅᑐᒥ 37 ᓈᓴᐅᑎᓕᑦ ᐃᓂᑦ ᐊᑕᐅᓯᖓ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐃᓂᒋᐊᖅ, ᖃᓪᓗᐊᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᑕᒪᒃᑭᓄᑦ 25 ᐃᓚᖏᓐᓂ 1 ᓴᖅᑭᑦᑐᓂᒃ 37 ᐃᓚᖏᓐᓂ 1 ᐊᓯᐊᓂ. ᒪᕐᕉᓄᑦ ᐱᙳᐊᕈᑎᐱᙳᐊᕈᑎᒪᕐᕉᓄᑦ ᐱᙳᐊᕈᑎᒪᕐᕉᒃ ᓈᓴᐅᑏᒃ ᓴᓂᓕᐅᑎᒌᒃᑐᒃ, ᐊᑭᓕᐅᑎ 17:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᑯᕐᖓᓂ ᐱᙳᐊᕈᑎᒋᒋᐊᖃᖅᐸ 17, 1-ᒧᑦ, ᐅᕝᕙᓘᓐᓃᑦ ᓈᓴᐅᑏᒃ ᑕᒪᒃᑭᓄᑦ ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᒋᓗᒋᒃ? ᑭᐊᓕ ᖃᔅᓯᓂᒃ ᐅᖃᖅᐸ, ᐱᙳᐊᕈᑎᒃᓴᐃᓪᓗ ᖃᓄᖅ ᓱᒃᑲᐃᓐᓂᖃᖅᑐᑎᒃ ᐊᖏᒡᓕᕙᓪᓕᐊᕙᑦ ᐃᓂᒥ ᐊᑕᐅᓯᕐᒥ ᐊᑐᓂ?
ᑭᐅᔾᔪᑎ ᑕᑯᓗᒍ
ᑭᐅᔾᔪᑎ ᐊᔾᔨᒌᙱᓐᓂᖃᙱᑦᑐᖅ: ᐱᙳᐊᕈᑎᒃᓴᐃᑦ 2.59%-ᖏᑦ ᒪᕐᕉᓄᑦ ᐱᙳᐊᕈᑎᒥ, ᐅᕝᕙᓘᓐᓃᑦ 1.29% ᓈᓴᐅᑎᒥ ᑕᒪᑐᒪᓂ. ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐊᒥᓲᓂᖅᐹᒥ ᐊᖏᒡᓕᕙᓪᓕᐊᔪᑦ ᖃᓂᒋᔭᖓ 155-ᕆᐊᖅᓗᒍ 1,000 ᑲᐃᕙᕐᓃᓐᓂ, 11.5-ᕆᐊᖅᓗᒍ ᐃᓂᒥ ᐊᑕᐅᓯᕐᒥ ᐊᑐᓂ.
ᒪᕐᕉᓄᑦ ᐱᙳᐊᕈᑎ ᐊᔪᒐᖅᑐᖅ ᐱᔪᓐᓇᕐᓂᓕᒃᓈᓴᐃᓂᖅᐱᔪᓐᓇᕐᓂᖅᐱᓐᓂᐅᑉ ᐱᔪᓐᓇᕐᓂᖓ, 0-ᒥᑦ 1-ᒧᑦ ᐅᕝᕙᓘᓐᓃᑦ 0%-ᒥᑦ 100%-ᒧᑦ. ᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ: 1/37 = 2.70%.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → 2/25 = 0.08 ᐊᑭᓕᐅᑎᖃᖅᑐᖅ 17, 1-ᒧᑦ, ᑕᐃᒪᐃᒻᒪᑦ ᐅᑎᖅᑎᑦᓯᔪᖅ 18 × 0.08 = 1.44 ᐊᑦᔨᐅᑎᒧᑦᑮᓇᐅᔭᖅᐊᑦᔨᐅᑎᐸᕐᓇᐅᑎᐅᑉ ᐅᕝᕙᓘᓐᓃᑦ ᐱᙳᐊᖅᑎᐅᑉ ᑐᙵᕕᒋᔭᖓ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ. ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᐅᔪᑦ ᐊᑦᔨᐅᑎᓄᑦ ᓇᓗᓇᐃᖅᑕᐅᕙᒃᑐᑦ, ᑕᐃᒪ ᓇᓕᐊᓂᑐᐃᓐᓇᖅ ᐱᙳᐊᕐᕕᒻᒥ ᐊᑐᕈᓐᓇᖁᓪᓗᒋᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᕈᑎᒋᔭᐅᔪᒧᑦ ᑕᒪᐃᓐᓄᑦ: ᐱᐅᓂᖅᓴᐅᓂᖅ 44%, ᓴᖑᓯᒪᔪᖅ ᐃᓂ ᐊᑕᐅᓯᖅ ᐊᔾᔨᒋᓪᓗᓂᐅᒃ. ᑭᐊᓕᐅᑉ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ ᐱᐅᓂᖅᓴᐅᓂᖅ ᐊᕕᒃᑕᐅᓪᓗᓂ ᐊᑭᓕᐅᑎᒧᑦ: 0.44/17 = 2.59%.
ᒪᕐᕉᒃ ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑏᒃ 1.29% ᑕᒪᒃᑭᓄᑦ ᓱᓕᓪᓚᕆᒃ ᐊᔾᔨᒋᔭᐅᔪᓂᒃ ᓴᖅᑭᑦᑎᔪᒃ. ᓈᓴᐅᑏᒃ ᐊᑕᐅᓯᖅ ᓴᖅᑭᑉᐸᑦ, ᓯᑉᑮᓇᐅᔭᖅᓯᑉᓇᓗᓇᐃᒃᑯᑎ ᐊᑭᖃᐃᓐᓇᖅᑐᖅ, ᐱᙳᐊᕈᑎᓕᕆᕝᕕᖕᒥ ᐃᓕᔭᐅᔪᖅ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᕐᒧᑦ. ᐊᓯᐊᓂ ᐊᑎᖓ: ᓯᐊᒃ (check).ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᑕᐅᓯᖅ ᐊᔪᒐᖅᑐᖅ 35, 1-ᒧᑦ, ᐊᓯᐊᓗ ᐊᓯᐅᔪᖅ, ᑲᑎᑕᐅᓪᓗᑎᒃ 34 × 1.29% = 44% ᐱᙳᐊᕈᑎᒃᓴᐃᑦ, ᒪᕐᕉᓄᑦ ᐱᙳᐊᕈᑎ ᐊᑭᓕᐅᑎᖃᕐᓂᖓᑐᑦ; ᓴᖅᑭᑦᑐᙱᑉᐸᑦ ᒪᕐᕉᒃ ᐊᓯᐅᔪᒃ.
ᐊᖏᒡᓕᕙᓪᓕᐊᓂᖓ ᑲᐃᕙᕐᓂᕐᒥ 0.00505, 0.00244 ᐃᓂᒥ ᐊᑕᐅᓯᕐᒥ ᐊᑐᓂ, ᑕᐃᒪᐃᒻᒪᑦ 1,000 ᑲᐃᕙᕐᓃᓐᓂ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐊᖏᒡᓕᕙᓪᓕᐊᔪᑦ e^5.046 ≈ 155-ᕆᐊᖅᓗᒍ, e^2.44 ≈ 11.5-ᕆᐊᖅᓗᒍ ᐊᓯᐊᓂ. ᒪᕐᕉᒃ ᓈᓴᐅᑏᒃ ᐱᐅᔪᒃ ᐊᑭᓕᓐᓂᖅᓴᐅᓗᐊᖅᑐᒃ ᐊᑕᐅᓯᕐᒥᑦ ᒪᕐᕉᕆᐊᖅᓗᒍ, ᑕᐃᒪᐃᒻᒪᑦ ᓴᖑᓯᒪᓂᕐᒥᒃ ᐱᙳᐊᖅᑏᑦ ᓈᓴᐅᑏᑦ ᑲᑎᖃᑎᒌᖕᓄᑦ ᐱᙳᐊᕈᑎᓕᐅᖅᐸᒃᑐᑦ. ᑐᐊᑉ (Thorp, 1984) ᐊᔾᔨᒋᔭᐅᔪᒥᒃ ᓇᓗᓇᐃᖅᓯᔪᖅ.
ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ
ᕉᓚᑦᒥ ᐊᖏᒡᓕᒋᐊᕐᓂᕐᒧᑦ ᐱᐅᓛᖅ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ ᓈᓴᐅᑎᐅᔪᖅ ᑭᓇᑐᐃᓐᓇᐅᑉ ᖃᐅᔨᒪᔭᖓ.
ᐱᕝᕕᒋᔭᐅᔪᑦ
- Kelly, J. L. “A new interpretation of information rate.”
- Breiman, L. “Optimal gambling systems for favorable games.”
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Haghani, V. & Dewey, R. “Rational decision-making under uncertainty: observed betting patterns on a biased coin.”