ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᓂᐊᕐᓂᖏᑦ
ᑐᕌᒐᕐᓄᑦ ᑎᑭᓚᐅᖅᑎᓐᓇᒋᑦ ᐱᙳᐊᕈᑎᒃᓴᑎᑦ ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᔾᔨᓂᕐᒧᑦ ᐱᔪᓐᓇᕐᓂᖅ.
ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᓐᓄᑦ ᐱᙳᐊᕈᑎᓄᑦ, ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᓂᐊᕐᓂᖏᑦ ᐱᙳᐊᖅᑎᐅᑉ ᓱᕋᐃᓂᖓᓄᑦ ᓈᓴᐅᑎᓕᐅᕈᑎᒥᒃ ᒪᓕᒃᑐᑦ. $500 ᐱᙳᐊᕈᑎᒃᓴᖃᖅᑐᑎᑦ, $10 ᐱᙳᐊᕈᑏᑦ ᐊᒻᒪ $600 ᑐᕌᒐᖅ, ᑐᕌᒐᕐᓄᑦ ᑎᑭᑉᐸᒃᑐᑎᑦ 57% ᖃᓂᒋᔮᓂ ᐊᓯᖏᓐᓂᓗ ᐃᓘᓐᓇᖏᓐᓂᒃ ᐊᓯᐅᔾᔨᕙᒃᑐᑎᑦ.
ᐊᐱᖅᑯᑎ
a ᐊᑦᔨᐅᑏᑦᑮᓇᐅᔭᖅᐊᑦᔨᐅᑎᐸᕐᓇᐅᑎᐅᑉ ᐅᕝᕙᓘᓐᓃᑦ ᐱᙳᐊᖅᑎᐅᑉ ᑐᙵᕕᒋᔭᖓ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ. ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᐅᔪᑦ ᐊᑦᔨᐅᑎᓄᑦ ᓇᓗᓇᐃᖅᑕᐅᕙᒃᑐᑦ, ᑕᐃᒪ ᓇᓕᐊᓂᑐᐃᓐᓇᖅ ᐱᙳᐊᕐᕕᒻᒥ ᐊᑐᕈᓐᓇᖁᓪᓗᒋᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᕈᑎᒃᓴᓂᒃᑮᓇᐅᔭᖅᐱᙳᐊᕈᑎᒃᓴᐃᑦᑮᓇᐅᔭᑦ ᐃᓘᓐᓇᖏᑦ ᐱᙳᐊᕐᓂᕐᒧᑦ ᐊᕕᒃᓯᒪᔭᐅᔪᑦ. ᐱᙳᐊᕈᑎᒃᓴᓂᒃ ᐊᐅᓚᑦᓯᓂᖅ ᑐᑭᖃᖅᑐᖅ ᖃᔅᓯᑦ ᐱᙳᐊᕈᑎ ᐊᑐᓂ ᐱᙳᐊᖅᑕᐅᓂᖓᓂᓗ ᐊᑐᓂ ᐊᓯᐅᔪᓐᓇᖅᑕᐅᓂᐊᕐᒪᖔᑕ ᐃᓱᒪᓕᐅᕐᓂᕐᒥᒃ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᑕᖃᖅᑐᑎᑦ ᐊᒻᒪ a + b ᐊᑦᔨᐅᑎᓄᑦ ᑎᑭᑕᐅᒐᓱᒃᑐᑎᑦ, ᐊᑦᔨᐅᑎᒥᒃ ᐊᑕᐅᓯᕐᒥᒃ ᐊᑕᐅᑦᑎᒃᑯᑦ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒻᒧᑦ ᐱᙳᐊᕈᑎᒧᑦᐱᙳᐊᕈᑎᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎᐊᐅᐸᓗᒃᑐᖅ/ᕿᕐᓂᖅᑐᖅ, ᐊᕕᒃᑕᐅᔪᓐᓇᙱᑦᑐᖅ/ᐊᕕᒃᑕᐅᔪᓐᓇᖅᑐᖅ, ᐊᖏᔪᑦ/ᒥᑭᔪᑦ. 18 ᓈᓴᐅᑏᑦ, ᐊᑭᓕᐅᑎ 1:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᕈᑎᓕᐅᖅᓗᑎᑦ, ᐊᔪᒐᕐᓂᕐᒧᑦ ᐱᔪᓐᓇᕐᓂᖓᓈᓴᐃᓂᖅᐱᔪᓐᓇᕐᓂᖅᐱᓐᓂᐅᑉ ᐱᔪᓐᓇᕐᓂᖓ, 0-ᒥᑦ 1-ᒧᑦ ᐅᕝᕙᓘᓐᓃᑦ 0%-ᒥᑦ 100%-ᒧᑦ. ᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ: 1/37 = 2.70%.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → p = 18/37 ᐊᓯᐅᔾᔨᓂᕐᒧᓪᓗ ᐱᔪᓐᓇᕐᓂᖓ q = 19/37. ᑐᕌᒐᕐᓄᑦ ᑎᑭᑦᑐᓂ ᓯᕉᒧᑦ ᑎᑭᓚᐅᖅᑎᓐᓇᒋᑦ ᐱᔪᓐᓇᕐᓂᖅ ᖃᓄᐃᓪᓗᐊᑦᑎᐊᖅ? ᑭᐅᔾᔪᑎ ᐸᓯᑲᓪ (Blaise Pascal), ᕗᐊᒫ (Fermat) ᕼᐊᐃᒐᓐᔅᓗ (Huygens) 1650-ᖏᓐᓂ ᓇᓂᓯᓯᒪᔭᖏᑦ, ᐊᒻᒪ ᐱᔪᓐᓇᕐᓂᕐᒥ ᑐᖃᓂᖅᐹᑦ ᓇᓂᓯᓃᑦ ᐃᓚᖓ.
ᐱᙳᐊᖅᑎᐅᑉ ᓱᕋᐃᓂᖓᓄᑦ ᓈᓴᐅᑎᓕᐅᕈᑎ
P(ᑐᕌᒐᕐᓄᑦ ᑎᑭᓐᓂᖅ) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ). ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᓂᐊᕐᓂᖏᑦᓈᓴᐃᓂᖅᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᓂᐊᕐᓂᖏᑦᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᔾᔨᑕᐅᓂᐊᕐᓂᖏᓐᓂᒃ ᐱᔪᓐᓇᕐᓂᖅ ᑐᕌᒐᖅ ᐅᕝᕙᓘᓐᓃᑦ ᑲᐃᕙᕐᓃᑦ ᐊᒥᓲᓂᖏᑦ ᑎᑭᐅᑎᔭᐅᓚᐅᖅᑎᓐᓇᒋᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᑕᐅᓯᖅ ᑖᔅᓱᒪ ᐲᔭᖅᑕᐅᓪᓗᓂ. q/p = 19/18 ≈ 1.0556-ᖑᑎᓪᓗᒍ, ᐊᔾᔨᒌᙱᓐᓂᖓ ᐊᑦᔨᐅᑏᑦ ᐊᒥᓲᓂᖏᑦ ᒪᓕᒃᓗᒋᑦ ᓱᒃᑲᔪᒥᒃ ᐊᖏᒡᓕᕙᒃᑐᖅ, ᑕᐃᒪ ᓈᓴᐅᑎᓕᐅᕈᑎ ᒥᑭᔪᓂᒃ ᐊᑦᔨᐅᑎᓂᒃ ᐊᒡᒍᐊᓗᒃ ᐊᓯᐅᔾᔨᑎᑦᓯᔪᖅ: ᐊᒥᓲᓂᖅᓴᓂᒃ ᐱᙳᐊᕈᑎᓂᒃ ᑐᕌᒐᕐᓄᑦ ᑎᑭᓐᓂᕐᒧᑦ ᐱᔭᕆᐊᖃᖅᐸᑦ, ᐊᒥᓲᓂᖅᓴᓂ 2.70% ᐊᑭᓕᐅᑎ ᐃᖏᕐᕋᓂᕐᒥ ᐊᑭᓕᖅᑕᐅᕙᒃᑐᖅ.
ᑐᑭᓯᓂᖓ
ᒥᑭᓂᖅᓴᐃᑦ ᐊᑦᔨᐅᑏᑦ ᐊᓯᐅᔾᔨᑎᑦᓯᓂᖅᓴᐅᔪᑦ. $500 ᒪᕐᕉᕆᐊᖅᑎᓇᓱᒃᓗᒍ $10 ᐱᙳᐊᕈᑏᑦ ᐊᑐᖅᓗᒋᑦ 6% ᐊᔪᕐᓇᙱᑦᑐᖅ; ᐱᙳᐊᕈᑎ ᐊᑕᐅᓯᖅ $500-ᓕᒃ 48.6% ᐊᔪᕐᓇᙱᑦᑐᖅ. ᐊᓂᖅᓵᕐᓇᙱᑦᑐᒥᒃ ᐱᙳᐊᕐᓂᖅ, ᐱᙳᐊᕈᑏᑦ ᐊᒥᓲᓐᖏᓂᖅᓴᐃᑦ ᐊᖏᓂᖅᓴᐃᓪᓗ, ᐊᓯᐅᔾᔨᓂᕐᒧᑦ ᓂᕆᐅᒋᔭᐅᔪᓕᒻᒥ ᐱᙳᐊᕐᓂᕐᒥ ᑐᕌᒐᕐᓄᑦ ᑎᑭᓐᓂᕐᒧᑦ ᐱᔪᓐᓇᕐᓂᖅ ᐊᖏᓛᖑᑎᑦᓯᔪᖅ, ᑳᓯᓅᑉ ᐃᓚᖓ ᐊᑐᖅᑕᐅᓂᖓ ᒥᑭᓛᖑᑎᑦᓯᒻᒪᑦ. ᐱᑦᑕᕐᓂᖏᑦ ᐊᔾᔨᒌᙱᓐᓂᖓᓂᒡᓗᓈᓴᐃᓂᖅᐊᔾᔨᒌᙱᓐᓂᖅᐱᓐᓂᐅᔪᑦ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓᑕ ᐊᕙᓗᐊᓂ ᖃᓄᖅ ᓯᐊᒻᒪᒃᓯᒪᓂᖏᓐᓂᒃ ᓈᓴᐅᑎ. ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᒥ ᐊᖏᔪᖅ, ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᖕᓂ ᐱᙳᐊᕈᑏᓐᓂ ᒥᑭᔪᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᖏᓛᖑᑎᑦᓯᔪᖅ, ᐅᓐᓄᐊᓗ ᓱᒃᑲᔪᒥᒃ ᐃᓱᓕᑦᑐᖅ. ᑖᓐᓇ ᓈᓴᐃᓂᕐᒥ ᓇᓗᓇᐃᖅᓯᓂᖅ “ᐊᓂᖅᓵᕐᓇᙱᑦᑐᒥᒃ ᐱᙳᐊᕐᓂᖅ ᐱᐅᓛᖑᔪᖅ” ᑕᐃᔭᐅᔪᖅ ᐊᒻᒪ ᑐᐱᓐᔅ (Dubins) ᓴᕕᑦᔾᓗ (Savage) 1965-ᒥ ᓱᓕᓂᖓᓂᒃ ᓇᓗᓇᐃᖅᓯᓯᒪᔪᒃ.
ᐊᐱᖅᑯᑎ ᓇᐅᓐᓂ ᐱᒋᐊᓚᐅᖅᐸ
ᐊᐱᖅᑯᑎ ᕉᓚᑦᒥᑦ ᑐᖃᓂᖅᓴᐅᔪᖅ. 1656-ᒥ ᐸᓯᑲᓪ ᕗᐊᒫᒧᑦ ᐊᐱᖅᑯᑎᒥᒃ ᑐᓂᓯᓯᒪᔪᖅ: ᐱᙳᐊᖅᑏᒃ ᒪᕐᕉᒃ ᐱᖓᓱᓂᒃ ᐱᙳᐊᕈᓯᐊᓂᒃ ᐃᒥᖅᑐᒃ, ᐊᑕᐅᓯᑐᑦ 12 ᓈᓴᐅᑎᓂᒃ ᐱᒋᐊᖅᓗᑎᒃ; ᐃᒥᖅᓂᖅ 11 ᓈᓴᐅᑎᒥᒃ ᐊᑕᐅᓯᕐᒧᑦ ᐅᐊᑦᑎᑦᓯᔪᖅ, ᐃᒥᖅᓂᖅ 14 ᐊᓯᐊᓄᑦ. ᒪᕐᕉᒃ ᑭᐅᔪᒃ, ᐊᒻᒪ ᕼᐊᐃᒐᓐᔅ, ᓈᓴᐃᓂᓕᕆᔨᒥᑦ ᐲᔭ ᑐ ᑲᕐᑲᕕᒥᑦ (Pierre de Carcavi) ᑎᑎᖅᑲᒃᑯᑦ ᑐᓴᖅᓯᒪᔪᖅ, 1657-ᒥ ᓴᖅᑭᑎᑦᓯᓯᒪᔪᖅ ᑕᓪᓕᒪᖓᓂ ᐊᐱᖅᑯᑎᒋᓪᓗᒍ ᐱᔪᓐᓇᕐᓂᕐᒥᒃ ᓯᕗᓪᓕᖅᐹᒥ ᐅᖃᓕᒫᒐᕐᒥ, ᑭᐅᔾᔪᑎᖃᖅᓗᓂ ᓇᓗᓇᐃᖅᓯᓂᖃᙱᓪᓗᓂ. ᖁᓕᑦ ᐊᑕᐅᓯᕐᓗ 27-ᓄᑦ ᐃᓕᒃᑯᓐᓄᑦ ᐃᒥᖅᑕᐅᔪᓐᓇᖅᑐᖅ, ᖁᓕᑦ ᓯᑕᒪᓪᓗ 15-ᓄᑦ ᑭᓯᐊᓂ, ᑕᐃᒪ ᓈᓴᐅᑎ ᑕᒪᐃᓐᓂ ᓯᕗᓪᓕᐅᔪᖅ ᐱᙳᐊᖅᑎᐅᑉ ᑐᖓᓕᐊᓄᑦ 9-ᓂ 14-ᓂᑦ ᐅᐊᑦᑎᕙᒃᑐᖅ, ᐊᒻᒪ ᐊᓂᒍᖅᑐᖅ ᓈᓴᐅᑎᓕᐅᕈᑎ, ᐊᑕᐅᓯᑐᑦ 12 ᓈᓴᐅᑎᓕᒃ, ᑕᒪᐃᓐᓂᒃ ᐊᔪᒐᕐᓂᕐᒧᑦ 1,157-ᕆᐊᖅᓗᒍ ᖃᓂᒋᔮᓂ ᐱᔪᓐᓇᕐᓂᖅᓴᐅᑎᑦᓯᔪᖅ ᑕᒪᐃᓐᓂᒃ ᐊᓯᐅᔾᔨᓂᕐᒥᑦ. 2.70% ᐃᓚᖓ ᒥᑭᓂᖅᓴᐅᔪᐊᓘᔪᖅ, ᑭᓯᐊᓂ ᐊᔾᔨᒌᒃᑐᖅ ᓈᓴᐅᑎᓕᐅᕈᑎ ᐊᒥᓱᓂ ᐱᙳᐊᕈᑎᓂ ᖃᓄᐃᓕᐅᕐᓂᖓᓂᒃ ᓇᓗᓇᐃᖅᓯᔪᖅ.
ᓱᓕᔪᖅ ᐊᓂᖅᓵᕐᓇᙱᑦᑐᖅ ᐱᙳᐊᕈᑎ
ᐄᐳᕆᓪ 2004-ᒥ ᐋᔅᓕ ᕆᕙᓪ (Ashley Revell), ᐃᖏᓕᓐᓄᑦ ᓄᓇᖓᓂᑦ ᐅᕕᒐᕐᓴᖅ, ᖃᓂᒋᔮᓂ ᑕᒪᐃᓐᓂᒃ ᐱᖁᑎᒥᓂᒃ ᓂᐅᕕᖅᑎᑦᓯᓯᒪᔪᖅ, ᐊᓐᓄᕌᒥᓂᒡᓗ, ᐊᒻᒪ $135,300 ᓛᔅ ᕖᒐᔅᒥ ᐳᓛᓴᒧᑦ (Plaza) ᑎᒍᒥᐊᓪᓗᒍ. ᒥᑭᔪᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖓᑕ ᑭᖑᓂᖓᓂ ᑕᒪᐃᓐᓂᒃ ᐊᐅᐸᓗᒃᑐᒧᑦᐱᙳᐊᕈᑎᐊᐅᐸᓗᒃᑐᖅᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎ 18 ᐊᐅᐸᓗᒃᑐᓄᑦ ᓈᓴᐅᑎᓄᑦ. ᕖᓇᓯᑐᑦ: ᕈᔾ (rouge).ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐃᓕᓯᓯᒪᔪᖅ, ᐊᑕᐅᑦᑎᒃᑯᑦ. ᐊᖅᓴᖅᐊᑐᖅᑕᐅᔪᑦᐊᖅᓴᖅᒥᑭᔪᖅ ᐊᖅᓴᖅ ᐊᖁᑎᖓᓂ ᑲᐃᕙᖅᑐᑉ ᐊᑉᐱᖓᓄᑦ ᐃᒋᑕᐅᔪᖅ. ᒫᓐᓇᐅᔪᖅ ᐊᖅᓵᑦ ᐃᕗᕆᓐ ᐅᕝᕙᓘᓐᓃᑦ ᑎᕙᓚᓐ, 18–21 mm.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᐅᐸᓗᒃᑐᒧᑦ 7-ᒧᑦ ᑎᑭᓯᒪᔪᖅ ᐊᒻᒪ $270,600-ᓂᒃ ᑎᒍᒥᐊᖅᓗᓂ ᐊᓂᓯᒪᔪᖅ. ᒪᕐᕉᒃ ᓯᕉᓕᒻᒥᐊᒃᓴᓗᐊᖅᓯᕉᐊᑕᐅᓯᖅ ᐅᔾᔪᐊᕌᔭᒃ ᐃᓂ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᖕᓄᑦ, ᑕᓴᓐᓄᑦ ᓇᑉᐸᖅᑐᓄᓪᓘᓐᓃᑦ ᐱᙳᐊᕈᑏᑦ ᐃᓚᐅᑎᙱᑕᖓ; ᑳᓯᓅᑉ ᐃᓚᖓᑕ ᐱᓇᓪᓗᑎᖓ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐊᑕᐅᓯᖅ ᓯᕉ, 0.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᒃᓴᓗᐊᕐᒥ ᑖᓐᓇ ᑲᐃᕙᕐᓂᖅ ᐊᑕᐅᓯᖅ 47.37% ᐱᔪᓐᓇᕐᓂᐅᓯᒪᔪᖅ ᐊᒻᒪ ᐊᔾᔨᒌᒃᑎᓪᓗᒋᑦ $7,121 ᐊᑭᓕᖅᑎᑦᓯᓯᒪᔪᖅ, 5.26% ᐃᓚᖓ ᐱᙳᐊᕈᑎᒥ ᐊᑕᐅᓯᕐᒥ. $10 ᐱᙳᐊᕈᑎᓄᑦ ᐊᕕᒃᑕᐅᓯᒪᒍᓂ, ᐊᔾᔨᒌᒃᑐᖅ ᑐᕌᒐᖅ ᖃᓂᒋᔮᓂ ᐊᔪᕐᓇᖅᓯᒪᓂᐊᖅᑐᖅ. ᐊᓂᖅᓵᕐᓇᙱᑦᑐᒥᒃ ᐱᙳᐊᕐᓂᖅ ᐱᙳᐊᕈᑎᒥᒃ ᐱᐅᓯᑎᑦᓯᙱᑦᑐᖅ; ᓇᐃᓛᖑᑎᑦᓯᔪᖅ ᑭᓯᐊᓂ.
ᑐᕌᒐᖃᙱᑦᑐᖅ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᓂᐊᕐᓂᖏᑦ
ᐱᙳᐊᑐᐃᓐᓇᖅᐸᑦᑎᑦ ᐃᓘᓐᓇᖏᓐᓂᒃ ᐊᓯᐅᔾᔨᓐᓂᒃᑯᑦ ᐅᕝᕙᓘᓐᓃᑦ N ᑲᐃᕙᕐᓃᑦ ᑭᖑᓂᖏᓐᓂ ᓄᖅᑲᖅᓗᑎᑦ, ᐊᐱᖅᑯᑎ ᐃᒪᓐᓇᐅᓕᖅᑐᖅ “ᐱᙳᐊᕈᑎᒃᓴᒪ N ᑲᐃᕙᕐᓃᑦ ᐃᓗᐊᓂ ᓯᕉᒧᑦ ᑎᑭᓐᓂᖏᓐᓄᑦ ᐱᔪᓐᓇᕐᓂᖅ ᖃᓄᐃᓪᓗᐊᑦᑎᐊᖅ?”. N ᓇᓕᐊᒃᑲᓐᓂᓄᑦ ᐃᓱᓕᑦᑐᒥᒃ ᓈᓴᐅᑎᓕᐅᕈᑎᖃᙱᑦᑐᖅ ᑭᓯᐊᓂ ᑖᒃᑯᐊ ᐊᔾᔨᐅᖅᑕᐅᑏᑦ ᐅᕙᓂ ᓈᓴᐃᔪᑦ: $500 ᐱᙳᐊᕈᑎᒃᓴᐃᑦ $10-ᒥ ᐊᐅᐸᓗᒃᑐᒧᑦ 100 ᑲᐃᕙᕐᓂᓂ ᖃᓂᒋᔮᓂ ᐊᓯᐅᑦᑕᙱᑦᑐᑦ (1% ᐊᑖᓂ), 500 ᑲᐃᕙᕐᓂᓂ 9% ᖃᓂᒋᔮᓂ ᐊᓯᐅᕙᒃᑐᑦ, ᐊᒻᒪ 5,000-ᓂ 95% ᖃᓂᒋᔮᓂ. ᓄᖅᑲᕐᓂᕐᒧᑦ ᒪᓕᒐᖃᙱᑉᐸᑦ ᐱᔪᓐᓇᕐᓂᖅ 100%-ᒧᑦ ᖃᓂᒡᓕᕙᒃᑐᖅ, ᑖᓐᓇ ᑳᓯᓅᑉ ᐃᓚᖓᑕᓈᓴᐃᓂᖅᑳᓯᓅᑉ ᐃᓚᖓᐱᙳᐊᕈᑎ ᐊᑐᓂ ᑳᓯᓅᑉ ᐊᔾᔨᒌᒃᑎᓪᓗᒋᑦ ᐱᓯᒪᓂᖅᓴᖅᑕᖓ: ᐃᐅᕌᐸ ᕉᓚᑦᒥ 2.70%.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᑯᓂᐅᓂᖅᓴᒥ ᐱᐅᓯᖓ.
- p10 −$500
- p25 −$500
- ᐊᑯᓐᓂᐊᓃᑦᑐᖅ −$500
- p75 +$0
- p90 +$350
ᖃᓄᖅ ᐊᑯᓂ, ᖃᓄᐃᓪᓗᐊᑦᑎᐊᓪᓗ ᑮᓇᐅᔭᒃᓴᕐᓂᖅ
ᐊᓯᖏᒃ ᒪᕐᕉᒃ ᑐᖃᓂᖅᓴᐃᑦ ᓇᓂᓯᓃᒃ ᐱᙳᐊᖅᑏᑦ ᓱᓕᔪᒥᒃ ᐊᐱᖅᑯᑎᖏᓐᓂᒃ ᑭᐅᔪᒃ. ᑐᕌᒐᖃᙱᑦᑐᖅ, ᐊᔾᔨᒌᒃᑐᑦ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑏᑦ ᐊᔾᔨᒌᒃᑎᓪᓗᒋᑦ 37 ᑲᐃᕙᕐᓂᓂ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐊᑦᔨᐅᑎᖓᓄᑦ ᑕᒪᐃᓐᓄᑦ ᐃᐅᕌᐸ ᐊᒃᓴᓗᐊᖓᓂ ᐊᑐᖅᐸᒃᑐᑦ, 19-ᓂᓗ ᐊᒥᐊᓕᑲ ᐊᒃᓴᓗᐊᖓᓂ, ᑲᐃᕙᕐᓂᖅ ᑕᒪᐃᓐᓂ ᐊᔾᔨᒌᒃᑎᓪᓗᒋᑦ 1/37 ᐊᑦᔨᐅᑎᒥᒃ ᐱᕙᒻᒪᑦ (1/19 ᐊᒥᐊᓕᑲ ᐊᒃᓴᓗᐊᖓᓂ): 100 ᐊᑦᔨᐅᑏᑦ ᐊᔾᔨᒌᒃᑎᓪᓗᒋᑦ 3,700 ᑲᐃᕙᕐᓂᓂ ᐊᑐᖅᐸᒃᑐᑦ, ᑭᓯᐊᓂ ᑖᒃᑯᐊ ᐱᙳᐊᖅᑕᐅᓂᖏᑦ ᓇᑉᐸᖏᑦ 3,134 ᐃᓗᐊᓂ ᐃᓱᓕᑉᐸᒃᑐᑦ (ᐱᙳᐊᖅᑕᐅᓂᖓᑕ ᐊᑯᓂᐅᓂᖓ ᐊᑭᖓᓗ ᑕᑯᓗᒍ). ᐊᒻᒪ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᖃᓄᐃᓪᓗᐊᑦᑎᐊᖅ ᐊᖏᒋᐊᖕᒪᖔᑕ, ᐃᐅᕌᐸ ᐊᒃᓴᓗᐊᖓᓂ k ᐊᑦᔨᐅᑏᑦ ᑮᓇᐅᔭᒃᓴᕐᓂᕐᒧᑦ ᐱᔪᓐᓇᕐᓂᖅ (18/19)ᵏ. ᑖᓐᓇ 95% ᐊᑦᔨᐅᑎᒧᑦ ᐊᑕᐅᓯᕐᒧᑦ ᐊᒻᒪ 58% ᖁᓕᓐᓄᑦ, ᑭᓯᐊᓂ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᖃᓄᐃᓪᓗᐊᑦᑎᐊᖅ ᐊᖏᒋᐊᖕᒪᖔᑕ 13 ᐊᑦᔨᐅᑏᑦ ᑮᓇᐅᔭᒃᓴᕐᓂᕐᒧᑦ ᓇᑉᐸᖓᓂᒃ ᐱᔪᓐᓇᕐᓂᖃᖅᑎᑦᓯᙱᑦᑐᑦ; ᐊᒥᐊᓕᑲ ᐊᒃᓴᓗᐊᖓᓂ ᐱᔪᓐᓇᕐᓂᖅ (9/10)ᵏ ᐊᒻᒪ 7 ᐊᑦᔨᐅᑎᓂ ᓇᑉᐸᖓᑕ ᐊᑖᓄᑦ ᒥᑭᓕᖅᑐᖅ.
ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᓇᑉᐸᖓᓄᑦ ᐱᔪᓐᓇᕐᓂᕐᒧᑦ
ᐊᐱᖅᑯᑎ ᐅᑎᖅᑕᖅᑎᓪᓗᒍ: ᖃᓄᐃᓪᓗᐊᑦᑎᐊᖅ ᑎᒍᒥᐊᖅᑐᖃᕆᐊᖃᖅᐸ ᐅᓄᓐᓂᖅᐹᖑᓪᓗᓂ ᓇᑉᐸᖓᓂᒃ ᐱᔪᓐᓇᕐᓂᖃᕐᓂᕐᒧᑦ ᓇᓗᓇᐃᖅᓯᒪᔪᒥᒃ ᐊᔪᒐᕐᓂᕐᒧᑦ ᑕᒪᐃᓐᓂᒃ ᐊᓯᐅᔾᔨᓚᐅᖅᑎᓐᓇᒋᑦ? ᒥᑭᔪᒧᑦ ᐊᔪᒐᕐᓂᕐᒧᑦ, ᐊᒥᓱᓗᐊᙱᑦᑐᑦ. ᐊᖏᓂᖅᓴᒧᑦ ᐱᔭᕆᐊᖃᖅᑕᐅᔪᑦ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᓱᒃᑲᔪᒥᒃ ᐊᖏᒡᓕᕙᒃᑐᑦ, ᐊᒻᒪ ᐃᓂᒥᑦ ᐊᓂᒍᖅᑐᖅ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᓇᓕᐊᑐᐃᓐᓇᖅ ᓈᒻᒪᙱᑦᑐᑦ, ᐃᓱᖃᙱᑦᑐᐃᑦ ᓇᑉᐸᖓᑕ ᐊᑖᓂ ᐱᔪᓐᓇᕐᓂᖃᖅᑎᑦᓯᓂᐊᕐᒪᑕ ᑕᐃᑲᓄᖓ ᑮᓇᐅᔭᒃᓴᕐᓂᕐᒧᑦ. ᑕᐃᓚ (Taylor) (2021) ᐊᓯᐊᒍᑦ ᐅᖃᖅᑐᖅ: ᐊᒥᐊᓕᑲ ᐊᒃᓴᓗᐊᖓᓂ, 100 ᐊᑦᔨᐅᑎᓄᑦ ᑎᑭᓐᓂᕐᒧᑦ ᓇᑉᐸᖓᓂᒃ ᐱᔪᓐᓇᕐᓂᖃᕈᒪᒍᕕᑦ 94-ᒥᒃ ᐱᒋᐊᕆᐊᖃᖅᑐᑎᑦ, 94 ᐊᓂᖅᓵᕐᓇᕐᓂᖓᓄᑦ ᐃᓕᓪᓗᒋᑦ 6 ᐊᔪᒐᕐᓂᕐᒧᑦ. ᐃᐅᕌᐸ ᐊᒃᓴᓗᐊᖓᓂ 88 ᐱᔭᕆᐊᖃᕐᓂᐊᖅᑐᑎᑦ.
ᐊᑐᐃᓐᓇᖅ ᐃᓕᓐᓂᐊᕐᓂᖅ
ᓱᓇᒥᒃ ᐱᓇᓱᒃᑐᓂᒃ ᐃᓱᒪᓕᐅᕐᓗᑎᑦ. ᑐᕌᒐᖅ ᓇᓗᓇᐃᖅᓯᒪᔪᖅ ᐊᔪᒐᕐᓂᐅᒃᐸᑦ, ᐊᖏᔪᓂᒃ ᐊᒥᓲᓐᖏᑦᑐᓂᒡᓗ ᐱᙳᐊᕈᑎᓕᐅᕐᓗᑎᑦ. ᑐᕌᒐᖅ ᐊᑯᓂᐅᔪᖅ ᐅᓐᓄᐊᖑᒃᐸᑦ, ᒥᑭᔪᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓗᑎᑦ ᐊᒻᒪ ᑳᓯᓅᑉ ᐃᓚᖓ 2.70%-ᖓᓂᒃ ᐊᖏᔪᒥᑦ ᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᓐᓂᑦᑮᓇᐅᔭᖅᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᑦᐱᙳᐊᖅᑕᐅᓂᖓᓂ ᐅᕝᕙᓘᓐᓃᑦ ᐱᕕᒃᓴᕐᒥ ᐱᙳᐊᕈᑎᒋᔭᐅᔪᑦ ᑲᑎᓪᓗᒋᑦ, ᐊᔪᒐᐅᑎᑦ ᐱᙳᐊᕈᑎᒋᖃᑦᑕᖅᑕᐅᔪᑦ ᐃᓚᓗᒋᑦ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᕼᐋᓐᑐᓪ, ᐋᒃᓴᓐ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᓂᐊᕐᓂᖓᓂᒃ ᐊᖏᓗᑎᑦ. ᑐᕌᒐᖅ ᒪᕐᕉᖏᓐᓂᒃ ᐱᑕᖃᖅᐸᑦ, ᐊᑕᐅᓯᖅ ᐲᔭᖅᑕᐅᔭᕆᐊᖃᖅᑐᖅ, ᐊᒻᒪ ᐊᑐᕐᓗᐊᖑᔪᒥᒃ ᑐᕌᒐᖅ ᐲᔭᖅᑕᐅᕙᒃᑐᖅ.
ᓈᓴᐅᑎᓕᐅᕈᑎ
ᐊᐱᖅᑯᑏᑦ
ᒫᑎᓐᒐᐃᓪᐸᕐᓇᐅᑎᒫᑎᓐᒐᐃᓪᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᖅ ᐊᓯᐅᔾᔨᓂᖅ ᑕᒪᐃᓐᓂ ᐱᙳᐊᕈᑎ ᒪᕐᕉᕆᐊᖅᑐᖅ. ᐸᕐᓇᐅᑏᑦ ᐃᓚᖓᓂ ᑕᑯᓗᒍ ᖃᓄᐃᓕᐅᕐᓂᖓ ᖃᓄᐃᓕᐅᙱᓐᓂᖓᓗ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᖅᑕᐅᓂᖏᓐᓂ ᓇᐃᑦᑐᓂ ᒥᑭᓕᖅᑎᑦᓯᔪᖅ ᐊᑯᓂᐅᔪᓂᓪᓗ ᐊᒡᒍᐊᓗᒃ ᐊᖏᒡᓕᖅᑎᑦᓯᓪᓗᓂ. ᐊᔾᔨᒌᒃᑐᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅᐸᕐᓇᐅᑎᐊᔾᔨᒌᒃᑐᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅᑲᐃᕙᕐᓂᖅ ᑕᒪᐃᓐᓂ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ. ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᖅ ᑕᒪᐃᑦ ᑕᒪᑐᒧᖓ ᐊᔾᔨᒌᒃᓯᔭᐅᕙᒃᑐᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᖏᓂᖅᓴᒥ ᐊᑦᔨᐅᑎᒥ ᓱᓕᔪᒥᒃ ᒥᑭᓕᖅᑎᑦᓯᓯᐅᑎ.
ᐊᓂᒍᖅᑐᖅ ᓈᓴᐅᑎᓕᐅᕈᑎ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᓐᓄᑦ. ᐊᔾᔨᒌᙱᓐᓂᖓ ᐊᖏᔪᓄᑦ ᐱᙳᐊᕈᑎᓄᑦ ᐃᓘᓐᓇᖏᓐᓂᒃ ᐊᓯᐅᔾᔨᓂᖅ ᒥᑭᔪᓂ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖏᓐᓂ ᐱᔪᓐᓇᕐᓂᖅᓴᐅᔪᖅ ᐊᒻᒪ ᑐᕌᒐᖅ ᐊᔾᔨᒌᙱᑦᑐᒥᒃ ᑎᑭᑕᐅᕙᒃᑐᖅ; ᓈᓴᐅᑎᓕᐅᕈᑎ ᐊᑐᕐᓗᒍ.
ᑐᕌᒐᕐᒧᑦ ᐊᒡᕕᐊᖅᑐᖅ ᑕᒪᐃᓐᓂ ᐃᓘᓐᓇᖏᓐᓂᒃ ᐊᓯᐅᔾᔨᓂᕐᒧᑦ ᐊᒡᕕᐊᖅᑐᒥᑦ ᒥᑭᔪᒥᒃ ᐱᔪᓐᓇᕐᓂᐅᓐᖏᓂᖅᓴᐅᔪᖅ; ᐊᔾᔨᒌᙱᓐᓂᖓ ᐊᒡᕕᐊᖅᑐᑦ ᐊᒥᓲᓂᖏᑦ ᒪᓕᒃᓗᒋᑦ ᐊᖏᒡᓕᕙᒃᑐᖅ.
ᓈᓴᐃᓂᕐᒥᒃ ᐱᙳᐊᕐᓂᖅ
ᓯᕗᓪᓕᐅᓪᓗᓂ ᐃᓕᖕᓂᒃ ᐆᒃᑐᕐᓗᑎᑦ. ᑭᐅᔾᔪᑏᑦ ᐃᓗᓕᖏᑦ ᒪᑐᔭᐅᓯᒪᔪᑦ; ᐅᐸᒍᓐᓇᕈᕕᑦ ᒪᑐᐃᖅᓯᓗᒍ.
$100 ᐱᑕᖃᖅᐳᑎᑦ $1,000-ᒥᒡᓗ ᐱᓯᒪᓇᓱᒃᐳᑎᑦ, ᐊᐅᐸᓗᒃᑐᒧᑦᐱᙳᐊᕈᑎᐊᐅᐸᓗᒃᑐᖅᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎ 18 ᐊᐅᐸᓗᒃᑐᓄᑦ ᓈᓴᐅᑎᓄᑦ. ᕖᓇᓯᑐᑦ: ᕈᔾ (rouge).ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᑭᓯᐊᓂ ᐱᙳᐊᕈᑎᓕᐅᕐᓗᑎᑦ. ᓯᕗᓪᓕᖅᐹᖅ ᐸᕐᓇᐅᑎ: $1 ᐊᑕᐅᑦᑎᒃᑯᑦ ᐱᙳᐊᕈᑎᒋᓗᒍ. ᑐᓪᓕᐊ ᐸᕐᓇᐅᑎ: ᐱᑕᖃᖅᑐᑦ ᑮᓇᐅᔭᑎᑦ ᑕᒪᕐᒥᒃ ᐱᙳᐊᕈᑎᒋᓗᒋᑦ $500 ᖄᖏᕐᓂᐊᕐᓂᐊᕐᕕᓐᓄᑦ, ᑕᐃᑦᓱᒪᓂᓗ $1,000-ᒧᑦ ᑎᑭᑦᑎᓇᓱᑦᑐᓂᒃ ᑭᓯᐊᓂ. ᓇᓕᐊ ᐸᕐᓇᐅᑎ ᐱᐅᓂᖅᓴᐅᕙ, ᖃᓄᖅ ᐊᖏᑎᒋᔪᒥᒃ?
ᑭᐅᔾᔪᑎ ᑕᑯᓗᒍ
ᑭᐅᔾᔪᑎ ᑐᓪᓕᐊ ᐸᕐᓇᐅᑎ, ᐱᐅᓂᖅᓴᐅᓗᐊᖅᑐᖅ. $1,000-ᒧᑦ ᑎᑭᑦᑐᖅ ᖃᓂᒋᔭᖓ 9.0% ᐱᕕᖏᓐᓂ, ᓈᒻᒪᒃᑐᖅ 10% ᖃᓂᒋᔭᐅᓪᓗᓂᐅᒃ. ᓯᕗᓪᓕᖅᐹᖅ ᐸᕐᓇᐅᑎ ᐊᔪᕈᓐᓃᖅᑐᖅ: 10²² ᐃᓚᖏᓐᓂ ᖃᓂᒋᔭᖓ 7-ᕆᐊᖅᓗᒍ.
ᓈᒻᒪᒃᑐᒥ ᐱᙳᐊᕐᓂᕐᒥᓈᓴᐃᓂᖅᓈᒻᒪᒃᑐᖅ ᐱᙳᐊᕐᓂᖅᐱᙳᐊᕐᓂᖅ ᓇᓕᐊᑐᐃᓐᓇᖅ ᐱᐅᓂᖅᓴᐅᓂᖃᙱᑦᑐᖅ: ᐱᙳᐊᕈᑎ ᑕᒪᐃᓐᓂ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓ ᓯᕉ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → $100-ᒥᑦ $1,000-ᒧᑦ ᑎᑭᑦᑐᓐᓇᖅᑐᑎᑦ ᖁᓕᓄᑦ ᐊᑕᐅᓯᕐᒥ, ᖃᓄᐃᓕᐅᕈᑐᐃᓐᓇᕈᕕᑦ, ᑮᓇᐅᔭᑎᑦ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ ᐊᑭᖓ $100-ᒥ ᐃᓂᖃᐃᓐᓇᕐᒪᑦ.
ᑳᓯᓅᑉ ᐃᓚᖓ ᐱᙳᐊᕈᑎᐅᑉ ᑕᒪᐃᓐᓇᑕ 2.70%-ᖓᓂᒃ ᐱᔪᖅ, ᑕᐃᒪᐃᒻᒪᑦ ᑕᒪᐃᓐᓂᒃ ᐱᙳᐊᕈᑎᒋᔭᑎᑦ ᒥᑭᓂᖅᓴᐅᑎᓪᓗᒋᑦ, ᖁᓕᓄᑦ ᐊᑕᐅᓯᕐᒧᑦ ᖃᓂᒋᔭᐅᓂᖅᓴᐅᔪᑎᑦ. ᑐᓪᓕᐊ ᐸᕐᓇᐅᑎ ᐱᙳᐊᕈᑏᓐᓂ ᐊᒥᓲᙱᑦᑐᓂ ᐃᓱᓕᑦᑎᔪᖅ: $100 $200-ᖑᓕᖅᑐᖅ, $400, $800, ᑕᐃᑦᓱᒪᓂᓗ $200 ᓈᒻᒪᒃᑐᖅ. ᖃᓂᒋᔭᖓ 9.0% ᐱᕕᖏᓐᓂ ᐊᔪᒐᖅᑐᖅ. ᓯᕗᓪᓕᖅᐹᖅ ᐸᕐᓇᐅᑎ ᑕᐅᓴᓐ ᐱᙳᐊᕈᑏᓐᓂᒃ ᐱᔭᕆᐊᖃᖅᑐᖅ ᐃᓱᓕᑦᑎᓚᐅᙱᓐᓂᖓᓂ, ᑳᓯᓅᑉ ᐃᓚᖓᓗ, ᒥᑭᔪᖅ ᐱᙳᐊᕈᑎᒧᑦ ᑕᒪᑐᒧᖓ, ᑲᑎᑕᐅᓪᓗᓂ ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᓂᐊᕐᓂᖏᓐᓄᑦ ᖃᓂᒋᔭᐅᓕᖅᑐᖅ.
ᑕᒪᓐᓇ ᑐᐱᓐᔅ–ᓴᕙᔾ (Dubins–Savage) ᓇᓂᓯᓯᒪᔭᖓ ᐱᐅᓯᑐᐊᓂ (Epstein, 2013): ᑳᓯᓄ ᐱᐅᓂᖅᓴᐅᑎᑦᑕᐅᔪᒥ ᐱᙳᐊᕐᓂᕐᒥ, ᐱᔭᕆᐊᖃᖅᑕᑎᑦ ᐱᙳᐊᕈᑎᒋᓗᒍ, ᐊᒥᓲᙱᑦᑐᓂ ᐱᙳᐊᕈᑏᓐᓂ.
$500 ᐱᑕᖃᖅᐳᑎᑦ $1,000-ᒥᒡᓗ ᐱᓯᒪᓇᓱᒃᐳᑎᑦ, ᐱᓯᒪᓕᕈᕕᐅᒃ ᓄᖅᑲᕐᓗᑎᑦ. ᐱᙳᐊᕈᑎ ᐊᑕᐅᓯᖅ ᓇᓚᐅᑦᑖᕐᓗᒍ ᐅᑎᒃᑲᓐᓂᕐᓗᒍᓗ ᐊᑕᐅᓯᕐᒥ ᐊᔪᒐᕐᓂᐊᕐᓂᐊᕐᒪᑦ ᐅᕝᕙᓘᓐᓃᑦ ᑮᓇᐅᔭᑦ ᓄᙳᓂᐊᕐᓂᐊᕐᒪᑕ. ᓇᓕᐊ ᐱᔪᓐᓇᕐᓂᖅᐹᖑᕙ?
ᑭᐅᔾᔪᑎ ᑕᑯᓗᒍ
ᑭᐅᔾᔪᑎ $500 ᐊᑕᐅᓯᕐᒥ ᐊᐅᐸᓗᒃᑐᒧᑦ: 48.6%. ᐸᕐᓇᐅᑏᑦ ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᕈᑏᓐᓄᑦ ᒥᑭᓂᖅᓴᓄᑦ ᐊᕕᒃᓯᔪᑦ ᑕᒪᕐᒥᒃ ᐱᐅᓂᖅᓴᐅᙱᑦᑐᑦ.
ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ ᑕᒪᐃᓐᓇ ᓇᓚᐅᑦᑖᕐᓗᒍ ᐊᔪᒐᕐᓂᖅ ᐊᑕᐅᓯᖅ ᓈᒻᒪᖁᓪᓗᒍ: $30 ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᒥᐱᙳᐊᕈᑎᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ, ᐊᑭᓕᐅᑎ 35:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → $1,050-ᒥᒃ ᐊᔪᒐᖅᑐᖅ, $60 ᒪᕐᕉᓄᑦ ᐱᙳᐊᕈᑎᒥᐱᙳᐊᕈᑎᒪᕐᕉᓄᑦ ᐱᙳᐊᕈᑎᒪᕐᕉᒃ ᓈᓴᐅᑏᒃ ᓴᓂᓕᐅᑎᒌᒃᑐᒃ, ᐊᑭᓕᐅᑎ 17:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → $1,020-ᒥᒃ ᐊᔪᒐᖅᑐᖅ, ᐊᓯᖏᓪᓗ. ᑕᐃᑦᓱᒪᓂ ᓈᓴᓗᒍ ᐱᔪᓐᓇᕐᓂᖅ ᐊᑕᐅᓯᕐᒥᒃ ᐅᖓᑖᓂᓘᓐᓃᑦ ᐱᙳᐊᕈᑎ ᐊᔪᒐᕐᓂᖓᓄᑦ ᑮᓇᐅᔭᑦ ᓄᙳᓚᐅᙱᓐᓂᖏᓐᓂ. ᖁᓕᑦ ᐱᖓᓲᔪᖅᑐᓪᓗ $30 ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑏᑦ ᑕᒪᕐᒥᒃ ᐊᓯᐅᔾᔨᔪᑦ ᐱᔪᓐᓇᕐᓂᓕᒃ (36/37)¹⁶ = 64.5%, ᑕᐃᒪᐃᒻᒪᑦ $1,000-ᒧᑦ ᑎᑭᑦᑐᑦ 35.5% ᐱᕕᖏᓐᓂ.
ᓈᓴᐅᑎᓕᐊᑦ ᐱᙳᐊᕈᑎ ᑕᒪᐃᓐᓇ ᑕᑯᑎᑦᓯᔪᑦ. ᐊᐅᐸᓗᒃᑐᖅ ᐱᐅᓂᖅᐹᖑᔪᖅ ᐱᙳᐊᕈᑎᒥ ᐊᑕᐅᓯᕐᒥ ᑎᑭᑦᑐᓐᓇᕐᒪᑦ, ᑕᐃᒪᐃᒻᒪᑦ ᑳᓯᓅᑉ ᐃᓚᖓ ᐊᑕᐅᓯᕐᒥ ᐊᑭᓕᖅᑕᐅᔪᖅ, $500-ᒥ. ᐱᖓᓲᔪᖅᑐᓄᑦ ᐱᙳᐊᕈᑎᐱᙳᐊᕈᑎᐱᖓᓲᔪᖅᑐᓄᑦ ᐱᙳᐊᕈᑎᐱᖓᓲᔪᖅᑐᑦ ᓈᓴᐅᑏᑦ ᒪᕐᕉᓐᓂ ᓴᓂᓕᐅᑎᒌᒃᑐᓂ ᑐᑭᓕᐊᓂ, ᐊᑭᓕᐅᑎ 5:1. ᕖᓇᓯᑐᑦ: ᓯᓴᓐ (sixain).ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᑐᓪᓕᐊᓂ ᐃᓂᖃᖅᑐᖅ ᐱᖓᓱᓂᒃ ᑭᓯᐊᓂ ᐱᔭᕆᐊᖃᕐᒪᑦ. ᑕᓴᓐᐱᙳᐊᕈᑎᑕᓴᓐ1–12, 13–24 ᐅᕝᕙᓘᓐᓃᑦ 25–36, ᐊᑭᓕᐅᑎ 2:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᕈᑎ ᐊᑕᐅᓯᖅ ᐱᐅᙱᓐᓂᖅᐹᖑᔪᖅ, 12/37 ᐱᔪᓐᓇᕐᓂᓕᒃ; $250 ᐊᑦᔨᐅᑏᓐᓂᑮᓇᐅᔭᖅᐊᑦᔨᐅᑎᐸᕐᓇᐅᑎᐅᑉ ᐅᕝᕙᓘᓐᓃᑦ ᐱᙳᐊᖅᑎᐅᑉ ᑐᙵᕕᒋᔭᖓ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ. ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᐅᔪᑦ ᐊᑦᔨᐅᑎᓄᑦ ᓇᓗᓇᐃᖅᑕᐅᕙᒃᑐᑦ, ᑕᐃᒪ ᓇᓕᐊᓂᑐᐃᓐᓇᖅ ᐱᙳᐊᕐᕕᒻᒥ ᐊᑐᕈᓐᓇᖁᓪᓗᒋᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᖅᑕᐅᒐᓗᐊᖅᑎᓪᓗᒍ $1,000 ᐅᖓᑖᓄᓘᓐᓃᑦ ᐱᓯᒪᓕᕐᓂᐊᕐᓂᐊᕐᕕᓐᓄᑦ, ᑕᓴᓐ 46.4% ᐱᕕᖏᓐᓂ ᑭᓯᐊᓂ ᑎᑭᑦᑐᖅ.
ᐳᓪᒪᓐ (Bollman, 2024) ᐊᔾᔨᒋᔭᐅᔪᒥᒃ ᓈᓴᐅᑎᓕᐊᓕᐅᖅᑐᖅ ᐊᒥᐊᓕᑲ ᐊᒃᓴᓗᐊᖓᓄᑦ. ᑕᓴᓐ ᑐᑭᖓ ᑕᒻᒪᖅᑐᖃᖅᑐᖅ: ᑎᑎᕋᖅᓯᒪᓴᕆᐊᖃᖅᑐᖅ 12/38 = 31.6%.
ᐱᙳᐊᕈᑎᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ × ᐱᙳᐊᕈᑏᑦ ᐊᒥᓲᓂᖏᑦ$1,000-ᒧᑦ ᑎᑭᑦᑐᓐᓇᕐᓂᖅᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎ$30 × 1635.5%ᒪᕐᕉᓄᑦ ᐱᙳᐊᕈᑎ$60 × 835.9%ᐱᖓᓱᓄᑦ ᐱᙳᐊᕈᑎ$90 × 534.5%ᓯᑕᒪᓄᑦ ᐱᙳᐊᕈᑎ$125 × 436.7%ᐱᖓᓲᔪᖅᑐᓄᑦ ᐱᙳᐊᕈᑎ$166, $166, $16841.2%ᑕᓴᓐ$500 × 132.4%ᐊᐅᐸᓗᒃᑐᖅ$500 × 148.6%ᐊᑦᔨᐅᑎ ᐊᑕᐅᓯᖅ ᐊᐅᐸᓗᒃᑐᒧᑦ ᐱᙳᐊᕈᑎᒋᕙᒃᑕᑎᑦ, ᑲᐃᕙᕐᓂᖅ ᑲᐃᕙᕐᓂᕐᒧᑦ, ᐱᙳᐊᕈᑎᒃᓴᖃᖅᓗᑎᑦᑮᓇᐅᔭᖅᐱᙳᐊᕈᑎᒃᓴᐃᑦᑮᓇᐅᔭᑦ ᐃᓘᓐᓇᖏᑦ ᐱᙳᐊᕐᓂᕐᒧᑦ ᐊᕕᒃᓯᒪᔭᐅᔪᑦ. ᐱᙳᐊᕈᑎᒃᓴᓂᒃ ᐊᐅᓚᑦᓯᓂᖅ ᑐᑭᖃᖅᑐᖅ ᖃᔅᓯᑦ ᐱᙳᐊᕈᑎ ᐊᑐᓂ ᐱᙳᐊᖅᑕᐅᓂᖓᓂᓗ ᐊᑐᓂ ᐊᓯᐅᔪᓐᓇᖅᑕᐅᓂᐊᕐᒪᖔᑕ ᐃᓱᒪᓕᐅᕐᓂᕐᒥᒃ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᓄᙳᕈᓐᓇᙱᑦᑐᓂᒃ. ᓯᕗᓪᓕᖅᐹᖅ ᑲᐃᕙᕐᓂᖅ ᐊᓂᒍᖅᑎᓪᓗᒍ ᐊᑦᔨᐅᑎᒥᒃ ᐊᑕᐅᓯᕐᒥᒃ ᐊᔪᒐᖅᓯᒪᔪᑎᑦ ᐅᕝᕙᓘᓐᓃᑦ ᐊᓯᐅᔾᔨᓯᒪᔪᑎᑦ. ᖃᓄᐃᑦᑐᒥᒃ ᐱᔪᓐᓇᕐᓂᖃᖅᐸᑦ ᐊᔪᒐᙱᓪᓗᑎᑦ ᐊᓯᐅᔾᔨᙱᓪᓗᑎᓪᓗ ᓱᓕᓪᓚᕆᒃ ᐅᑎᕐᓂᐊᕐᓂᕐᒥᒃ?
ᑭᐅᔾᔪᑎ ᑕᑯᓗᒍ
ᑭᐅᔾᔪᑎ 37 ᐃᓚᖏᓐᓂ 36, 97.3%. ᐊᒥᐊᓕᑲ ᐊᒃᓴᓗᐊᖓᓂ 38 ᐃᓚᖏᓐᓂ 36, 94.7%.
ᓯᕗᓪᓕᖅᐹᖅ ᑲᐃᕙᕐᓂᖅ ᐊᔪᒐᖅᐸᑦ (37 ᐃᓚᖏᓐᓂ 18), ᐊᑦᔨᐅᑎᒥᒃ ᐊᑕᐅᓯᕐᒥᒃ ᐊᔪᒐᖅᓯᒪᔪᑎᑦ, ᑳᓯᓅᓪᓗ ᐃᓚᖓ ᐱᙳᐊᖅᑕᐅᓂᖏᑦ ᓄᖅᑲᙱᑦᑐᑦ ᑕᒪᕐᒥᒃ ᐊᑖᓄᑦ ᓄᓱᒃᐸᒃᑕᖏᑦ, ᑕᐃᒪᐃᒻᒪᑦ ᑭᖑᓂᐊᒍᑦ ᐊᔪᒐᙱᓪᓗᑎᑦ ᐊᓯᐅᔾᔨᙱᓪᓗᑎᓪᓗ ᐅᑎᕐᓂᐊᖅᑐᑎᑦ: ᑕᒪᓐᓇ ᖃᐅᔨᒪᔭᐅᔪᖅ. ᐊᓯᐅᔾᔨᑉᐸᑦ (37 ᐃᓚᖏᓐᓂ 19), ᐊᑦᔨᐅᑎᒥᒃ ᐊᑕᐅᓯᕐᒥᒃ ᖁᕝᕙᖅᓯᔭᕆᐊᖃᖅᑐᑎᑦ, ᐊᑦᔨᐅᑎᒥᒡᓗ ᐊᑕᐅᓯᕐᒥᒃ ᓯᕗᓪᓕᐅᓂᐊᕐᓂᕐᒧᑦ ᐱᔪᓐᓇᕐᓂᖅ 18/19 (ᖁᓛᓂ ᓈᓴᐅᑎᓕᐊᑦ ᑕᑯᓗᒋᑦ).
ᐊᑕᐅᑦᑎᒃᑯᑦ: 18/37 + 19/37 × 18/19 = 18/37 + 18/37 = 36/37.
ᑕᒪᐃᓐᓂ ᐱᔪᓐᓇᕐᓂᖅ 1 ᐊᑯᕐᖓᓂᑦ ᐲᖅᑕᐅᓪᓗᓂ ᑲᐃᕙᕐᓂᕐᒥ ᐊᔪᒐᕐᓂᐅᑉ ᐊᓯᐅᔾᔨᓂᐅᓪᓗ ᐱᔪᓐᓇᕐᓂᖏᑕ ᐊᑯᕐᖏᓐᓂᑦ: 1 − 1/37 ᐃᐅᕌᐸ ᐊᒃᓴᓗᐊᖓᓂ, 1 − 2/38 ᐊᒥᐊᓕᑲ ᐊᒃᓴᓗᐊᖓᓂ. ᓯᕉᐊᒃᓴᓗᐊᖅᓯᕉᐊᑕᐅᓯᖅ ᐅᔾᔪᐊᕌᔭᒃ ᐃᓂ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᖕᓄᑦ, ᑕᓴᓐᓄᑦ ᓇᑉᐸᖅᑐᓄᓪᓘᓐᓃᑦ ᐱᙳᐊᕈᑏᑦ ᐃᓚᐅᑎᙱᑕᖓ; ᑳᓯᓅᑉ ᐃᓚᖓᑕ ᐱᓇᓪᓗᑎᖓ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐊᑕᐅᓯᖅ ᓯᕉ, 0.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →ᖃᙱᑦᑐᒥ ᐱᙳᐊᕐᓂᕐᒥ ᐊᑯᕐᖓ ᓄᙳᔪᖅ ᐱᔪᓐᓇᕐᓂᕐᓗ 1: ᓈᓴᐅᑎ ᐊᔪᒐᙱᓪᓗᓂ ᐊᓯᐅᔾᔨᙱᓪᓗᓂ ᐅᑎᖅᐸᒃᑐᖅ. ᐃᑉᔅᑕᐃᓐ (Epstein, 2013) ᒪᓕᒐᕐᒥᒃ ᑕᒪᐃᓐᓄᑦ ᑐᓂᓯᔪᖅ.
ᐸᓯᑲᓪ (Pascal) 1656-ᒥ ᐊᐱᖅᑯᑎᖓ: ᐱᙳᐊᖅᑏᒃ ᐱᖓᓱᓂᒃ ᐱᙳᐊᒃᑲᓐᓂᕐᓂᒃ ᐃᒋᔪᒃ, ᑕᒪᒃᑭᓄᑦ 12 ᓈᓴᐅᓯᐅᑎᓂᒃ ᐱᒋᐊᖅᑐᒃ. 11 ᑕᒪᐃᓐᓇ ᓈᓴᐅᓯᐅᑎᒥᒃ ᓯᕗᓪᓕᖅᐹᒧᑦ ᐱᙳᐊᖅᑎᒧᑦ ᓄᑦᑕᖅᑎᑦᓯᔪᖅ, 14 ᑕᒪᐃᓐᓇ ᑐᓪᓕᐊᓄᑦ; ᐊᓯᖏᑦ ᐃᒋᓃᑦ ᐃᓚᐅᙱᑦᑐᑦ. ᓯᕗᓪᓕᖅᐹᖅ ᐱᙳᐊᖅᑎ 24 ᑕᒪᕐᒥᒃ ᐊᔪᒐᕐᓂᕐᒧᑦ ᖃᓄᖅ ᐱᔪᓐᓇᕐᓂᖃᖅᐸ? ᐊᐅᐸᓗᒃᑐᒧᓪᓗ 1 ᐊᑦᔨᐅᑎᒥᒃ ᑲᐃᕙᕐᓂᕐᒥ ᑕᒪᐃᓐᓂ ᐱᙳᐊᕈᑎᓕᐅᕈᕕᑦ ᐱᓗᐊᖅᑕᐃᑦ ᐊᑐᓂ ᑳᓯᓅᑐᐃᓐᓇᖅᑐᖅ, ᑕᒪᒃᑭᓄᑦ 12 ᐊᑦᔨᐅᑏᑦ, 24 ᑕᒪᕐᒥᒃ ᐊᔪᒐᕐᓂᕐᒧᑦ ᖃᓄᖅ ᐱᔪᓐᓇᕐᓂᖃᖅᐸᑦ?
ᑭᐅᔾᔪᑎ ᑕᑯᓗᒍ
ᑭᐅᔾᔪᑎ ᓯᕗᓪᓕᖅᐹᖅ ᐱᙳᐊᖅᑎ ᐊᔪᒐᖅᑐᖅ ᖃᓂᒋᔭᖓ 1,158 ᐃᓚᖏᓐᓂ 1,157. ᐃᓕᖅᐱᑦ, ᐊᐅᐸᓗᒃᑐᒧᑦ, 24 ᐊᑦᔨᐅᑏᑦ ᑕᒪᕐᒥᒃ ᐊᔪᒐᖅᑐᑎᑦ ᖃᓂᒋᔭᖓ 34% ᐱᕕᖏᓐᓂ ᑭᓯᐊᓂ.
ᐱᖓᓱᑦ ᐱᙳᐊᒃᑲᓐᓂᖅ 11-ᒥᒃ ᓴᖅᑭᑦᑎᔪᑦ 27-ᓄᑦ ᐱᐅᓯᓄᑦ 14-ᒥᒡᓗ 15-ᓄᑦ ᐱᐅᓯᓄᑦ, ᑕᐃᒪᐃᒻᒪᑦ ᓈᓴᐅᓯᐅᑎ ᓄᑦᑕᖅᑐᖅ ᑕᒪᐃᓐᓇ ᓯᕗᓪᓕᖅᐹᒧᑦ ᐱᙳᐊᖅᑎᒧᑦ ᐃᖏᕐᕋᔪᖅ 42 ᐃᓚᖏᓐᓂ 27, 14 ᐃᓚᖏᓐᓂ 9. ᐊᓪᓚᖓ ᑕᒪᐃᓐᓇ 12-ᒥ ᐱᒋᐊᖅᑎᓪᓗᒍ, ᑕᒪᐃᓐᓂᒃ ᐱᓂᕐᒧᑦ ᐱᔪᓐᓇᕐᓂᖅ 1/(1 + r¹²), r ᐊᓯᐊᑕ ᐱᔪᓐᓇᕐᓂᖓ ᐃᓕᖃᓄᑦ ᐊᔾᔨᒌᙱᓐᓂᖓ.
ᓯᕗᓪᓕᖅᐹᒧᑦ ᐱᙳᐊᖅᑎᒧᑦ r = 5/9, (5/9)¹² ≈ 0.00086-ᓗ, ᑕᐃᒪᐃᒻᒪᑦ ᐱᔪᓐᓇᕐᓂᖅ ᖃᓂᒋᔭᖓ 0.99914: ᐱᔪᓐᓇᕐᓂᖏᑦ ᐊᔾᔨᒌᙱᓐᓂᖏᑦ 9¹² 5¹²-ᒧᑦ, ᐅᕝᕙᓘᓐᓃᑦ 282,429,536,481 244,140,625-ᒧᑦ, ᖃᓂᒋᔭᖓ 1,157, 1-ᒧᑦ. ᕼᐃᐅᒍᓐᔅ (Huygens) ᑕᒪᒃᑯᓂᖓ ᓈᓴᐅᑎᓂᒃ ᓱᓕᓪᓚᕆᒃᑐᓂᒃ ᓈᓚᐅᑎᓕᐅᖅᓯᒪᔪᖅ 1657-ᒥ.
ᐊᐅᐸᓗᒃᑐᒥ, r = 19/18 ᓯᕉ ᐱᔾᔪᑎᒋᓪᓗᒍ, (19/18)¹² ≈ 1.913-ᓗ: ᐱᔪᓐᓇᕐᓂᖅᐱᑦ 1/2.913 ≈ 34.3%. ᑮᓇᐅᔭᓯᐊᖅ ᐃᒋᓪᓗᒍ 50% ᐱᔪᓐᓇᕐᓂᖃᕐᓂᐊᖅᑐᖅ. 2.70% ᑳᓯᓅᑉ ᐃᓚᖓ ᐱᙳᐊᕈᑎᒥ ᑕᒪᐃᓐᓂ ᑲᑎᑕᐅᔪᖅ, ᐱᙳᐊᕈᑏᓐᓂ ᐊᒥᓱᓂ ᐱᔭᕆᐊᖃᖅᑐᓂ, 16 ᓈᓴᐅᑎᓂᒃ ᐊᑯᕐᖓᓄᑦ.
ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ
ᐊᓂᖅᓵᕐᓇᙱᑦᑐᒥᒃ ᐱᙳᐊᕐᓂᖅ ᐱᐅᓛᖑᔪᖅ. ᓱᒃᑲᔪᒥᒡᓗ ᐃᓱᓕᑉᐸᒃᑐᖅ.
ᐱᕝᕕᒋᔭᐅᔪᑦ
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- 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.
- Carcavi, P. de. ᕼᐊᐃᒐᓐᔅᒧᑦ ᑎᑎᖅᑲ, ᓯᑎᐱᕆ 28, 1656, ᐸᓯᑲᓪ ᕗᐊᒫᒧᑦ ᑐᓂᓯᓯᒪᔭᖓᓂᒃ ᐊᐱᖅᑯᑎᒥᒃ.
- Huygens, C. De Ratiociniis in Ludo Aleae.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Reuters. “Briton bets it all on roulette spin, and wins.”
- Las Vegas Sun. “Man wagers life’s worth.”