ᐊᐱᖅᑯᑎ: ᑕᓴᓐ ᒪᕐᕉᒃ ᓯᑉᓗ ᐊᑕᐅᓯᖅ
ᑕᓴᓐ ᒪᕐᕉᒃ 24 ᓈᓴᐅᑏᑦ ᐱᙳᐊᕈᑎᒋᔪᒃ. ᓯᑉ ᓯᕉᒧᑦ ᐃᓚᓗᒍ, 25 ᐱᙳᐊᕈᑎᒋᓕᖅᑕᑎᑦ. ᓴᐳᔾᔨᔾᔪᑎ ᐃᑲᔪᖅᐸ?

ᐋᒃᑲ. ᐃᓚᖏᑦ ᐊᑐᓂ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᑕ −2.70%-ᖓ, ᑕᐃᒪ ᑲᑎᑕᐅᓂᖏᑦ ᐃᓘᓐᓇᖓᑕ −2.70%-ᖓ. ᐊᐱᖅᑯᑎ ᐅᓇ ᓱᒻᒪᑦ ᐃᒪᐃᒻᒪᖔᑦ ᓇᓗᓇᐃᖅᓯᔪᖅ, ᐊᕕᒃᓯᒪᓂᖏᓐᓂᒃ ᓱᓕᔪᒥᒃ ᓈᓴᐃᔪᖅ, ᑕᑯᑎᑦᓯᔪᓪᓗ ᓱᓇ ᐊᓯᑦᑐᕐᒪᖔᑦ (ᐱᐅᓯᖓ) ᓱᓇᓗ ᐊᓯᑦᑐᙱᒻᒪᖔᑦ (ᐊᑭᖓ).
ᐊᐱᖅᑯᑎ
$10-ᒥᒃ ᓯᕗᓪᓕᖅᐹᒧᑦ ᑕᓴᓐᒧᑦᐱᙳᐊᕈᑎᑕᓴᓐ1–12, 13–24 ᐅᕝᕙᓘᓐᓃᑦ 25–36, ᐊᑭᓕᐅᑎ 2:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᕈᑎᓕᐅᖅᑐᑎᑦ, $10-ᒥᒃ ᑐᓪᓕᐊᓄᑦ ᑕᓴᓐᒧᑦ, $1-ᒥᒡᓗ ᓯᕉᒧᑦᐊᒃᓴᓗᐊᖅᓯᕉᐊᑕᐅᓯᖅ ᐅᔾᔪᐊᕌᔭᒃ ᐃᓂ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᖕᓄᑦ, ᑕᓴᓐᓄᑦ ᓇᑉᐸᖅᑐᓄᓪᓘᓐᓃᑦ ᐱᙳᐊᕈᑏᑦ ᐃᓚᐅᑎᙱᑕᖓ; ᑳᓯᓅᑉ ᐃᓚᖓᑕ ᐱᓇᓪᓗᑎᖓ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐊᑕᐅᓯᖅ ᓯᕉ, 0.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →. (a) ᓴᖅᑭᔪᓐᓇᖅᑐᑦ ᐱᔪᓐᓇᕐᓂᖏᓪᓗ ᖃᓄᐃᑦᑑᕙᑦ? (b) ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓᓈᓴᐃᓂᖅᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓᐱᙳᐊᕈᑎ ᐊᑐᓂ ᐊᑯᓂᐅᓂᖅᓴᒥ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ ᐱᓐᓂᖓ. ᐃᐅᕌᐸ ᐱᙳᐊᕈᑎ ᑕᒪᐃᓐᓂ −1/37 ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᓂᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᖃᓄᐃᑦᑑᕙ? (c) ᓯᕉᒧᑦ ᓯᑉᑮᓇᐅᔭᖅᓯᑉᓇᓗᓇᐃᒃᑯᑎ ᐊᑭᖃᐃᓐᓇᖅᑐᖅ, ᐱᙳᐊᕈᑎᓕᕆᕝᕕᖕᒥ ᐃᓕᔭᐅᔪᖅ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᕐᒧᑦ. ᐊᓯᐊᓂ ᐊᑎᖓ: ᓯᐊᒃ (check).ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᕈᑎᒥᒃ ᐱᐅᓯᑦᑎᕙ?
ᑭᐅᔾᔪᑎ (a) (b)-ᓗ
ᓴᖅᑭᔪᓐᓇᖅᑐᑦ: ᐊᖅᓴᖅᐊᑐᖅᑕᐅᔪᑦᐊᖅᓴᖅᒥᑭᔪᖅ ᐊᖅᓴᖅ ᐊᖁᑎᖓᓂ ᑲᐃᕙᖅᑐᑉ ᐊᑉᐱᖓᓄᑦ ᐃᒋᑕᐅᔪᖅ. ᒫᓐᓇᐅᔪᖅ ᐊᖅᓵᑦ ᐃᕗᕆᓐ ᐅᕝᕙᓘᓐᓃᑦ ᑎᕙᓚᓐ, 18–21 mm.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → 1–24-ᒥ (24 ᐃᓂᑦᐊᑐᖅᑕᐅᔪᑦᐃᓂᑲᐃᕙᖅᑐᒥ 37 ᓈᓴᐅᑎᓕᑦ ᐃᓂᑦ ᐊᑕᐅᓯᖓ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐃᓂᒋᐊᖅ, ᖃᓪᓗᐊᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →): ᑕᓴᓐ ᐊᑕᐅᓯᖅ $20-ᒥᒃ ᐊᑭᓕᖅᑐᖅ, ᐊᓯᖓ $10-ᒥᒃ ᐊᓯᐅᔾᔨᔪᖅ, ᓯᕉ $1-ᒥᒃ ᐊᓯᐅᔾᔨᔪᖅ: ᑲᑎᑕᐅᔪᑦ +$9. ᐊᖅᓴᖅ 25–36-ᒥ (12 ᐃᓂᑦ): ᑕᓴᓐ ᒪᕐᕉᒃ ᐊᓯᐅᔾᔨᔪᒃ, ᓯᕉᓗ ᐊᓯᐅᔾᔨᔪᖅ: −$21. ᐊᖅᓴᖅ ᓯᕉᒥ (1 ᐃᓂ): ᑕᓴᓐᑦ $20-ᒥᒃ ᐊᓯᐅᔾᔨᔪᑦ, ᓯᕉ $35-ᒥᒃ ᐊᑭᓕᖅᑐᖅ: +$15. EV = (24 × 9 + 1 × 15 − 12 × 21)/37 = (216 + 15 − 252)/37 = −21/37 ≈ −$0.57 ᑲᐃᕙᕐᓂᕐᒧᑦ, $21 ᐱᙳᐊᕈᑎᐅᑎᓪᓗᒍ: 2.70%.
ᑭᐅᔾᔪᑎ (c)
ᓯᕉᒧᑦ ᓯᑉᖃᙱᑦᑎᓪᓗᒍ: (24 × 10 − 13 × 20)/37 = (240 − 260)/37 = −20/37 ≈ −$0.54, $20 ᐱᙳᐊᕈᑎᐅᑎᓪᓗᒍ, ᐊᒻᒪᓗᑦᑕᐅᖅ 2.70%. ᓯᕉᒧᑦ ᓯᑉ ᓯᕉ ᓴᖅᑭᒃᐸᑦ −$20-ᒥᒃ +$15-ᒧᑦ ᐊᓯᑦᑐᖅᓯᔪᖅ ($35-ᒥᒃ ᐱᐅᓯᑦᑎᓂᖅ 37-ᓂ ᐊᑕᐅᓯᐊᓂ, ᑲᐃᕙᕐᓂᕐᒧᑦ $0.95-ᒥᒃ ᐊᑭᓕᒃ), ᐊᑭᖃᖅᑐᓗ $1-ᒥᒃ ᐊᓯᖏᓐᓂ 36 ᑲᐃᕙᕐᓂᓂ (ᑲᐃᕙᕐᓂᕐᒧᑦ $0.97). ᐊᓯᑦᑐᕐᓂᖅ: −$0.03 ᑲᐃᕙᕐᓂᕐᒧᑦ, ᑕᒪᓐᓇ ᐃᓚᒋᐊᖅᑕᐅᔪᖅ ᑕᐃᓚ ᐊᑕᐅᓯᐅᑉ 2.70%-ᖓ. ᓴᐳᔾᔨᔾᔪᑎ ᐊᑭᖃᖅᑐᖅ ᓱᓕᓪᓚᕆᒃᑐᒥᒃ ᐊᓯᖏᑎᑐᑦ.
ᓱᒻᒪᑦ ᑕᒪᐃᓐᓄᑦ ᐊᑐᕐᒪᑦ
ᓂᕆᐅᒋᔭᐅᔪᑦ ᐊᑭᖏᑦ ᑲᑎᑕᐅᔪᓐᓇᖅᑐᑦ. ᐱᙳᐊᕈᑏᑦ ᐃᓚᒌᒃᑐᑦ ᐊᑕᐅᑦᑎᒃᑯᑦ ᐱᙳᐊᕈᑎᐅᔪᑦ EV-ᖏᑦ ᐃᓚᖏᑦ EV-ᖏᑕ ᑲᑎᑕᐅᓂᖏᑦ, ᐊᑐᓂᓗ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᑕ −1/37-ᖓ. ᑕᐃᒪ ᓇᓪᓕᐊᑐᐃᓐᓇᖅ ᑲᑎᑕᐅᓂᖅ ᐱᙳᐊᕈᑏᑦ ᑮᓇᐅᔭᖏᑕ ᐃᓘᓐᓇᖏᑕ −1/37-ᖓ. ᐱᙳᐊᕈᑎᓕᕆᕝᕕᖕᒥᐊᑐᖅᑕᐅᔪᑦᐱᙳᐊᕈᑎᓕᕆᕝᕕᒃᐱᙳᐊᕐᕕᒻᒥ ᑎᑎᕋᖅᓯᒪᔪᑦ ᐱᙳᐊᕈᑏᑦ ᐊᓪᓚᖏᑦ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐱᙳᐊᕐᕕᒃ, ᐅᓗᐱᓕᒐᖅ, ᐊᓐᓄᕌᒃᓴᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᓯᑉᐳᑦ ᖃᓄᐃᑦᑐᒥᒃ ᐃᓕᔭᐅᒃᑲᓗᐊᖅᐸᑕ, ᖃᑦᓯᐅᒃᑲᓗᐊᖅᐸᑕ, ᑕᒪᑐᒥᖓ ᖁᐃᓐᓇᔪᓐᓇᙱᑦᑐᑦ; ᐱᙳᐊᕈᑎᓕᐅᕈᑎ ᓴᓇᕐᕈᑎ ᓇᓗᓇᐃᖅᓯᓂᐊᖅᑐᖅ ᐃᓕᔪᓐᓇᖅᑕᑎᓐᓂᒃ ᐃᓘᓐᓇᖏᓐᓂ. ᑲᑎᑕᐅᓃᑦ ᐊᓯᑦᑐᖅᓯᔭᖏᑦ ᐊᕕᒃᓯᒪᓂᖏᑦ: ᖃᓄᖅ ᐊᑲᐅᓪᓗ ᐊᔪᒐᖅᐸᓚᐅᕐᓂᐊᕐᒪᖔᖅᐱᑦ, ᖃᓄᐃᓪᓗ ᐊᒥᓱᓂᒃ, ᐱᐅᙱᓛᖅᓗ ᖃᓄᐃᑦᑑᓂᐊᕐᒪᖔᑦ.
ᐊᔪᓂᖅᓴᖅ ᑐᓪᓕᐊ ᐊᐱᖅᑯᑎ
ᐱᙳᐊᕈᑏᑦ ᐊᑐᖅᑕᐅᒐᔪᒃᑐᑦ ᑲᑎᑕᐅᓂᖏᓐᓂᒃ 37 ᓈᓴᐅᑏᑦ ᐃᓘᓐᓇᖏᓐᓂᒃ ᐱᙳᐊᕈᑎᒋᔪᓂᒃ ᓇᓂᓯᓗᑎᑦ. ᑕᓴᓐ ᐱᖓᓱᑦ (ᐊᑐᓂ $10) $1-ᓗ ᓯᕉᒧᑦ: 1–36-ᒥ ᓇᓪᓕᐊᑐᐃᓐᓇᖅ −$1 (ᑕᓴᓐ ᐊᑕᐅᓯᖅ $20-ᒥᒃ ᐊᑭᓕᖅᑐᖅ, ᐊᓯᖏᒃ ᒪᕐᕉᒃ $20-ᒥᒃ ᐊᓯᐅᔾᔨᔪᒃ, ᓯᕉ $1-ᒥᒃ ᐊᓯᐅᔾᔨᔪᖅ), ᓯᕉᓗ +$35 − $30 = +$5. EV = (36 × (−1) + 5)/37 = −31/37, $31 ᐱᙳᐊᕈᑎᐅᑎᓪᓗᒍ: 2.70%. ᑕᒪᐃᓐᓂ ᑕᑯᓐᓇᐃᓐᓇᕆᐊᖃᙱᑦᑐᖅ ᐃᒪᐃᓐᓂᐊᕐᓂᖓᓂᒃ ᓇᓗᓇᐃᖅᓯᔪᓐᓇᖅᑐᑎᑦ, ᑭᓯᐊᓂ ᓱᓕ ᐊᔾᔨᒋᔭᖓᓂᒃ ᐊᑭᓕᖅᑐᑎᑦ ᑕᒪᑐᒧᖓ.
ᓈᓴᐅᑎᓕᐅᕈᑎ
ᐊᐱᖅᑯᑏᑦ
ᐋᒃᑲ, ᐃᐅᕌᐸ ᐱᙳᐊᕐᕕᖓᓂ. ᕖᓇᓯ ᐱᙳᐊᕐᕕᖓᓂ, ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑏᑦᐱᙳᐊᕈᑎᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎᐊᐅᐸᓗᒃᑐᖅ/ᕿᕐᓂᖅᑐᖅ, ᐊᕕᒃᑕᐅᔪᓐᓇᙱᑦᑐᖅ/ᐊᕕᒃᑕᐅᔪᓐᓇᖅᑐᖅ, ᐊᖏᔪᑦ/ᒥᑭᔪᑦ. 18 ᓈᓴᐅᑏᑦ, ᐊᑭᓕᐅᑎ 1:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᑐᐊᖅ 1.35%; ᐊᓯᐊ ᐃᓚᒋᐊᖅᐸᑦ ᑳᓯᓅᑉ ᐃᓚᖓ ᐃᓚᒌᖅᑎᑕᐅᔪᖅ ᐊᖏᓕᖅᑐᖅ.
ᓯᕉ ᓴᖅᑭᒃᐸᑦ ᑐᐊᖅ $1-ᒧᑦ $1-ᒥᒃ ᐊᓯᐅᔾᔨᔪᖅ, ᐊᓯᐊᒍᑦ ᓱᓇᒥᒡᓗ ᐊᔪᒐᙱᑦᑐᖅ. EV −2.70%, ᐱᐅᔪᖃᙱᑦᑐᖅ: ᑲᑎᑕᐅᓂᖅ ᐊᑕᐅᓯᖅ ᓱᓕᓪᓚᕆᒃᑐᒥᒃ ᐱᔾᔪᑎᖃᙱᑦᑐᖅ.
ᐱᙳᐊᖅᑕᐅᓂᖓᑕ ᐱᐅᓯᖓᓂᒃ ᖁᕕᐊᓱᒡᓗᒍ ᓇᓚᐅᑦᑖᕐᓂᐊᕐᓗᒍ. ᑕᒪᓐᓇ ᓱᓕᔪᖅ ᐱᔾᔪᑎ, ᐊᑕᐅᓯᐊᖑᓪᓗᓂᓗ.
ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ

ᕉᓚᑦ ᐱᙳᐊᕐᕕᖓᓂ ᓴᐳᔾᔨᔾᔪᑎ ᓱᓕᓪᓚᕆᒃᑐᒥᒃ ᓴᐳᔾᔨᔭᒥᓂᒃ ᐊᑭᖃᖅᑐᖅ.
ᐱᕝᕕᒋᔭᐅᔪᑦ
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.