ᕉᓚᑦ: ᓈᓴᐃᓂᖅ · ᓈᓴᐃᓂᕐᒧᑦ ᐊᐱᖅᑯᑎ · 7 ᒥᓂᑦ

ᐊᐱᖅᑯᑎ: ᑕᓴᓐ ᒪᕐᕉᒃ ᓯᑉᓗ ᐊᑕᐅᓯᖅ

ᑕᓴᓐ ᒪᕐᕉᒃ 24 ᓈᓴᐅᑏᑦ ᐱᙳᐊᕈᑎᒋᔪᒃ. ᓯᑉ ᓯᕉᒧᑦ ᐃᓚᓗᒍ, 25 ᐱᙳᐊᕈᑎᒋᓕᖅᑕᑎᑦ. ᓴᐳᔾᔨᔾᔪᑎ ᐃᑲᔪᖅᐸ?

ᓇᐃᑦᑐᖅ ᑭᐅᔾᔪᑎ

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).

ᑕᓴᓐ ᒪᕐᕉᒃ
24/37 · +1 ᐅᕝᕙᓘᓐᓃᑦ −2
ᓯᕉᓗ
25/37 ᐱᙳᐊᕈᑎᒋᔭᐅᔪᑦ
ᐊᑦᔨᐅᑎᒧᑦ EV
−1/37 ᖃᓄᐃᒃᑲᓗᐊᖅᐸᑦ
ᐃᓕᓐᓂᐊᒃᓴᖅ
EV-ᑦ ᑲᑎᑕᐅᔪᓐᓇᖅᑐᑦ

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%.

ᓴᖅᑭᑦᑐᖅᐃᓂᑦᐱᔪᓐᓇᕐᓂᖅᑲᑎᑕᐅᔪᑦ
1–242464.9%+$9
25–361232.4%−$21
012.7%+$15
ᓂᕆᐅᒋᔭᐅᔪᖅ−$0.57 = $21-ᑉ 2.70%-ᖓ

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.

ᐊᔾᔨᒋᔭᖓ $21 ᐱᖓᓱᑎᒍᑦ: ᐊᔪᒐᕐᓂᕐᒧᑦ ᐱᔪᓐᓇᕐᓂᖅ ᐱᐅᙱᓛᖅᓗ
$21 ᐊᐅᐸᓗᒃᑐᒧᑦ: p(ᐊᔪᒐᕐᓂᖅ)
48.6% · ᐱᐅᙱᓛᖅ −$21
ᑕᓴᓐ ᒪᕐᕉᒃ + ᓯᕉ: p(ᐊᔪᒐᕐᓂᖅ)
67.6% · ᐱᐅᙱᓛᖅ −$21
$21 17-ᒧᑦ: p(ᐊᔪᒐᕐᓂᖅ)
2.7% · ᐱᐅᙱᓛᖅ −$21
033.8067.6% · ᐱᐅᙱᓛᖅ −$21
ᐱᖓᓱᑦ ᐃᓘᓐᓇᑎᒃ EV −$0.57-ᖃᖅᑐᑦ ᑲᐃᕙᕐᓂᕐᒧᑦ. ᐱᐅᓯᖏᓐᓂ ᑐᐊᖅ ᐊᔾᔨᒌᙱᑦᑐᑦ.

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

EV(ᑲᑎᑕᐅᓂᖅ) = Σ EV(ᐃᓚᖏᑦ) = −(ᐱᙳᐊᕈᑏᑦ ᑮᓇᐅᔭᖏᑦ ᐃᓘᓐᓇᖏᑦ)/37

ᐊᐱᖅᑯᑏᑦ

ᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᑦ ᑳᓯᓅᑉ ᐃᓚᖓᓂᒃ ᒥᑭᓂᖅᓴᒥᒃ ᐱᑕᖃᖅᐸ?

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.

ᐊᐅᐸᓗᒃᑐᒧᑦ ᕿᕐᓂᖅᑐᒧᓪᓗ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ ᖃᓄᐃᑦᑐᐊ?

ᓯᕉ ᓴᖅᑭᒃᐸᑦ ᑐᐊᖅ $1-ᒧᑦ $1-ᒥᒃ ᐊᓯᐅᔾᔨᔪᖅ, ᐊᓯᐊᒍᑦ ᓱᓇᒥᒡᓗ ᐊᔪᒐᙱᑦᑐᖅ. EV −2.70%, ᐱᐅᔪᖃᙱᑦᑐᖅ: ᑲᑎᑕᐅᓂᖅ ᐊᑕᐅᓯᖅ ᓱᓕᓪᓚᕆᒃᑐᒥᒃ ᐱᔾᔪᑎᖃᙱᑦᑐᖅ.

ᑕᐃᒪ ᓱᒻᒪᑦ ᐱᙳᐊᕈᑏᑦ ᑲᑎᖅᓱᖅᑕᐅᕙᑦ?

ᐱᙳᐊᖅᑕᐅᓂᖓᑕ ᐱᐅᓯᖓᓂᒃ ᖁᕕᐊᓱᒡᓗᒍ ᓇᓚᐅᑦᑖᕐᓂᐊᕐᓗᒍ. ᑕᒪᓐᓇ ᓱᓕᔪᖅ ᐱᔾᔪᑎ, ᐊᑕᐅᓯᐊᖑᓪᓗᓂᓗ.

ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ

ᕉᓚᑦ ᐱᙳᐊᕐᕕᖓᓂ ᓴᐳᔾᔨᔾᔪᑎ ᓱᓕᓪᓚᕆᒃᑐᒥᒃ ᓴᐳᔾᔨᔭᒥᓂᒃ ᐊᑭᖃᖅᑐᖅ.

ᕉᓚᑦ ᐱᙳᐊᕐᕕᖓᓂ ᓴᐳᔾᔨᔾᔪᑎ ᓱᓕᓪᓚᕆᒃᑐᒥᒃ ᓴᐳᔾᔨᔭᒥᓂᒃ ᐊᑭᖃᖅᑐᖅ.

ᐱᕝᕕᒋᔭᐅᔪᑦ

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. ᐃᓚᖓ 13, ᕉᓚᑦ.
ᕿᒥᕐᕈᔭᐅᓚᐅᖅᑐᖅ 2026-09-28ᐊᔾᔨᐅᖅᑕᐅᑎ: ᐃᐅᕌᐸ, ᐊᑕᐅᓯᖅ ᓯᕉᖃᓄᖅ ᓈᓴᐃᓂᖅ ↗ᐱᕝᕕᒋᔭᐅᔪᑦ ↗