ᖃᐅᔨᓴᕐᕕᒃᖃᐅᔨᓴᕐᓂᖅ 06df = 36α = 0.05ᐱᒋᐊᕐᕕᒃ (seed) 99

ᕉᓚᑦ ᐊᒃᓴᓗᐊᖓᑕ ᓴᖑᓯᒪᓂᖓ

ᓴᖑᓯᒪᔪᖅ ᕉᓚᑦ ᐊᒃᓴᓗᐊᖓ ᐃᓚᖏᓐᓂᒃ ᐃᓂᓂᒃ ᐱᐅᒋᓂᖅᓴᖃᖅᑐᖅ ᐊᒃᓱᕈᕐᓇᖅᑐᒥᒃ ᓱᕋᒃᓯᒪᓂᖓᓄᑦ: ᐃᓂᑦ ᐊᕕᒃᓯᒪᐅᑎᖓ ᓯᖁᒥᑦᑐᖅ, ᑲᐃᕙᖅᑐᖅ ᓈᒻᒪᙱᑦᑐᖅ, ᐃᓂᑦ ᐊᑐᓗᐊᖅᓯᒪᔪᑦ. ᕉᓚᑦ ᐊᒃᓴᓗᐊᖓᑕ ᓴᖑᓯᒪᓂᖓ ᐱᑕᖃᖅᑐᖅ ᐊᑐᖅᑕᐅᓯᒪᓪᓗᓂᓗ. ᐊᒃᓱᕈᕐᓇᖅᑐᖅ ᓈᒻᒪᑦᑎᐊᖅᑐᖅ ᐊᒃᓴᓗᐊᖅ “ᐆᓇᖅᑐᓂᒃ ᓈᓴᐅᑎᓂᒃ” ᓴᖅᑭᑦᑎᐃᓐᓇᕐᒪᑦ, ᑕᐃᒪ ᐊᐱᖅᑯᑎ ᓈᓴᐅᑎ ᐆᓇᕐᒪᖔᑦ ᐱᐅᙱᑦᑐᖅ, ᐃᓘᓐᓇᖓᓕ ᐊᔾᔨᒌᙱᓐᓂᖓ ᐱᔪᓐᓇᕐᓂᐅᑉ ᐱᔪᓐᓇᖅᑎᑦᑕᖓᓂᑦ ᐊᖏᓂᖅᓴᐅᒻᒪᖔᑦ.

1. ᓈᒻᒪᒃᑐᒥᑦ ᐊᒃᓴᓗᐊᕐᒥᑦ ᑕᑯᔭᐅᓯᒪᔪᑦ

ᑲᐃᕙᕐᓃᑦ ᐊᔾᔨᐅᖅᑕᐅᔪᒥᑦ ᐊᒃᓴᓗᐊᕐᒥᑦ ᓴᖑᓯᒪᙱᓪᓚᕆᒃᑐᒥᑦ. ᑕᑯᔭᐅᓯᒪᔪᑦ ᐊᒥᓲᓂᖏᑦ ᐊᓯᑦᑐᖅᓯᓗᒋᑦ ᐆᓇᓛᖅ ᐃᓂ ᑕᑯᓗᒍ.

0321519421225173462713361130823105241633120143192218297281235326
ᑲᐃᕙᕐᓃᑦ370
ᓂᕆᐅᒋᔭᐅᔪᑦ ᐃᓂᑕᒫᑦ10.0
ᐆᓇᓛᖅ ᐃᓂ20 · 16 ᓴᖅᑭᓃᑦ (4.32%)
ᐆᓇᓛᖅ, ᓂᕆᐅᒋᔭᐅᔪᒥᒃ ᐊᔾᔨᒋᓗᒍ+60% · 1.9σ
ᑲᐃ-ᔅᑯᐃᐅ · p32.8 · 0.622
ᐃᓱᒪᓕᐅᕈᑎᓴᖑᓯᒪᓂᕐᒥᒃ ᓇᓗᓇᐃᖅᓯᔪᖃᙱᑦᑐᖅ

2. ᑕᑯᔭᐅᓯᒪᔪᑦ ᓂᕆᐅᒋᔭᐅᔪᓪᓗ

ᓇᑉᐸᐅᑎ ᑕᒪᑐᒧᖓ ᐃᓂᐅᔪᖅ ᐊᒃᓴᓗᐊᕐᒥ ᑐᓪᓕᖅᑐᓂ. ᓄᖅᑲᖃᑦᑕᖅᑐᖅ ᑐᑭᓕᐊᖅ ᓂᕆᐅᒋᔭᐅᔪᑦ ᐅᓄᓐᓂᖏᑦ, n/37. ᑕᕐᕋᓕᒃ ᐃᓚᖓ ±2 ᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᐊᑦᔨᐅᑎᖏᑦ: ᓈᒻᒪᒃᑐᒥ ᐊᒃᓴᓗᐊᕐᒥ ᐊᑕᖃᓂᒃ ᐃᓂ ᐊᑕᐅᓯᖅ ᒪᕐᕉᓄᑦ ᖁᓖᓐᓄᑦ ᓯᓚᑖᓄᑦ ᐊᓂᒍᐃᕙᑦᑐᖅ ᐱᔪᓐᓇᕐᓂᑐᐊᒃᑯᑦ.

0ᐃᓂᑦ ᐊᒃᓴᓗᐊᕐᒥ ᑐᓪᓕᖅᑐᑦ →26

3. ᑲᐃ-ᔅᑯᐃᐅ ᖃᐅᔨᓴᕈᑎ

ᖃᐅᔨᓴᕈᑎ ᑲᑎᑦᓯᔪᖅ ᐃᓂ ᑕᒪᑐᒧᖓ ᓂᕆᐅᒋᔭᐅᔪᒥᑦ ᖃᓄᖅ ᐅᖓᓯᒃᑎᒋᒻᒪᖔᑦ, ᐃᒻᒥᓂᒃ ᐊᐅᓚᑦᑕᐅᓪᓗᓂ ᐊᑦᔨᐅᑎᒧᓪᓗ ᐊᑦᔨᒋᔭᐅᓪᓗᓂ. ᓈᒻᒪᒃᑐᒥ ᐊᒃᓴᓗᐊᕐᒥ ᑲᑎᑕᐅᓂᖓ ᑲᐃ-ᔅᑯᐃᐅ ᐊᕕᒃᓯᒪᓂᖏᓐᓂᒃ ᒪᓕᒃᑐᖅ 36 ᐃᒻᒥᓂᖅᑐᑦ ᐊᒥᓲᓂᖏᓐᓂ; p ᐊᑭᖓ 0.05-ᒥᑦ ᒥᑭᓂᖅᓴᐅᒍᓂ ᐊᑐᒐᔪᒃᑐᒥᒃ ᓈᓴᐃᓂᒃᑯᑦ ᐱᒻᒪᕆᐅᔪᒥᒃ ᑕᐃᔭᐅᕙᑦᑐᖅ.

χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ Eᵢ = n/37 df = 36
n = 370 · E = 10.00 · χ² = 32.80 · p = 0.622
ᑕᑯᔭᐅᓯᒪᔪᑦ ᐊᒥᓲᓂᖏᓐᓄᑦ ᖃᐅᔨᒋᐊᖅᑎᑦᓯᓂᖅ1,000 ᑲᐃᕙᕐᓂᕐᓂᑦ ᐊᑕᖃᓂᒃ ᒥᑭᓂᖅᓴᐅᒍᓂ ᖃᐅᔨᓴᕈᑎ ᓴᙱᓐᖏᓪᓚᕆᐅᔭᖅᑐᖅ ᓱᓕᔪᓂᒃ ᓴᖑᓯᒪᓂᕐᓂᒃ ᖃᐅᔨᓂᕐᒧᑦ, “ᓈᓴᐃᓂᒃᑯᑦ ᐱᒻᒪᕆᐅᔪᖅ” ᓇᓂᔭᐅᔪᖅ p < 0.05-ᒥ ᐱᔪᓐᓇᕐᓂᒃᑯᑦ ᐱᑦᑕᕐᓂᐊᖅᑐᖅ 1-ᒥᒃ 20 ᓈᒻᒪᒃᑐᓂ ᑕᑯᔭᐅᓯᒪᔪᓂ ᑕᑯᔭᑎᑦ. ᐊᒥᓱᓂᒃ ᐊᒃᓴᓗᐊᓂᒃ ᖃᐅᔨᓴᕐᓂᖅ, ᐅᕝᕙᓘᓐᓃᑦ ᐊᒃᓴᓗᐊᕐᒥᒃ ᐊᑕᐅᓯᕐᒥᒃ ᖃᐅᔨᓴᖅᑭᑦᑕᕐᓂᖅ ᑕᐃᒪ ᐊᓂᒍᐃᓪᓗᓂ, ᓱᓕᙱᑦᑐᓂᒃ ᓇᓂᔭᐅᔪᓂᒃ ᓴᖅᑭᑦᑎᑦᑎᓐᓇᓱᐊᖅᑐᖅ.

4. ᖃᔅᓯᓂᒃ ᑲᐃᕙᕐᓂᕐᓂᒃ ᐱᔭᕆᐊᖃᕐᓂᐊᕐᒪᖔᑎᑦ

ᑲᐃᕙᕐᓃᑦ ᐱᔭᕆᐊᖃᖅᑕᐅᔪᑦ ᐃᓂᒥᒃ ᐊᑕᐅᓯᕐᒥᒃ 1/37-ᒥᑦ ᐊᒥᓲᓂᖅᓴᐃᑦ ᓴᖅᑭᑦᑐᒥᒃ ᖃᐅᔨᓂᕐᒧᑦ, ᓴᓂᓕᐊᖅ ᐊᑕᐅᓯᖅ 5% ᑭᒡᓕᖓᓂ 80% ᓴᙱᓂᖓᓂᓗ. ᐃᓂ 1-ᒥᒃ 35-ᓂ ᓴᖅᑭᑦᑐᖅ, 1-ᒥᒃ 37-ᓂ ᐱᓐᖏᓪᓗᓂ, ᐱᙳᐊᖅᑎᒧᑦ ᐱᐅᓂᖅᓴᐅᓂᐅᓪᓚᕆᓐᓂᐊᖅᑐᖅ, ᓱᓕᔪᒥᒃ ᑕᑯᑦᑎᑦᓯᓂᕐᒧᓪᓗ ᖁᓕᓪᓗᐊᑦ ᑕᐅᓴᓐᓂᒃ ᑎᑎᕋᖅᓯᒪᔪᓂᒃ ᑲᐃᕙᕐᓂᕐᓂᒃ ᐱᔭᕆᐊᖃᖅᑐᖅ.

ᓱᓕᔪᖅ ᐅᓄᓐᓂᖓᐱᙳᐊᖅᑎᐅᑉ ᐱᐅᓂᖅᓴᐅᓂᖓᑲᐃᕙᕐᓃᑦ ᐱᔭᕆᐊᖃᖅᑕᐅᔪᑦ40 ᑲᐃᕙᕐᓃᑦ/ᐃᑲᕐᕋᖅ
1, 25-ᓂᑦ+44.0%1,10828 ᐃᑲᕐᕋᐃᑦ
1, 30-ᓂᑦ+20.0%4,392110 ᐃᑲᕐᕋᐃᑦ
1, 33-ᓂᑦ+9.1%15,747394 ᐃᑲᕐᕋᐃᑦ
1, 35-ᓂᑦ+2.9%69,4611,737 ᐃᑲᕐᕋᐃᑦ
ᓴᖑᓯᒪᓂᕐᒥᒃ ᓱᓕᔪᒥᒃ ᑕᑯᑦᑎᑦᓯᓂᖅ ᑐᑭᖃᖅᑐᖅ ᑲᐃᕙᕐᓂᕐᓂᒃ ᐅᓐᓄᐊᖅᑕᒫᑦ ᑎᑎᕋᐃᓂᕐᒥᒃ, ᖁᓕᓪᓗᐊᑦ ᑕᐅᓴᓐᓂᒃ.

ᖃᓄᖅ ᓈᓴᐃᓂᖅ

ᑕᑯᔭᐅᓯᒪᔪᓂᒃ ᓇᓚᐅᑦᑖᕐᓂᖅ. 37 ᐃᓂᓂᑦ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐱᔪᓐᓇᕐᓂᓖᑦ ᓇᓚᐅᑦᑖᖅᑕᐅᔪᑦ ᓈᓴᐅᑏᑦ ᓴᖅᑭᑦᑎᒋᐊᕈᑎᒥᒃ ᐱᒋᐊᕐᕕᓕᒻᒥᒃ (mulberry32, seed 99), ᑕᐃᒪ ᒪᑉᐱᒐᖅ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐱᒋᐊᖅᑭᑦᑕᐅᔪᓐᓇᖅᑐᖅ.
ᖃᐅᔨᓴᕈᑎ. ᐱᐊᓴᓐ (Pearson) ᑲᐃ-ᔅᑯᐃᐅ ᖃᐅᔨᓴᕈᑎ ᓈᒻᒪᓂᖓᓄᑦ, 36 ᐃᒻᒥᓂᖅᑐᑦ ᐊᒥᓲᓂᖏᑦ, p ᐊᑭᖓ ᒑᒪ ᐊᐅᓚᑦᑎᔾᔪᑎᒥᑦ (regularized incomplete gamma function).
ᓴᙱᓂᖓ. ᐊᑐᖅᑕᐅᒐᔪᒃᑐᖅ ᐊᔾᔨᐅᔭᖅᑐᖅ ᐊᑕᐅᓯᕐᒧᑦ ᐊᕕᒃᑐᖅᓯᒪᔪᒧᑦ ᖃᐅᔨᓴᕈᑎᒧᑦ, α = 0.05 ᓴᓂᓕᐊᖅ ᐊᑕᐅᓯᖅ, ᓴᙱᓂᖓ 0.80.
ᐃᓗᓕᖏᑦ. ᓈᓴᐃᓂᒃᑯᑦ ᖃᐅᔨᓂᖅ ᑭᓯᐊᓂ. ᐊᒃᓱᕈᕐᓇᖅᑐᑦ ᐱᔾᔪᑎᖏᑦ ᐊᒃᓴᓗᐊᑉ ᐃᓚᖏᓐᓄᓪᓗ (ᐃᓂᓄᑦ ᐱᐅᙱᑦᑐᖅ) ᖃᐅᔨᓴᕐᓂᖅ ᓇᓗᓇᐃᖅᑕᐅᔪᑦ ᐊᒃᓴᓗᐊᑉ ᐃᓚᖏᓐᓂᒃ ᖃᐅᔨᓴᕐᓂᕐᒥ.

ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ

ᓈᒻᒪᒃᑐᖅ ᐊᒃᓴᓗᐊᖅ ᐅᓐᓄᐊᖅᑕᒫᑦ ᐆᓇᖅᑐᓂᒃ ᓈᓴᐅᑎᓂᒃ ᓴᖅᑭᑦᑎᕙᒃᑐᖅ. ᓴᖑᓯᒪᓂᕐᒥᒃ ᓱᓕᔪᒥᒃ ᑕᑯᑦᑎᑦᓯᓂᖅ ᖁᓕᓪᓗᐊᑦ ᑕᐅᓴᓐᓂᒃ ᑲᐃᕙᕐᓂᕐᓂᒃ ᐱᔭᕆᐊᖃᖅᑐᖅ.

ᓈᒻᒪᒃᑐᖅ ᐊᒃᓴᓗᐊᖅ ᐅᓐᓄᐊᖅᑕᒫᑦ ᐆᓇᖅᑐᓂᒃ ᓈᓴᐅᑎᓂᒃ ᓴᖅᑭᑦᑎᕙᒃᑐᖅ. ᓴᖑᓯᒪᓂᕐᒥᒃ ᓱᓕᔪᒥᒃ ᑕᑯᑦᑎᑦᓯᓂᖅ ᖁᓕᓪᓗᐊᑦ ᑕᐅᓴᓐᓂᒃ ᑲᐃᕙᕐᓂᕐᓂᒃ ᐱᔭᕆᐊᖃᖅᑐᖅ.

ᐱᕝᕕᒋᔭᐅᔪᑦ

  1. Pearson, K. (1900). On the criterion that a given system of deviations… Philosophical Magazine, 50(302).
  2. Thorp, E. O. (1969). Optimal gambling systems for favorable games. Review of the International Statistical Institute, 37(3).
  3. Ethier, S. N. (2010). The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer. Ch. 13, Roulette.