## 2011年5月20日星期五

### 又六合彩

Preliminaries

(∗): p = (p1, p2, p3, p4, p5, p6, p7)
= (1, 6, 252, 630, 12915, 17220, 229600) / 13983816.

T = turnover = 你未下注前的投注額
N = 你未下注前的投注總注數 = T/10
t = 大包圍所需投注額
J = Jackpot = 多寶彩金

P4 = 9600 × 四獎中獎注數
P5 = 640 × 五獎中獎注數
P6 = 320 × 六獎中獎注數
P7 = 40 × 七獎中獎注數

P4 = 9600 × (W4 + 630)
P5 = 640 × (W5 + 12915)
P6 = 320 × (W6 + 17220)
P7 = 40 × (W7 + 229600)

A = [0.54 × (T+t) - (P4 + P5 + P6 + P7)] × 0.91.

P1 = 0.45 × A + J1
P2 = 0.15 × A + J2
P3 = 0.40 × A + J3

P'1 = (0.45 × A + J) / (W1 + 1)
P'2 = (0.15 × A) × 6 / (W2 + 6)
P'3 = (0.40 × A) × 252 / (W3 + 252)
P'4 = 9600 × 630
P'5 = 640 × 12915
P'6 = 320 × 17220
P'7 = 40 × 229600

E[Wj / (Wi + c)] ≈ E(Wj) / E(Wi + c) = (N × pj) /  (N × pi + c)

(P'1 + P'2 + P'3 + P'4 + P'5 + P'6 + P'7)
=  [0.54 × t - (P4 + P5 + P6 + P7)] × 0.91 + J + (P4 + P5 + P6 + P7)
=  0.4914 × t + 0.09 × (P4 + P5 + P6 + P7)] + J

J = 0.5086 × t - 0.09 × (P4 + P5 + P6 + P7) = \$68,510,968.176 今期多寶獎金有 J = \$85,618,703。如果真係得你一條友投注，兼且大包圍，咁就穩賺 \$17,107,735。 現實 今期開彩前約五分鐘（即我寫上一篇吹水文嘅時候），馬會公佈投注總額為 T = \$319,943,790（三億幾），所以 N = T/10 = 31994379。如前述，設 J1 = J，而 J2 = J3 = 0。夾夾埋埋，可以計到
P'1 ≈ 45083723
P'2 ≈ 6347879
P'3 ≈ 16927677
P'4 = 6048000
P'5 = 8265600
P'6 = 5510400
P'7 = 9184000