游戏规则
可选号码: 1 – 49, 共49个
下注号码: 6个
开奖号码: 6个普通+ 1个特别, 共7个
49个号码按开奖结果可以分为3类: 6个普通(A), 1个特别(B), 42个无奖©
这样六合彩搅珠就可以变成一条普通的颜色球问题, 即是从袋中的49个球抽出6个, 中途不放回
下注组合数(49个抽6个): 49C6 = 13,983,816
开奖组合数(49个抽7个): 49C7 = 85,900,584
中奖结果: aA bB cC, 0 <= a <= 6, 0 <= b <= 1, 0 <= c <= 6
概率: P = 6Ca * 1Cb * 42Cc / 49C6
预期可获奖金: E = Sum(Pi$i)
概率计算
中0个: 6C
P = 42C6 / 49C6 = 37.5%
中0.5个: 1B 5C
P = 1C1 * 42C5 / 49C6 = 6.08%
中1个: 1A 5C
P = 6C1 * 42C5 / 49C6 = 36.5%
中1.5个: 1A 1B 4C
P = 6C1 * 1C1 * 42C4 / 49C6 = 4.80%
中2个: 2A 4C
P = 6C2 * 42C4 / 49C6 = 12.0%
中2.5个: 2A 1B 3C
P = 6C2 * 1C1 * 42C3 / 49C6 = 1.23%
中3个(七奖): 3A 3C
P = 6C3 * 42C3 / 49C6 = 1.64%
中3.5个(六奖): 3A 1B 2C
P = 6C3 * 1C1 * 42C2 / 49C6 = 0.123%
中4个(五奖): 4A 2C
P = 6C4 * 42C2 / 49C6 = 0.0924%
中4.5个(四奖): 4A 1B 1C
P = 6C4 * 1C1 * 42C1 / 49C6 = 0.00451%
中5个(三奖): 5A 1C
P = 6C5 * 42C1 / 49C6 = 0.00180%
中5.5个(二奖): 5A 1B
P = 6C5 * 1C1 / 49C6 = 0.0000429%
中6个(头奖): 6A
P = 6C6 / 49C6 = 0.00000715% (1/13,983,916)
无奖: 中0 – 2.5个
P = 37.5% + 6.08% + 36.5% + 4.80% + 12.0% + 1.23% = 98.1%
有奖: 中3 – 6个
P = 1.64% + 0.123% + 0.0924% + 0.00180% + 0.0000429% + 0.00000715% = 1.9%
预期收益
每注金额= $10
例1
假设头奖, 二奖, 三奖0注中, 可分发头奖基金$10,000,000 (actually it doesn’t matter)
预期可获奖金= $40 * 1.64% + $320 * 0.123% + $640 * 0.0924% + $9600 * 0.00451% = $2.07
例2
假设头奖1注中, 二奖16 = 6注中, 三奖642 = 252注中, 可分发头奖基金$10,000,000
预期可获奖金= $40 * 1.64% + $320 * 0.123% + $640 * 0.0924% + $9600 * 0.00451% + $10000000 * 40% / 252 * 0.00180% + $10000000 * 15% / 6 * 0.0000429% + $10000000 * 45% * 0.00000715% = $2.79
例3
假设头奖1注中, 二奖16 = 6注中, 三奖642 = 252注中, 可分发头奖基金$50,000,000
预期可获奖金= $40 * 1.64% + $320 * 0.123% + $640 * 0.0924% + $9600 * 0.00451% + $50000000 * 40% / 252 * 0.00180% + $50000000 * 15% / 6 * 0.0000429% + $50000000 * 45% * 0.00000715% = $5.65
例4
假设头奖2注中, 二奖26 = 12注中, 三奖1242 = 504注中, 可分发头奖基金$50,000,000
预期可获奖金= $40 * 1.64% + $320 * 0.123% + $640 * 0.0924% + $9600 * 0.00451% + $50000000 * 40% / 504 * 0.00180% + $50000000 * 15% / 12 * 0.0000429% + $50000000 * 45% / 2 * 0.00000715% = $3.86
以上例子中, 预期收益皆为负数
结论
买六合彩做善事是个不错的选择
但不是可靠的发达工具
头奖基金越高, 收益不一定越高
平均每买约50注可中1注
