万能万字中奖机率

万能万字中最传统的玩法。容易明白，简单的玩法，是玩家们最喜爱的玩法之一。

万字是从 0000 到 9999 选出一对号码，然后万能将会选出 23 组得奖号码。如果你所选的号码在那 23 组得奖号码里，你将获奖。奖金如下：


中奖机率 ：
从 0000 到 9999，一共有 10，000 组号码。从 10，000 中选出 1 组号码的机率为 0.01 %。

1/10，000 = 0.0001 = 0.01 %

每期共选出 23 组得奖号码，每一组号码的都有可能出现一次或以上，最多为 23 次，23 次有可能会选出你的号码。

0.0001 为选中的机率。
每期 23 组得奖号码。

以二项分布（Binomial distribution）来计算每期的中奖机率：

我们希望在 n 组得奖号码中，有 k 次中奖，而 k 的中奖率为 0.0001.



n = 23 组得奖号码
k = 0。0 为没被选中。
p = 0.0001

每期没中奖的机率为 99.77025282 %
而
每期中奖的机率为 0.22974718 % (= 100 % - 99.77025282 %)

如以下的机率表来看，你中的机率少过 0.

每期中奖次数	中奖的机率(%)
0	99.770252822988600000000000000000
1	0.229494530945968000000000000000
2	0.000252469230963662000000000000
3	0.000000176746136288192000000000
4	0.000000000088381906334729400000
5	0.000000000000033588483255522700
6	0.000000000000000010077552731930
7	0.000000000000000000002447650429
8	0.000000000000000000000000489579
9	0.000000000000000000000000000082
10	0.000000000000000000000000000000
11	0.000000000000000000000000000000
12	0.000000000000000000000000000000
13	0.000000000000000000000000000000
14	0.000000000000000000000000000000
15	0.000000000000000000000000000000
16	0.000000000000000000000000000000
17	0.000000000000000000000000000000
18	0.000000000000000000000000000000
19	0.000000000000000000000000000000
20	0.000000000000000000000000000000
21	0.000000000000000000000000000000
22	0.000000000000000000000000000000
23	0.000000000000000000000000000000

如何增加机率：
如果要增加中奖机率，我们必须利用可能得到的奖金来降低没中奖的机率。

就以最低奖金 RM 60 来买 60 组号码：
1. 从 10,000 中选出 1 组号码的机率也提升为 0.6 %
2.  再以二项分布（Binomial distribution）来计算每期的中奖机率：

每期中奖次数	中奖的机率(%)
0	87.073668306734700000000000000000
1	12.088698416830400000000000000000
2	0.802670116208053000000000000000
3	0.033915638713016300000000000000
4	0.001023610826348580000000000000
5	0.000023479202053066000000000000
6	0.000000425176697138017000000000
7	0.000000006232828845656470000000
8	0.000000000075245418659836600000
9	0.000000000000756996163579845000
10	0.000000000000006397150678139540
11	0.000000000000000045635426458285
12	0.000000000000000000275465350855
13	0.000000000000000000001406958146
14	0.000000000000000000000006066218
15	0.000000000000000000000000021970
16	0.000000000000000000000000000066
17	0.000000000000000000000000000000
18	0.000000000000000000000000000000
19	0.000000000000000000000000000000
20	0.000000000000000000000000000000
21	0.000000000000000000000000000000
22	0.000000000000000000000000000000
23	0.000000000000000000000000000000

以奖金 RM 180 来买 180 组号码：

每期中奖次数	中奖的机率(%)
0	65.851279699346100000000000000000
1	27.762148467952400000000000000000
2	5.597663336715460000000000000000
3	0.718233788621332000000000000000
4	0.065825907307454000000000000000
5	0.004585022464185190000000000000
6	0.000252129544873727000000000000
7	0.000011223689370288100000000000
8	0.000000411459080784493000000000
9	0.000000012570033017856200000000
10	0.000000000322571112067186000000
11	0.000000000006987746734282670000
12	0.000000000000128084970689499000
13	0.000000000000001986591273423220
14	0.000000000000000026010069043947
15	0.000000000000000000286057785819
16	0.000000000000000000002621710868
17	0.000000000000000000000019787682
18	0.000000000000000000000000120902
19	0.000000000000000000000000000583
20	0.000000000000000000000000000002
21	0.000000000000000000000000000000
22	0.000000000000000000000000000000
23	0.000000000000000000000000000000

以奖金 RM 500 来买 500 组号码：

每期中奖次数	中奖的机率(%)
0	30.735686772502400000000000000000
1	37.206357671976600000000000000000
2	21.540522862723300000000000000000
3	7.935982107319100000000000000000
4	2.088416344031340000000000000000
5	0.417683268806269000000000000000
6	0.065949989811516100000000000000
7	0.008429697945832890000000000000
8	0.000887336625877146000000000000
9	0.000077836546129574200000000000
10	0.000005735324451652840000000000
11	0.000000356742669241564000000000
12	0.000000018775929960082300000000
13	0.000000000836175018465205000000
14	0.000000000031435151070120500000
15	0.000000000000992688981161700000
16	0.000000000000026123394241097400
17	0.000000000000000566141670859695
18	0.000000000000000009932310015082
19	0.000000000000000000137566620708
20	0.000000000000000000001448069692
21	0.000000000000000000000010887742
22	0.000000000000000000000000052094
23	0.000000000000000000000000000119

以奖金 RM 1000 来买 1000 组号码：

每期中奖次数	中奖的机率(%)
0	8.862938119652510000000000000000
1	22.649730750223100000000000000000
2	27.683004250272700000000000000000
3	21.531225527989800000000000000000
4	11.961791959994400000000000000000
5	5.050534383108730000000000000000
6	1.683511461036240000000000000000
7	0.454280870438351000000000000000
8	0.100951304541856000000000000000
9	0.018694686026269600000000000000
10	0.002908062270753050000000000000
11	0.000381866762826158000000000000
12	0.000042429640314017600000000000
13	0.000003989111482514470000000000
14	0.000000316596149405911000000000
15	0.000000021106409960394000000000
16	0.000000001172578331133000000000
17	0.000000000053647374627000100000
18	0.000000000001986939801000000000
19	0.000000000000058097655000000100
20	0.000000000000001291059000000000
21	0.000000000000000020493000000000
22	0.000000000000000000207000000000
23	0.000000000000000000001000000000

以奖金 RM 2500 来买 2500 组号码：

每期中奖次数	中奖的机率(%)
0	0.133785503673778000000000000000
1	1.025688861498960000000000000000
2	3.760859158829530000000000000000
3	8.775338037268910000000000000000
4	14.625563395448200000000000000000
5	18.525713634234400000000000000000
6	18.525713634234400000000000000000
7	14.997006275332600000000000000000
8	9.998004183555050000000000000000
9	5.554446768641700000000000000000
10	2.592075158699460000000000000000
11	1.021120517063420000000000000000
12	0.340373505687808000000000000000
13	0.096002783655535500000000000000
14	0.022857805632270400000000000000
15	0.004571561126454070000000000000
16	0.000761926854409012000000000000
17	0.000104578195703198000000000000
18	0.000011619799522577500000000000
19	0.000001019280659875220000000000
20	0.000000067952043991681400000000
21	0.000000003235811618651500000000
22	0.000000000098054897534893800000
23	0.000000000001421085471520200000

由以下图表来看，你最少要买 297 组号码才有 50 % 的中奖机率。

n 组号码	中奖的机率(%)
300	50.369358565801700000000000000000
299	50.251544114506600000000000000000
298	50.133462179540700000000000000000
297	50.015112181278000000000000000000
296	49.896493538896500000000000000000