A New System For Roulette

I have devised a system for playing roulette which gives a pretty chance of leaving from the table richer than you arrived. No doubt it has already been thought of and some fatal flaw discovered which my poor brain could not detect. If so, please accept my apologies for wasting your time. If not, please read through what follows and give it a try. If it works, please post here and let everyone know - that will be payment enough. If it fails,, please post here and let everyone know!

Background

The game of roulette relies on the spin of a wheel bearing 37 numbers (in the French version) or 38 (American). My system does not care which version you play, so please substitute the correct details for your location.

I am in France, so I use the French notation.

When the wheel is spun, a ball is introduced and eventually comes to rest on one of the numbers. In this way can the winners be determined. There are many ways to bet on the result, but my systems assumes you will bet on a single number unswervingly until you win. After winning, the system is reset and you may choose another number.

Mathematical basis

In this scenario, you have a 1/37 chance of matching the winning number. If you do so, your stake is returned to you, along with winnings of 35 times your stake. Thus in total you receive back 36 times your stake. Over time, you have a return of 36/37, that is YOU LOSE! The trick is to win in the meantime...

The approach I have taken is to calculate at each spin of the wheel the sum of cash flows in the 2 cases - case 1, you fail to match the winning number and your money is taken; case 2, you win. In this way can we see the necessary level of stake for the next bet to ensure that when your number is eventually correct so you have made a profit during your stay at the table. If these calculations are correctly performed, you will be certain that once you have eventually won on a certain spin, then the total you have lost will at worst be equivalent in value to the pile of chips the croupier pushes towards you.

Limitations

Of course, the chances of winning on average are 1/37 - that is, if you stay at the table for more than 37 spins, you should see your number come up. However, that’s life: sometimes your number won’t come up for a very long time.

I have assumed that you are able to play in chips of 1 currency unit and that you have a stack of 1000 currency units in front of you. With this method, you can survive at the table 139 unsuccesful spins in succession and still make an overall profit of 19 units on the 140th play. A return on capital of <2%, but tax-free and you had a very good time.If you only have 100 currency units, you can survive 62 unsuccesful spins in succession and still make an overall profit of 9 units on the 63rd play.

If your number doesn’t come up by the 140th spin, the gods hate you and you should go home!

How it works

Let us work through the example of the first 10 spins:

A--- B---- C----- | D------ E--------- F------------

Spin Stake Spent | Paid Stake back Profit if won so far | on win on win (= D + E - C)

---- ----- ------ | ------- ---------- -------------

1 1 1 | 35 1 35

2 1 2 | 35 1 34

3 1 3 | 35 1 33

4 1 4 | 35 1 32

5 1 5 | 35 1 31

6 1 6 | 35 1 30

7 1 7 | 35 1 29

8 1 8 | 35 1 28

9 1 9 | 35 1 27

10 1 10 | 35 1 26 It can be seen that the profit diminishes by 1 each spin and then let us move ahead to the 36th spin:

A--- B---- C----- | D------ E--------- F------------

Spin Stake Spent | Paid Stake back Profit if won so far | on win on win (= D + E - C)

---- ----- ------ | ------- ---------- -------------

36 1 36 | 35 1 0 This is break even - the stake must be increased

37 2 38 | 70 2 34

38 2 40 | 70 2 32

and then move ahead again to the 54th spin:

A--- B---- C----- | D------ E--------- F------------

Spin Stake Spent | Paid Stake back Profit if won so far | on win on win (= D + E - C)

---- ----- ------ | ------- ---------- -------------

54 2 72 | 70 2 0 This is break even - the stake must be increased

55 3 75 | 105 3 33

56 3 78 | 105 3 30

...and so on.

Clearly, the effect of increasing the stake at periodic intervals allows the player to always have a profitable result when his number eventually comes up. The frequency table is as follows:

A-------- B------ C--------- D------

From spin To spin Spin count Stake

--------- ------- ---------- -------

1            36          36          1

37          54          18          2

55          66          12          3

67          75          9            4

76          82          7            5

83          88          6            6

89          93          5            7

94          97          4            8

98          101       4            9

102       105       4            10

106       108       3            11

109       111       3            12

112       114       3            13

115       116       2            14

117       119       3            15

120       121       2            16

122       123       2            17

124       125       2            18

126       127       2            19

128       130       3            21

131       132       2            22

133       133       1            23

134       135       2            24

136       136       1            25

137       138       2            26

139       139       1            27

140       140       1            28

141       141       1            29

142       143       2            30

144       144       1            31

145       145       1            32

146       146       1            33

147       147       1            34

148       148       1            35

149       149       1            36

150       150       1            37

151       151       1            38

152       152       1            39

153       153       1            40

154       154       1            41

155       155       1            43

156       156       1            44

157       157       1            45

158       158       1            46

159       159       1            48

160       160       1            49

161       161       1            50

162       162       1            52

163       163       1            53

164       164       1            55

165       165       1            56

166       166       1            58

167       167       1            60

168       168       1            61

169       169       1            63

170       170       1            65

171       171       1            67

172       172       1            69

173       173       1            71

174       174       1            73

175       175       1            75

176       176       1            77

177       177       1            79

178       178       1            81

179       179       1            84

180       180       1            86

181       181       1            89

182       182       1            91

183       183       1            94

184       184       1            96

185       185       1            99

186       186       1            102

187       187       1            105

188       188       1            108

189       189       1            111

190       190       1            114

191       191       1            117

192       192       1            121

193       193       1            124

194       194       1            128

195       195       1            131

196       196       1            135

197       197       1            139

198       198       1            143

199       199       1            147

200       200       1            151

That’s all there is to it - play well and have fun!