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================================================    Saturday, November 13, 2004
 
Betting on 2 Dozens in Roulette

Hello everyone,

Betting on 2 dozens simultaneously in Roulette is a strategy used by many.  The simplest one is to use a Martingalish approach.  If a dozen repeated say about 7 times, some feel it's time to bet on the other 2 dozens.  So one places 1 unit on each 2 dozens.  If you lose your bet, you triple the amount of your previous bet and place them on the same 2 dozens.  You keep tripling your bet on every loss until you win.  Your eventual win will eliminate the previous losses and will profit you 1 unit.  Like every Martingale approach, this can give you some profits, but the fact that you are increasing your bet drastically will also endanger your bankroll greatly.  The progression is indeed very steep: 1 3 9 27 81 243 on each 2 dozens, and after those 6 steps, you would probably reach the table's maximum betting limit.

There was an interesting post by Al in the discussion forum on a 2 dozen bet strategy, that I would like to share with you:

"Start with 1 chip on 1st dozen and 2 chips on 2nd dozen.  If you win with 1st dozen, then put 1 chip on 2nd dozen, and 2 chips on 3rd dozen; however, if win with 2nd dozen, then put 1 chip on 3rd dozen and 2 chips on 1st dozen.  If you lose, then increase 1st dozen to 2 chips and 2nd dozen to 3 chips.  Keep increasing those 2 selections by 1-chip each spin until a win, then go back to original 1 and 2 chips betting pattern in accordance with preceding paragraph.

At the point where you have 1 chip on 2nd dozen, and 2 chips on 3rd dozen.  If win with 2nd dozen, then put 1 chip on 3rd dozen, and 2 chips on 1st dozen; however, if win with 3rd dozen, then put 1 chip on 1st dozen and 2 chips on 2nd dozen.  If you lose, then increase 2nd dozen to 2 chips and 3rd dozen to 3 chips, and keep increasing until your win."

In other words, if the dozen on which you had chips wins, then you bet nothing on that dozen for the next spin and bet 1 unit on the next dozen, and 2 units on the next one, looking at dozens 1, 2, 3 in wrap around mode.

This strategy works well for a while, until one reaches a situation when a dozen wins, but then repeats over quite a few spins thereafter, and the progression is applied to the other 2 dozens, which keep losing. 

One solution for the above is to always circulate the no bet dozen around also in a wrap around mode.  For instance if the bet on dozen 1 won, then there will be no bet on dozen 1 on the next spin.  But if dozen 1 comes up again, then the no bet dozen will be the second one.  And in the case, dozen 2 comes up on the next spin, then the no bet dozen will be the third one, etc.  This solves the problem of sometimes repeating dozens and escalating the bets on the non-winning ones.

It's funny, this strategy was the very first one I used when I stepped into a casino for the first time at the age of 18 in Den Haag - Scheveningen - capital of Netherlands (Holland Casino Scheveningen).  I thought by betting 1 unit on one dozen and betting 2 units on another one and leaving the third dozen empty would give me 66% chances of either making a profit or breaking even and a 34% chances of losing my bet.  If the dozen with the 1 unit would win, I would get 3 units back for my 3 unit investment and would break even.  If the dozen with the 2 unit bet would win, I would get back 6 units for my 3 unit investment thus profiting 3 units.  If the dozen with no bet on would win, I would lose 3 units.

That day, I won the equivalent of $475 using that strategy and bought myself a suit.  When my sister asked me during dinner where I had the money form to buy the suit , I replied that I won it at the casino and she laughed in disbelief. 

One important factor to notice in this strategy, is that I was not using any progression but flat bets and betting always the same amounts on the same 2 dozens.  That surely does not give the player an edge and the strategy is not a long run winning one, as the appearance of the zeros and the dozen with no bet coming up one third of the time gradually decreases your bankroll.

Despite that, I have also noticed that before your bankroll starts decreasing, there is a high chance that you will cross the profit barrier a few times.  I wouldn't be sure that this is a matter of luck only.  In fact, what we will do now is to run this strategy 6 times on the first few spins of the Zumma Roulette tester book by Erick St. Germain.  Why 6 times? Because we would like to try it on every single combination of betting 1 unit on one dozen, 2 units on another dozen and nothing on the remaining third dozen. 

So following are the 6 permutations: 

Permutation Dozen 1 Dozen 2 Dozen 3
1) 0 1 2
2) 0 2 1
3) 1 0 2
4) 1 2 0
5) 2 0 1
6) 2 1 0

The numbers inside under Dozen 1, 2, 3 represent the number of units bet on each Dozen.

Here is the test for permutation 1), that is betting nothing on Dozen 1, 1 unit on Dozen 2 and 2 units on Dozen 3 on Zumma roulette tester:

Spin Zumma Numbers Dozen Bet on Dozen 1 W/L Dozen 1 Units Dozen 1 Bet on Dozen 2 W/L Dozen 2 Units Dozen 2 Bet on Dozen 3 W/L Dozen 3 Units Dozen 3 Total Units Net
1 13 2 0 L 0 1 W 2 2 L -2 0 0
2 9 1 0 W 0 1 L -1 2 L -2 -3 -3
3 22 2 0 L 0 1 W 2 2 L -2 0 -3
4 32 3 0 L 0 1 L -1 2 W 4 3 0
5 2 1 0 W 0 1 L -1 2 L -2 -3 -3
6 6 1 0 W 0 1 L -1 2 L -2 -3 -6
7 13 2 0 L 0 1 W 2 2 L -2 0 -6
8 6 1 0 W 0 1 L -1 2 L -2 -3 -9
9 21 2 0 L 0 1 W 2 2 L -2 0 -9
10 18 2 0 L 0 1 W 2 2 L -2 0 -9
11 15 2 0 L 0 1 W 2 2 L -2 0 -9
12 24 2 0 L 0 1 W 2 2 L -2 0 -9
13 18 2 0 L 0 1 W 2 2 L -2 0 -9
14 21 2 0 L 0 1 W 2 2 L -2 0 -9
15 32 3 0 L 0 1 L -1 2 W 4 3 -6
16 9 1 0 W 0 1 L -1 2 L -2 -3 -9
17 34 3 0 L 0 1 L -1 2 W 4 3 -6
18 3 1 0 W 0 1 L -1 2 L -2 -3 -9
19 32 3 0 L 0 1 L -1 2 W 4 3 -6
20 5 1 0 W 0 1 L -1 2 L -2 -3 -9
21 26 3 0 L 0 1 L -1 2 W 4 3 -6
22 19 2 0 L 0 1 W 2 2 L -2 0 -6
23 31 3 0 L 0 1 L -1 2 W 4 3 -3
24 2 1 0 W 0 1 L -1 2 L -2 -3 -6
25 6 1 0 W 0 1 L -1 2 L -2 -3 -9
26 3 1 0 W 0 1 L -1 2 L -2 -3 -12
27 9 1 0 W 0 1 L -1 2 L -2 -3 -15
28 1 1 0 W 0 1 L -1 2 L -2 -3 -18
29 29 3 0 L 0 1 L -1 2 W 4 3 -15
30 5 1 0 W 0 1 L -1 2 L -2 -3 -18
31 18 2 0 L 0 1 W 2 2 L -2 0 -18
32 19 2 0 L 0 1 W 2 2 L -2 0 -18
33 26 3 0 L 0 1 L -1 2 W 4 3 -15
34 30 3 0 L 0 1 L -1 2 W 4 3 -12
35 37 0 0 L 0 1 L -1 2 L -2 -3 -15
36 31 3 0 L 0 1 L -1 2 W 4 3 -12
37 17 2 0 L 0 1 W 2 2 L -2 0 -12
38 26 3 0 L 0 1 L -1 2 W 4 3 -9
39 20 2 0 L 0 1 W 2 2 L -2 0 -9
40 17 2 0 L 0 1 W 2 2 L -2 0 -9
41 30 3 0 L 0 1 L -1 2 W 4 3 -6
42 22 2 0 L 0 1 W 2 2 L -2 0 -6
43 14 2 0 L 0 1 W 2 2 L -2 0 -6
44 29 3 0 L 0 1 L -1 2 W 4 3 -3
45 25 3 0 L 0 1 L -1 2 W 4 3 0
46 12 1 0 W 0 1 L -1 2 L -2 -3 -3
47 3 1 0 W 0 1 L -1 2 L -2 -3 -6
48 22 2 0 L 0 1 W 2 2 L -2 0 -6
49 8 1 0 W 0 1 L -1 2 L -2 -3 -9
50 14 2 0 L 0 1 W 2 2 L -2 0 -9
51 30 3 0 L 0 1 L -1 2 W 4 3 -6
52 26 3 0 L 0 1 L -1 2 W 4 3 -3
53 5 1 0 W 0 1 L -1 2 L -2 -3 -6
54 32 3 0 L 0 1 L -1 2 W 4 3 -3
55 26 3 0 L 0 1 L -1 2 W 4 3 0
56 21 2 0 L 0 1 W 2 2 L -2 0 0
57 12 1 0 W 0 1 L -1 2 L -2 -3 -3
58 36 3 0 L 0 1 L -1 2 W 4 3 0
59 11 1 0 W 0 1 L -1 2 L -2 -3 -3
60 1 1 0 W 0 1 L -1 2 L -2 -3 -6
61 37 0 0 L 0 1 L -1 2 L -2 -3 -9
62 28 3 0 L 0 1 L -1 2 W 4 3 -6
63 36 3 0 L 0 1 L -1 2 W 4 3 -3
64 24 2 0 L 0 1 W 2 2 L -2 0 -3
65 27 3 0 L 0 1 L -1 2 W 4 3 0
66 32 3 0 L 0 1 L -1 2 W 4 3 3
67 27 3 0 L 0 1 L -1 2 W 4 3 6
68 11 1 0 W 0 1 L -1 2 L -2 -3 3
69 5 1 0 W 0 1 L -1 2 L -2 -3 0
70 25 3 0 L 0 1 L -1 2 W 4 3 3
71 22 2 0 L 0 1 W 2 2 L -2 0 3
72 4 1 0 W 0 1 L -1 2 L -2 -3 0
73 11 1 0 W 0 1 L -1 2 L -2 -3 -3
74 34 3 0 L 0 1 L -1 2 W 4 3 0
75 25 3 0 L 0 1 L -1 2 W 4 3 3
76 27 3 0 L 0 1 L -1 2 W 4 3 6
77 25 3 0 L 0 1 L -1 2 W 4 3 9
78 0 0 0 L 0 1 L -1 2 L -2 -3 6
79 21 2 0 L 0 1 W 2 2 L -2 0 6
80 22 2 0 L 0 1 W 2 2 L -2 0 6
81 33 3 0 L 0 1 L -1 2 W 4 3 9
82 19 2 0 L 0 1 W 2 2 L -2 0 9
83 32 3 0 L 0 1 L -1 2 W 4 3 12
84 3 1 0 W 0 1 L -1 2 L -2 -3 9
85 14 2 0 L 0 1 W 2 2 L -2 0 9
86 7 1 0 W 0 1 L -1 2 L -2 -3 6
87 33 3 0 L 0 1 L -1 2 W 4 3 9
88 31 3 0 L 0 1 L -1 2 W 4 3 12
89 11 1 0 W 0 1 L -1 2 L -2 -3 9
90 23 2 0 L 0 1 W 2 2 L -2 0 9
91 28 3 0 L 0 1 L -1 2 W 4 3 12
92 24 2 0 L 0 1 W 2 2 L -2 0 12
93 4 1 0 W 0 1 L -1 2 L -2 -3 9
94 31 3 0 L 0 1 L -1 2 W 4 3 12
95 4 1 0 W 0 1 L -1 2 L -2 -3 9
96 30 3 0 L 0 1 L -1 2 W 4 3 12
97 13 2 0 L 0 1 W 2 2 L -2 0 12
98 34 3 0 L 0 1 L -1 2 W 4 3 15
99 10 1 0 W 0 1 L -1 2 L -2 -3 12
100 12 1 0 W 0 1 L -1 2 L -2 -3 9
101 33 3 0 L 0 1 L -1 2 W 4 3 12
102 18 2 0 L 0 1 W 2 2 L -2 0 12
103 28 3 0 L 0 1 L -1 2 W 4 3 15
104 29 3 0 L 0 1 L -1 2 W 4 3 18
105 16 2 0 L 0 1 W 2 2 L -2 0 18
106 13 2 0 L 0 1 W 2 2 L -2 0 18
107 34 3 0 L 0 1 L -1 2 W 4 3 21
108 37 0 0 L 0 1 L -1 2 L -2 -3 18
109 5 1 0 W 0 1 L -1 2 L -2 -3 15
110 29 3 0 L 0 1 L -1 2 W 4 3 18
111 4 1 0 W 0 1 L -1 2 L -2 -3 15
112 29 3 0 L 0 1 L -1 2 W 4 3 18
113 37 0 0 L 0 1 L -1 2 L -2 -3 15
114 1 1 0 W 0 1 L -1 2 L -2 -3 12
115 6 1 0 W 0 1 L -1 2 L -2 -3 9
116 32 3 0 L 0 1 L -1 2 W 4 3 12
117 33 3 0 L 0 1 L -1 2 W 4 3 15
118 23 2 0 L 0 1 W 2 2 L -2 0 15
119 0 0 0 L 0 1 L -1 2 L -2 -3 12
120 32 3 0 L 0 1 L -1 2 W 4 3 15
121 18 2 0 L 0 1 W 2 2 L -2 0 15
122 27 3 0 L 0 1 L -1 2 W 4 3 18
123 15 2 0 L 0 1 W 2 2 L -2 0 18
124 8 1 0 W 0 1 L -1 2 L -2 -3 15
125 22 2 0 L 0 1 W 2 2 L -2 0 15
126 9 1 0 W 0 1 L -1 2 L -2 -3 12
127 8 1 0 W 0 1 L -1 2 L -2 -3 9
128 2 1 0 W 0 1 L -1 2 L -2 -3 6
129 3 1 0 W 0 1 L -1 2 L -2 -3 3
130 37 0 0 L 0 1 L -1 2 L -2 -3 0

It took 130 spins to have a drawdown, come back to even, make a profit and go back to breaking even.  If we had a win target of say 9 units, that would have been accomplished in numerous occasions, spin 77 being the first one. 

Let's take now permutation 2, that is betting nothing on Dozen 1, 2 units on Dozen 2 and 1 unit on Dozen 3 on the same first few spins of Zumma roulette tester:

Spin Zumma Numbers Dozen Bet on Dozen 1 W/L Dozen 1 Units Dozen 1 Bet on Dozen 2 W/L Dozen 2 Units Dozen 2 Bet on Dozen 3 W/L Dozen 3 Units Dozen 3 Total Units Net
1 13 2 0 L 0 2 W 4 1 L -1 3 3
2 9 1 0 W 0 2 L -2 1 L -1 -3 0
3 22 2 0 L 0 2 W 4 1 L -1 3 3
4 32 3 0 L 0 2 L -2 1 W 2 0 3
5 2 1 0 W 0 2 L -2 1 L -1 -3 0
6 6 1 0 W 0 2 L -2 1 L -1 -3 -3
7 13 2 0 L 0 2 W 4 1 L -1 3 0
8 6 1 0 W 0 2 L -2 1 L -1 -3 -3
9 21 2 0 L 0 2 W 4 1 L -1 3 0
10 18 2 0 L 0 2 W 4 1 L -1 3 3
11 15 2 0 L 0 2 W 4 1 L -1 3 6
12 24 2 0 L 0 2 W 4 1 L -1 3 9
13 18 2 0 L 0 2 W 4 1 L -1 3 12
14 21 2 0 L 0 2 W 4 1 L -1 3 15
15 32 3 0 L 0 2 L -2 1 W 2 0 15
16 9 1 0 W 0 2 L -2 1 L -1 -3 12
17 34 3 0 L 0 2 L -2 1 W 2 0 12
18 3 1 0 W 0 2 L -2 1 L -1 -3 9
19 32 3 0 L 0 2 L -2 1 W 2 0 9
20 5 1 0 W 0 2 L -2 1 L -1 -3 6
21 26 3 0 L 0 2 L -2 1 W 2 0 6
22 19 2 0 L 0 2 W 4 1 L -1 3 9
23 31 3 0 L 0 2 L -2 1 W 2 0 9
24 2 1 0 W 0 2 L -2 1 L -1 -3 6
25 6 1 0 W 0 2 L -2 1 L -1 -3 3
26 3 1 0 W 0 2 L -2 1 L -1 -3 0
27 9 1 0 W 0 2 L -2 1 L -1 -3 -3
28 1 1 0 W 0 2 L -2 1 L -1 -3 -6
29 29 3 0 L 0 2 L -2 1 W 2 0 -6
30 5 1 0 W 0 2 L -2 1 L -1 -3 -9
31 18 2 0 L 0 2 W 4 1 L -1 3 -6
32 19 2 0 L 0 2 W 4 1 L -1 3 -3
33 26 3 0 L 0 2 L -2 1 W 2 0 -3
34 30 3 0 L 0 2 L -2 1 W 2 0 -3
35 37 0 0 L 0 2 L -2 1 L -1 -3 -6
36 31 3 0 L 0 2 L -2 1 W 2 0 -6
37 17 2 0 L 0 2 W 4 1 L -1 3 -3
38 26 3 0 L 0 2 L -2 1 W 2 0 -3
39 20 2 0 L 0 2 W 4 1 L -1 3 0
40 17 2 0 L 0 2 W 4 1 L -1 3 3
41 30 3 0 L 0 2 L -2 1 W 2 0 3
42 22 2 0 L 0 2 W 4 1 L -1 3 6
43 14 2 0 L 0 2 W 4 1 L -1 3 9
44 29 3 0 L 0 2 L -2 1 W 2 0 9
45 25 3 0 L 0 2 L -2 1 W 2 0 9
46 12 1 0 W 0 2 L -2 1 L -1 -3 6
47 3 1 0 W 0 2 L -2 1 L -1 -3 3
48 22 2 0 L 0 2 W 4 1 L -1 3 6
49 8 1 0 W 0 2 L -2 1 L -1 -3 3
50 14 2 0 L 0 2 W 4 1 L -1 3 6
51 30 3 0 L 0 2