The ZONE for other bets?

[Bayes]

As we're in ZONE fever right now, I was wondering whether it might apply to other bets, such as streets or single numbers. How might you discover what the ZONE is for these?

One way might be to calculate the standard deviation for the ZONE (as applied to dozens - the original we have all come to love, or hate as the case may be).

The ZONE is between spins 5 and 8, so you could think of this as two triggers: one to start (after no hits at spin 4) and one to stop (after no hits at spin 8 ).
If we calculate the standard deviation for these values (what it is at spins 4 and 8 assuming no hits) we get the following:

For a dozen to not hit in 4 spins, the standard deviation (or z-score) is z_i = -1.38556
If it doesn't hit after 8 spins the z-score is z_f = -1.95948

Now we can use these values and the formula for the z-score to calculate what the ZONE is for each of the other bets (from betting 1 number upwards).

Here is the result: 

[table=,]
Numbers to Bet,   Trigger to Start,   Trigger to Stop
1,   69.00,   138.00
2,   34.00,   67.00
3,   22.00,   44.00
4,   16.00,   32.00
5,   12.00,   25.00
6,   10.00,   20.00
7,   8.00,   16.00
8,   7.00,   14.00
9,   6.00,   12.00
10,   5.00,   10.00
11,   5.00,   9.00
12,   4.00,   8.00
13,   4.00,   7.00
14,   3.00,   6.00
15,   3.00,   6.00
16,   3.00,   5.00
17,   2.00,   5.00
18,   2.00,   4.00
[/table]

If you don't have a clue what the standard deviation is, don't worry about it! (but you owe it to yourself to find out).

This seems like a reasonable and objective way of extrapolating the parameters of the ZONE to other bets, that's all. I make no claims neither have I done any testing - this is the brainstorming section!

[buffalowizard]

Hi Bayes

I play the ZOne with splits, and it works very well. I prefer getting a larger payout and laying down less bets. Probably a fallacy but oh well!

I also am working on a 9 number variant which is exciting too.

I may start to try working with Atlantis' labouchere progression he posted in the main Zone thread not too long ago, as i think that this is fundamental to the success of the system.

[Iceboy]

Was this done for a single zero? If so, could you provide the values for double zero as well? It's not clear to me how the numbers are derived.

Signed,
Mathematically Challenged

[Carpanta]

As we're in ZONE fever right now, I was wondering whether it might apply to other bets, such as streets or single numbers. How might you discover what the ZONE is for these?

You are right Bayes about other zones for different bets. I can tell you the ZONE exists for the streets too. You'll see very frecuetly that a street repeats in the interval of 5 spins. So the stakes will be for 5 spins.
So as to make it clear i put an example from real wheel land casino ( 0 wheel) :


26   street 9   start betting on street 9  1 chip
17              6   bet on street 9 and 6      1 chip
2                1   bet on street 9 6 1          1 chip
22              8   bet on street 9 6 1 8       2 chips       
2                1   win                                 +10               this is the new trigger so bet street 1 1 chip
0               just a loss and no street   bet street 1  1 chip
28             10 bet on street 1 and 10   1 chip
32             11 bet on streets 1 10 and 11  2 chip
25              9 bet on streets 1 10 11 8   3 chips
3               1 win                                    +12  street 1 trigger again  bet 1 chip
28             10  bet on streets 1 and 10  1 chip
19             7  bet on streets 1 10 7   1 chip
31            11  bet on streets 1 10 7 11  2 chips
11             4 bet on streets 1 10 7 11 4  3 chips
19             7 win                                    + 7          here starts again
16
25
17             win street 6
35
20
13
35               win street 12
4
25
36              win street 12
20
35              win street 12
12
0
16
34               win street 12
15
9
6
8                 win street 3
27
1
14
28
15               win street 5
26
29
13                win street 5
7
18
23
8                   win street 3
7                   win street 3
5
26
14
20
36                a loss  -29 chips
26
5
20
30
19


Playing this flat betting you dont win. You have an edge , like in fender's Zone, trying to skip the bad runs coz they dont appear commonly in bunches of 2 or more series but they can of course. A mild progression requiered and most important tracking how coming the bad runs so as to "guess" when best moment to start playng.

Later ill explain some interesting things about this cycles named The Cycles of the Streets.
And to be fair i dicnt discover these events with the streets. The italian guy who taught it to me is called ETABETA (well it is a nick). He  did a very fine research.

Have a good time,
Carlos.

[Bayes]

Was this done for a single zero? If so, could you provide the values for double zero as well? It's not clear to me how the numbers are derived.

Iceboy, yes single zero.

The formula for the z-score is  z = (w - np)/√np(1 - p)

You can find info on it here:
nolinks://vlsroulette.com/reference-area/how-to-know-when-you-have-a-good-strategy/

To get the numbers I posted above for the ZONE dozens, you first calculate the z-score for n = 4, w = 0 and p = 12/37, which gives you -1.38556. Repeat but this time use n = 8 which will result in -1.95948.

So far, so good. But for other bets, we don't want the z-score, we want to use the z-score found for the ZONE dozens to find the values of n for the other bets - see what I mean? we want to find triggers for the other bets which correspond to an "interval" (or ZONE) of -1.38556 standard deviations to -1.95948 standard deviations.

In that case you have to re-arrange the formula to get n on the left-hand side. This is easier to do if you set w = 0 in the formula. This is allowed because the ZONE is defined as a sequence of spins for which there are no winners in the first 8 spins (in the case of the dozens).

z = (0 - np)/√np(1 - p) = -np/√np(1 - p)

z² = n²p²/np(1 - p) = np/(1 - p)

n = z²(1 - p)/p

Now, using this new formula, we can calculate two values of n, using the values of z we calculated previously. The first  n will be calculated using z = -1.38556 and this will be the initial trigger (to start betting). To find the second value of n  which corresponds to the second trigger (the trigger to stop betting), use the other value of z (-1.95948).

So let's check this for betting on 3 numbers (a street).

The probability (p) of a street hitting is 3/37 = 0.08108

The trigger to start is:

n = (-1.38556)²(1 - 0.08108)/0.08108 = 21.7579

which rounded up gives 22.

The trigger to stop is:

n = (-1.95948)²(1 - 0.08108)/0.08108 = 43.5157  which rounded up gives 44.

You can probably see now how you calculate the values for double-zero wheel - just use 38 instead of 37 in the value of p. Actually they aren't much different:

[table=,]
1,   71.00,    142.00
2,   35.00,    69.00
3,   22.00,    45.00
4,   16.00,    33.00
5,   13.00,    25.00
6,   10.00,    20.00
7,   9.00,    17.00
8,   7.00,    14.00
9,   6.00,    12.00
10,   5.00,    11.00
11,   5.00,    9.00
12,   4.00,    8.00
13,   4.00,    7.00
14,   3.00,    7.00
15,   3.00,    6.00
16,   3.00,    5.00
17,   2.00,    5.00
18,   2.00,    4.00
[/table]

[Iceboy]

Thanks much, Bayes.

[Iceboy]

-