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Previous chapters:

The roulette bias winning method of García Pelayo

Betting system for

biased wheels

As we can observe, if we have a 😗 thousand spins taken from a truly random

table, without bias, we would hardly find the most spun number having something 😗 beyond

15 positives. Likewise, we have a soft limit for the best two numbers, the two which

have been spun 😗 the most, of +26. If we continue searching for different groups of best

numbers, we can center in the sum 😗 of the best nine, which have a soft limit of +67. Why

the soft limit only? Because the hard limit 😗 is too erratic and luck might make a number

to fire-up without actually having any bias. It is more trustworthy 😗 to work with the

soft limit, which occurs 95% of the time, making decisions based on it. These tables

are 😗 more reliable the larger the numerical group is. Application to a single number

being more doubtful than the sum of 😗 the best six, where it is harder for luck to

interfere in a decisive manner. I make the study only 😗 up to the best nine, because if

there are ten or more best numbers outside the limit, it tells the 😗 table is entirely

good, and this is already studied on the first part.

How do these tables complement the

previous analysis? 😗 It might be the case that a roulette as a whole doesn’t goes beyond

the soft limit, as we studied 😗 at the beginning, but the best four numbers do go beyond.

They can be bet without much risk, awaiting to 😗 collect more data which defines with a

higher accuracy the quality of the current roulette table. When a roulette is 😗 truly

good, we will likewise reinforce on its quality by proving it does go outside of the

limits set on 😗 these tables.

Always using simulation tests on the computer, this is, in

a experimental non-theoretical way, I studied other secondary limits 😗 which assist to

complete the analysis of any statistics taken from a roulette. For instance, “how many

consecutive numbers, as 😗 they are ordered on the wheel, can be throwing positives?”, or

“How many positives can two consecutive numbers have as 😗 a maximum?”. I do not show

these tables because they are not essential and only confirm BIAS which should have

😗 been detected by the tables previously shown. Any way, we will see some practical

examples below.

So far the system was 😗 based on evidence that -although simulated- was

being empirical; these were made with the help of the computer in order 😗 to verify the

behavior of a random roulette.

I found the limits up to where luck alone could take it,

then 😗 I was able to effectuate a comparison with real-life statistics from machines

which were clearly showing result outside the limits 😗 of pure chance, this is, they

pointed to trends that would remain throughout its life if their materials would not

😗 suffer alterations. These physical abnormalities could be due to pockets of unequal

size, however small this inequality, lateral curvatures leaving 😗 sunken areas with the

counterweight of other raised areas. Or even a different screwing of the walls from the

pockets 😗 collecting the ball so that a harder wall means more bounce. With the

consequent loss of results that are increased 😗 in the neighboring pockets which collect

these bounced balls with a higher frequency than normal.

On theoretical grounds I

studied areas 😗 of mathematics unknown to me, in the probability branch, and worked a lot

with the concept of variance and standard 😗 deviations. They helped me, but I could not

apply them correctly given the complexity of roulette, that is more like 😗 a coin with 18

sides and 19 crosses bearing different combinatorial situations, which invalidate the

study with binomials and similar.

The 😗 major theoretical discovery was forwarded to me

by a nephew, who was finishing his career in physics. He referred me 😗 some problems on

the randomness of a six-sided die. To do this they were using a tool called the « 😗 chi

square », whose formula unraveled -with varying degrees of accuracy- the perfection or

defects from each drawn series. How 😗 come nobody had applied that to roulette?

I handled

myself with absolute certainty in the study of the machines, to which 😗 the fleet had

already pulled out great performance up to that date, thanks to our experimental

analysis, but theoretical confirmation 😗 of these analyzes would give me a comforting

sense of harmony (In such situations I’m always humming «I giorni

dell’arcoballeno»*.

We 😗 carefully adapt this formula to this 37-face die and it goes as

follows:

The chi square of a random roulette should 😗 shed a number close to 35.33. Only

5% of the time (soft limit) a number of 50.96 can be reached 😗 -by pure luck- and only

0.01% of the time it will be able to slightly exceed the hard limit of 😗 67.91.

We had to

compare these numbers with those from the long calculations to be made on the

statistics from the 😗 real wheel we were studying. How are these calculations made?

The

times the first number has showed minus all tested spins 😗 divided by 37, all squared,

and divided by the total of analyzed spins divided by 37.

Do not panic. Let’s suppose

😗 the first number we analyze is the 0, to follow in a clockwise direction with all other

roulette numbers. Let’s 😗 suppose on a thousand spins sample number 0 has come out 30

times:

(30-1000/37) squared and the result divided by (1000/37) 😗 = 0.327

The same should

be done with the following number, in this case in wheel order, proceeding with 32 and

😗 following with all roulette numbers. The total sum of results is the chi square of the

table. When compared with 😗 the three figures as set out above we will find if this

machine has a tendency, more or less marked, 😗 or it is a random table instead.

The

calculation, done by hand, frightens by its length but using a computer it 😗 takes less

than a flash.

Statistical analysis of numbers and wheel bias identification

strategy

While in my experimental tests I only watched 😗 leader numbers , this chi-square

test also has in mind those numbers that come out very little and also unbalance 😗 the

expected result.

There was a moment of magic when I found that the results of the

previous tables were perfectly 😗 in accordance with the results that the chi-square test

threw.

With all these weapons for proper analysis I did a program 😗 from which, finally,

we’ll see some illustrations:

TOTAL POSITIVE + 127 HIGHER + 24 L1 + 41 L2 + 70 L3 😗 + 94

L4 + 113

LB + 174 A + 353 B + 243 C + 195 NA 4 AG 60 😗 AD 46 N.° P 12 SPINS 10.000

CHI

37,18 50,96 67,91 35,33 DV-7,51 ROULETTE/DAY: RANDOM

*LB = Límite blando = Soft

limit.

In 😗 this chart I created throwing 10,000 spins to simulate a random table, we can

find all patterns of randomness; this 😗 will serve to compare with other real tables

we’ll see later.

In the bottom of the table, to the left at 😗 two columns, there are all

European roulette numbers placed on its actual disposition starting at 0 and continuing

in clockwise 😗 direction (0, 32 15, 19, 4, 21, 2, 25, etc.). We highlighted those which

have appeared more, not only based 😗 on their probability, which is one time out of 37,

but also based on the need to profit, i.e. more 😗 than once every 36.

If the average to

not lose with any number would be 1.000/36 = 27.77, our 0 has 😗 come out forty times;

therefore it is on 40, to which we subtract 27.77 = 12.22. Which are its positives, 😗 or

extra shows; therefore we would have gain. When 20 is – 4 4, 7 8 it is the number 😗 of

chips lost on the 10,000 spins thrown.

In the first row we find the total positive sum

of all the 😗 lucky numbers is +127 (the mean of a random table in our first table is

+126), away from the soft 😗 limit* (*Soft limit = Límite blando = LB), which is at the

beginning of the second row, and which for 😗 that amount of spins is +174. Next to it is

the reference of known biased tables, (All taken from the 😗 first table) which shows that

even the weakest (table C) with +195 is far from the poor performance which begins 😗 to

demonstrate that we are in front of a random table where drawn numbers have come out by

accident, so 😗 it will possibly be others tomorrow.

Returning to the first row we see

that our best number has +24 (it is 😗 2) but that the limit for a single number ( L l )

is +41, so it is quite normal 😗 that 2 has obtained that amount, which is not

significant. If we want to take more into account we are 😗 indicated with L2, L3 and L4

the limits of the two, three and four best numbers, as we saw in 😗 the second tables (our

two best would be 2 and 4 for a total of +42 when their limit should 😗 be +70). Nothing

at all for this part.

In the middle of the second row NA 4 it means that it 😗 is

difficult to have over four continuous single numbers bearing positives (we only have

two). AG 60 tells us that 😗 the sum of positives from continuous numbers is not likely to

pass sixty (in our case 0 and 32 make 😗 up only +21). AD 46 is a particular case of the

sum of the top two adjacent numbers (likewise 0 😗 and 32 do not reach half that limit).

After pointing out the amount of numbers with positives (there are 12) 😗 and the 10,000

spins studied we move to the next row which opens with the chi square of the table.

In

😗 this case 37,18 serves for comparison with the three fixed figures as follow: 50.96

(soft limit of chi), 67.91 (hard 😗 limit) and 35.33 which is a normal random table. It is

clear again that’s what we have.

Follows DV-751 which is 😗 the usual disadvantage with

these spins each number must accumulate (what the casino wins). Those circa this amount

(the case 😗 of 3) have come out as the probability of one in 37 dictates, but not the one

in 36 required 😗 to break even. We conclude with the name given to the table.

From this

roulette’s expected mediocrity now we move to 😗 analyze the best table that we will see

in these examples. As all of the following are real tables we 😗 played (in this case our

friends “the submarines” *) in the same casino and on the same dates. The best, 😗 table

Four:

(* Note: “Submarines” is the euphemism used by Pelayo to name the hidden players

from his team).

TOTAL POSITIVES + 😗 363 HIGHER + 73 L1 + 46 L2 + 78 L3 + 105 L4 + 126

LB

+ 185 A + 😗 447 B + 299 C + 231 NA 4 AG 66 AD 52 N.° P 13 SPINS 13.093

CHI 129,46 50,96

😗 67,91 35,33 DV-9,83 ROULETTE/DAY: 4-11-7

What a difference! Here almost everything is

out of the limits: the positive (+363) away from 😗 the soft limit of 185. The table does

not reach A but goes well beyond the category of B. The 😗 formidable 129.46 chi, very far

from the fixed hard limit of 67.91 gives us absolute mathematical certainty of the very

😗 strong trends this machine experience. The magnificent 11 with +73 reaches a much

higher limit of a number (L1 46), 😗 11 and 17 break the L2, if we add 3 they break the

L3, along with 35 they break the 😗 L4 with a whopping +221 to fulminate the L4 (126). It

doesn’t beat the mark for contiguous numbers with positives 😗 (NA 4), because we only

have two, but AG 66 is pulverized by the best group: 35 and 3,along with 😗 that formed by

17 and 37, as well as the one by 36 and 11. The contiguous numbers that are 😗 marked as

AD 52 are again beaten by no less than the exact three same groups, showing themselves

as very 😗 safe. Finally it must be noted that the large negative groups ranging from 30

to 16 and 31 to 7 😗 appear to be the mounds that reject the ball, especially after seeing

them in the graph on the same arrangement 😗 as found in the wheel.

Playing all positive

numbers (perhaps without the 27) we get about 25 positive gain in one 😗 thousand played

spin (the table is between B and A, with 20 and 30 positives of expectation in each

case). 😗 It is practically impossible not winning playing these for a thousand spins,

which would take a week.

Another question is chip 😗 value, depending on the bank we have.

My advice: value each chip to a thousandth of the bank. If you 😗 have 30,000 euros, 30

euros for each unit. These based on the famous calculations of “Ruin theory” precisely

to avoid 😗 ruining during a rough patch.

Another interesting table for us, the

Seven:

TOTAL POSITIVES + 294 HIGHER + 83 L1 + 56 😗 L2 + 94 L3 + 126 L4 + 151

LB + 198 A +

713 B + 452 C + 325 😗 NA 4 AG 77 AD 62 N.° P 13 SPINS 21.602

CHI 77,48 50,96 67,91 35,33

DV-16,22 ROUILETTE/DAY: 7-9-3

This table seven, 😗 with many spins, is out of bounds in

positives and chi, but the quality is less than C. It has, 😗 however, a large area

ranging from 20 to 18 having almost +200 by itself, that breaks all NA, AG and 😗 AD,

which while being secondary measures have value here. No doubt there’s something,

especially when compared with the lousy zone 😗 it is faced with from 4 to 34 (I wouldn’t

save the 21). Here should be a “downhill area” which 😗 is detected in this almost

radiography. The slope seems to end at the magnificent 31. Also add the 26. Finally, 😗 a

typical roulette worth less than average but more than B and C which is out of bounds

with three 😗 well defined areas that give a great tranquility since even as it doesn’t

has excessive quality, with many balls it 😗 becomes very safe.

Table Eight:

TOTAL

POSITIVES + 466 HIGHER + 107 L1 + 59 L2 + 99 L3 + 134 L4 😗 + 161

LB + 200 A + 839 B + 526

C + 372 NA 4 AG 83 AD 73 N.° 😗 P 14 SPINS 25.645

CHI 155,71 50,96 67,91 35,33 DV-19,26

ROULETTE/DAY: 8-12-7

It is the first time that we publish these authentic 😗 soul

radiographies of roulette. My furthest desire is not to encourage anyone who,

misunderstanding this annex, plays happily the hot 😗 numbers on a roulette as seen out

while dining. That’s not significant and I certainly do not look forward to 😗 increase

the profits of the casinos with players who believe they are practicing a foolproof

system. It takes many spins 😗 to be sure of the advantage of some numbers. Do no play

before.

Be vigilant when you find a gem to 😗 detect they do not touch or modify it in

part or its entirety. If this happens (which is illegal but 😗 no one prevents it), your

have to re-study it as if it were a new one.

Regardless of how much advantage 😗 you have

(and these roulette tables are around 6% advantage, ie, more than double the 2.7%

theoretical advantage of the 😗 casino) it does not hurt that luck helps. I wish so to

you.

I refer to all the days as "Bonus Days." Now that I am in my golden years I refer to them as "Double Bonus Days!"