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.
