Garcia Pelayo BIAS wheels

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How to spot biased wheels

 

In order to spot a possible wheel bias, since we don’t own them to make physical measures, we have to recur to statistical analysis of its behavior, and here we really have to use Mathematics.

 

It is necessary to investigate if a roulette wheel does have a behavior which deviates from the expected for a perfect machine, and in order to achieve this we have to know first how would this machine work perfectly. For this purpose I created the “positive” concept. If after 36 spins a number comes out once, there won’t be any positive nor negative. If it comes out twice, we have a positive (+1), if it appears three times, we have two positives (+2), etc. If it doesn’t show at all, then we have a negative (-1). We base this on the accounting for the actual financial payout, not its real probability which is to come out once every 37 spins.

 

How many positives a number can have after a certain amount of spins at a perfectly balanced wheel? Or rephrasing the same –and this question is valid for the game and many other aspects-: What are the limits of pure random luck?

 

I built a computer software which emulated a perfectly random game, this means, without any bias, and I ran millions of spins on it. I deducted I’d need at least 2,000 separated trials per each numerical segment considered, being these segments going in an augmentation at a rate of 100-spin intervals. For instance, for the 1,000 spins segment, I had to process 2 million samples, and likewise for every new block of numbers, there was the need to execute as many tests as the result of the multiplication of said block by 2,000 needed trials. Let’s see:

 

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Let’s analyze the tables above with four different amounts of spin samples.

 

If we have to use a 300-spin length sampling, we can observe the sum of “positives” (times above the expected considering 36-spin cycles) for numbers is around +37. Let’s turn it the other way around; if there have been 300 spins, each numbers has to have been spun 300/36 = 8.33 in order to be breaking even. This means those which have been spun 8 times are losing a little, and those which have showed 9 times are winning something. If a number has appeared 14 times it is clear it has 14-8.33 = 5.67 which we will express in an abbreviated form like +5. Let’s suppose the exact same situation has occurred for 6 other numbers also, they all will make a total sum of 5.67 + 5.67 + 5.67 + 5.67 + 5.67 + 5.67+ 5.67 = 39.69. as no other number has been spun over 9 times, then we say the amount of total positives at this table at 300 spins is +39. We can declare the table is a bit above the “randomly expected “ (+37) yet in addition it is far from the “soft limit” which is located at +46.

 

What is the “Soft Limit”? It is the maximum reached by 95% of those 2,000 trials. Only 5% of trials went over this amount of positives, then we can affirm it is hard to pass the soft limit, as this only happens at this 5% of instances by pure random luck at an wheel without any bias.

 

What is the “Hard Limit”? It is the one which has only happened once at these 2,000 trials. Therefore it is something belonging to a probability factor of 1 in 2,000, a tiny 0.05% to be spun by pure “random luck”, which finds here the limit we were looking for.

 

Previous example with its 39 positives doesn’t unveil anything about this particular table. Some numbers have appeared more than others but not in a significant enough scenario. If would be significant shall the sum of the positives at this table were +50, which albeit not being one 100% certain, it does places the table past the Soft Limit and makes us think this wheel points to the right direction. The true wonder would, be if its positives get to sum +64, which would clearly state this table as having a very strong tendency, which we can consider like a savings account for us to take the money from. When doing a 300-spin sample I haven’t accounted for such a deviation. We need to collect more spins for statistics, as the best wheel we have found (we call them “Tables type A”) have to go with this amount of spins at a +39 approximately. Please allow me to make a pause in our walk to further explaining what is a “Table type A”.

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Table types:

 

If we have reliable statistics, gathered from what we know is a single table after 5,000 spins, we have to know, by looking up at chart above, that the regular outcome is for total positives to go around +109, if they pass over +143 we can be in front of something interesting, and if they are above +192 we have in presence of an authentic bomb. This happened to our “Tables type A”, which by this time have left behind every doubt, as they have gone past –in average- with their +197, the mythical hard limit. So we have more than 99.95% degree of certainty this particular table has bias, and therefore, the expected is for those deviated numbers to continue their sustained deviation as they have been doing.

 

Most common wheels we found when scouting, “Tables type B”, were at +153 positives, and the worst ones, “Tables type C”, with some (but very little) bias, were already at +135, still within the boundaries of the Soft Limit.

 

We started our bias attack when the numbers which have been appearing the most at target Wheel do have passed the Soft Limit. By having 95% certainty of their bias, we tought it was worth risking remaining 5% (only once out of every 20 occasions) having the regular outcome of these attacks being the table “moving forward” and deviating in favor of those numbers while we were betting, till it passed by the “hard limit” which gave us absolute security (no wheel passed this hard limit and went back; unless it is manipulated, there is no way back from it). If the target wheel went back from SOFT limit -as we mentioned, this can happen 1 ouf of every 20 times-, we simply stopped betting on it and its losses were compensated by the wins obtained from those which have been faithful to their spotted biases.

 

If we have recorded 10,000 spins from a single table (this record could be at intervals, made at several days, several different sessions, without it being an impediment for going off the table a half-hour to have diner, but we must always be 100% certain they are from the same table, which hasn’t been replaced in any of its elements; reason for which we have to take note of any identifiable physical traits which ensure us proper identification of this particular wheel), with this record we already have a clear definition from what this machine can offer us. Even if its quality for the effect of our attack is reduced (“Table type C”) for the purpose of eligibility it should have gone past “Soft Limit” already (+174) and must be at least at +195. If it doesn’t has reached these numbers, it is better to just forget about what this table has to offer, as there is little to no advantage to be derived from it.

 

When a random table reaches a 30,000-spin sample, its average and soft limit start to descend and it it expected to continue under this fashion until the point on which, after many spins analyzed, there won’t be any number with “positives” remaining, as house advantage has imposed over all of them and none achieves appearing above the expected when averaged against 1 per every 36 spins, as its actual probability is to make it once per every 37 spins and that “flagstone” has been imposed over them in a definitive way. But is the table has Bias, some number would have been “catapulted” or “rocketed” and they will continue going upwards. Even at a “Table type C” it would have passed above the hardest limit, guaranteeing its advantage, even if a small one. IF the table has any quality and it is a “Table type A”, it sails now at an stratospherically high +966 which is impossible to find at a truly unbiased level wheel which has its “random maximum” (by pure luck) placed at a hard limit of only +294.

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Betting methodology for biased wheels

 

When we find a wheel which has passed the HARD limit, the procedure to follow is to bet every number which is in positive. If only the SOFT limit has been surpassed, we used to execute a cut on those numbers which positives didn’t pass from +8 in order to avoid “false positive” numbers which could be at this amount of positives by pure random. We made an exception with those numbers with lesser than eight positives which were surrounded -at the numerical wheel disc disposition- by other within a range of large “positivity”.For instance we had number 4 at +2 but its two neighbours 19 and 21 were both above +20: we’d play the three numbers.

 

The study about wheels’ performance with lighter or bolder biases (Types A, B and C), was made in an elaborated computerized fashion simulating roulettes with a similar behavior to those real tables we have been at, this way we could study its future behavior and their possible level of advantage. A “Table type A” should provide us with an amount of 30 “positives” at a 1000-spin sample. This mean we’d be winning the equivalent to thirty straight-up number payout once we played this amount of hands. At a “Table type B” net earning was 20 positives, being this amount shrunk to only 12 positives when dealing with “Tables type C”. With these calculations I did a forecast on earnings (70 million “pesetas”), which happened to be so exact at “Casino de Madrid” during summer ’92. I also calculated possible yield or return for our first month in Amsterdam, which was absolutely necessary in order to balance the high costs attached to staying plus the mandatory previous study we had to perform at the “city of canals”.

 

Let’s have a look at another interesting table created by those results provided by the computer at millions of simulations from an unbiased wheel:

 

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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.

 

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.

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Har du vunnit något eller myttare du bara? För du sa ju att CC stockholm skulle byta ut sina rulle hjul med scalopped, men det är inte sant. De kör ju fortfarande standard huxley. Visst biasad wheel fungerar, det gäller att bara hitta dom.

 

Tilted wheel

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Fungerar också..

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Har du vunnit något eller myttare du bara? För du sa ju att CC stockholm skulle byta ut sina rulle hjul med scalopped, men det är inte sant. De kör ju fortfarande standard huxley. Visst biasad wheel fungerar, det gäller att bara hitta dom.

 

Tilted wheel

Dealers signature (under vissa förutsättningar)

Fungerar också..

 

Visst finns det fungerande metoder.

Du kan t.o.m skriva om dom på ett öppet forum utan att någon fattar att dom kan skaffa sig en edge över Kasinot.

Det krävs dock en hel del kunskap om visual ballistics - physics - ifall man ska lyckas.