... back to roulette simulator
Presumably if you have reached this page, you have run the simulation. Hopefully, you have tried to run it for at least 10 million spins with various betting systems. If you have done so, you have probably reached the same conclusion that I did: all systems lose pretty close to the "house advantage".
The remaining comments focus on the "Reverse Labourchere" system described in "13 Against the Bank". It is that system that I originally created the simulation for. The many questions that I have received so far have been directed at that system.
I was initially disappointed when I created the simulator and saw its results. I had read the book "13 Against the Bank" when I was a teenager and had often thought about it. I created the simulation with the expectation that it would demonstrate that the system worked as the author described.
In one sense, the results shouldn't really be too surprising. If a simple system let any roulette player consistently "beat the bank", surely a large number of customers would be using it. Since casinos exist to make money, they would then have to "drop" the money-losing game or radically change its rules (which they have not).
There are a few possible answers that could explain why Norman Leigh's experience in "13 Against the Bank" differ from the results of this simulation. Each possibility is explored below:
One possibility is that my simulation doesn't play the betting system correctly. I plan to add an "audit" feature so that interested parties can see each spin and each bet themselves and so convince themselves that the simulation is faithful to the betting system. I have already spent time checking the simulation step-by-step myself. I have discovered and corrected a few minor errors in the process but the final result has been consistent.
Another suspicion is that the book was simply made up. The book was pleasant entertainment and probably garnered some good royalties for its author. I personally discount this scenario now. I have heard from a person in England who personally has the press clippings of Norman Leigh and his group making their triumphant return from France. I don't have a copy of these clippings myself but I believe that I could track them down if I took the time. Therefore, I personally believe that this group did make money using this system at that time.
Another reasonable explanation is that the group was lucky. The system worked for them because they got favourable spins. Since 12 were playing simultaneously, they may have effectively played for about 100,000 spins. By using an advanced simulation feature (not yet available on the Internet), I estimate that there is about a 10% chance that the system would appear to make money after 100,000 spins (but not an especially large amount of money). However, in games of chance, luck is possibility.
In deciding whether the simulation itself is at fault, there are two major aspects to consider:
As mentioned in the earlier point, I believe that I simulated the betting system properly (it's really not that tough to get correct).
However, the other aspect of creating an accurate simulation is correctly simulating the spin of a roulette wheel. In the computer, a "spin" is simulated using a random-number generator -- the computer generates a number that maps to a number on the roulette wheel. You may think that the random generator does a bad job. The fact is that random number generation is a well understood science and Java (the language I have used) has a solid random-number underlying generator.
Before getting back to random number generation, let's discuss roulette wheels. Are the numbers that appear on a roulette wheel truly random? Doing some research, a number of respectable authors believe that the one "weakness" in roulette may be that the wheel is a mechanical device run continuously by a person. In fact, the wheel might not be totally random. Some non-random aspects on a real wheel may include:
In any respectable casino, these imperfections are likely to be slight but, in the real world, they will be tough to completely eliminate to ensure total randomness.
Now let's assume that the author and his team of twelve were playing at wheels with slight imperfections. Remember the overall team was divided into two teams: one team of six on each wheel. Each member of a "wheel team" was assigned their own job: high, low, even, odd, black, red.
Let's assume that the wheel's imperfections tended to favour certain odd number and certain black numbers. What would happen when playing the Reverse Labourchere? The players betting "odd" and "black" would win more spins and tend to bet higher amounts (remember the system increases bets when winning and decreases bets when losing). Conversely those players playing "even" and "red" would tend to bet lower amounts (losers keep crossing off their numbers which keeps their betting amount small).
So the "wheel team of six" playing the system tends to bet higher on those numbers that come up more often (odd, black) and bet lower on numbers that come up less often (even, red). Assuming the wheel is not a perfectly random device, the players now have an advantage! In Europe, they only need to overcome the relatively small house advantage of 1.35%.
What if the casino changes the roulette wheels around the next day (as they do in practice, and surely would have done when losing money). Well the "wheel team of six" starts betting on the new wheel (from all angles). Maybe the new wheel slightly favours a few "high" numbers. The system will exploit this imperfection because the "high" player will tend to place higher bets while the "low" player will tend to place lower bets (the system works that way). Again, the system exploits any non-random imperfections in any wheel.
... back to roulette simulator
So what is the answer? Were the wheels in Monaco sufficiently non-random to allow these teams to overcome the 1.35% house advantage? Was the team on the lucky side for their 100,000 spins worth of bets? These questions cannot be answered objectively after the fact. It may be some combination of the two.
What is probably unlikely is that the system could be exploited in North America. In North America, the house advantage in roulette is almost four times as high at 5.26%. That is a much steeper advantage for any system to overcome.
First of all, my simulation sometimes does make money when simulating 100,000 spins (press the start button enough times with 100000 spins and European rules and see for yourself -- also change the Update Frequency to 100000 for faster repetition). So you see that the simulation does not discount the possibility of making money through luck.
Perhaps, more importantly, the simulation's random number generator can be more "truly" random than a mechanical spinning device run by a human. With good mathematics and electronics, the random number generator doesn't "wear down" and start to produce numbers that are not quite random. Therefore the simulation does have the sort of imperfections which the betting system can exploit (by placing higher bets on the more frequent numbers, as described above).
I believe that the best the Reverse Labourchere betting system can do is exploit imperfections in a roulette wheel. I don't know whether modern wheels have imperfections large enough to exploit by using such a system. If the system did work in the 1970s when the author tried it, I am sure that intelligent people in casinos quickly zeroed in on how this system overcame the house advantage. Perhaps the casinos learned that they had to maintain their roulette wheel to a higher standard to provide better "randomness". If the system did exploit a true weakness, then I strongly suspect that the casinos have managed to "plug" the weakness so that they can continue to make money. In other words, I wouldn't spend my money on trying to exploit the system.
The simulator that I created "plays" a series of very different betting systems. Each system seems to consistently lose money close to the house advantage (this surely would not surprise the casinos). In statistical terms, certain systems have a higher standard deviation but they all tend towards the same mean or average -- i.e. the house advantage. This has convinced me that roulette should be viewed as occasional entertainment where low bets are placed. You will lose some money, on average. However, if you control yourself, the experience shouldn't be too costly (and you might even lucky on some occasions and come out ahead).