# Parrondos paradox betting

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Metrics details In a game of chess, pieces can sometimes be sacrificed in order to win the overall game. Similarly, engineers know that two unstable systems, if combined in the right way, can paradoxically become stable. But can two losing gambling games be set up such that, when they are played one after the other, they becoming winning?

The answer is yes. This is a striking new result in game theory called Parrondo's paradox, after its discoverer, Juan Parrondo 1 , 2. Here we model this behaviour as a flashing ratchet 3 , in which winning results if play alternates randomly between two games. There are actually many ways to construct such gambling scenarios, the simplest of which uses three biased coins Fig. Game A consists of tossing a biased coin coin 1 that has a probability p1 of winning of less than half, so it is a losing game.

Figure 1: Game rules and simulation. But coin 3 has a poor probability of winning, so B is a losing game. The paradox is that playing games A and B in any sequence leads to a win. Full size image Game B Fig. The rule is that we play coin 2 if our capital is a multiple of an integer M and play coin 3 if it is not.

This means that, on average, coin 3 would be played a little more often than coin 2. Thus both A and B are losing games, as can be seen in Fig. If we play two games of A followed by two of B and so on, this periodic switching results in the upper line in Fig. I believe that there is indeed something here.

With all of the great players on this forum we can possibly figure it out. Enjoy and I look forward to your thoughts It's called Parrondo's Paradox after Dr. Juan Parrondo, a renowned physics professor from Madrid, Spain. I first learned about it by reading a late December article in the science journal Nature. Parrondo's Paradox shows how two losing games can be played alternately to produce a genuine positive expectation.

That's right It's based on a physics phenomenon called Brownian Ratchets. Early applications have Wall Street researchers achieving positive results in initial trials applying Parrondo's Paradox to losing stocks. I've been tinkering with Parrondo's concepts applied to casino roulette and believe I've got an adaptation that works. This is all brand new, but it's already getting a lot of immediate attention in the world of academia.

A brief article even appeared in the New York Times' science section a few weeks back. I've collected as much information as possible The math is very deep, but understanding the general principles is not difficult. The key to developing a successful casino play strategy seems to lie in the identification of particular casino bets that fit Parrondo's model. From my brief work, it appears that random roulette is suited to exploit the phenomenon.

Before I get to a roulette system using Parrondo's Paradox, a quick review of the principles: The Paradox proves that, when two losing games are played in a prescribed alternating fashion, they win. That's right. Two games that lose on their own may be combined to produce long-term consistent wins. It makes no logical sense, but it's a true, proven mathematically sound fact. That's why it's called a "paradox. His coins are weighted to produce consistent losing results. In our game of Roulette, we can closely approximate Parrondo's coin and game rotation parameters, but not perfectly.

In casino Roulette, we have a huge built-in mathematical disadvantage of minus 5. Parrondo's math doesn't predict whether or not his method is strong enough to overcome that big a disadvantage in the real world. It's up to us to find out.

Our initial testing has yielded promising results. The step-by-step instructions are given here. But, again, please realize that this is for testing only. It is yet an unproven Advantage Method. You will alternate play with each game. The three games will be labeled A, B1 and B2. Essentially, you will play in four-spin rotations. On the first spin, you will play A. On the second spin, you will again play A.

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