Parrondo's Paradox

[amk]

Parrondo's Paradox is very interesting especially for all the math experts out there. Some say it has no merit with regards to roulette. Others I have found have turned the wheel in their favor. First you will find the work of Jeff Patterson. Then after the explanation you will find a few hints which I discovered on the VLS forum. 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...........

                                                             PARRONDO'S PARADOX

There's a potential blockbuster new development in casino gaming theory. 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 ... two games that lose individually can be structured and played in an alternating fashion to produce consistent, long-term winnings ... and it can be proven mathematically. 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 ... which is substantial. 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."

Parrondo's math and computer models use coin tosses to demonstrate and prove his 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 5.26%. 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.


1) Start with a session bankroll of 503 units. (I suggest no greater than $1units after testing in "free play.")

2) With this method, you are actually going to play three games in one, all while seated at a single table. 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. On the third spin, you will play either B1 or B2. And on spin four, you will play either B1 or B2. Then, on spin five, you start the rotation all over again. To simplify, you alternate your play at two spins with game A, then two spins with game B, two spins with game A, two spins with game B, and so on. When playing game B, you have to choose between B1 and B2. This decision is based on the total value of your session bankroll at the time.

3) Game A is simple … $10 on Red. That's it, just a simple $10 even-money bet on Red.

4) Game B is also simple, but a little more involved. There are two games within B - B1 and B2. With B1, you bet $2 on 1, $2 on 2, $2 on 35 and $2 on 36 at four inside numbers, straight-up, for a total bet of $8 on the spin. With B2, you bet $10 on Red and $10 on Even two outside, even-money bets, for a total of $20. B1 is played when your total session bankroll (all of the money in front of you) is divisible by three. B2 is played when your bankroll is not divisible by three. For example, when the rotation calls for you to play game B, you total your bankroll. If it is divisible by three, you play B1. If it is not divisible by three, then you play B2. For a numerical example, if, when the rotation calls for you to play game B you have 105 units remaining in your session bankroll, then you play B1 (105 is divisible by three). If you have 235 units in your session bankroll, then you will play B2 (235 is not divisible by three).

5) Your session starts with a 503-unit bankroll and ends when you have played 100 spins. Each session is defined as 100 spins.

6) Theoretically, you should be slightly ahead at the end of each 100-spin session.


                                                                       HINTS:

These are posts from Rocky on the VLS forum who had great insight into applying the Parrondo's Paradox with success.........

link:://vlsroulette.com/index.php?topic=15067.0


POST 1:
What you say here is absolutely correct!

To tweak it, the secret lies in how you apply a money management system that works for this.

To give you a "hint" think about what is happening with 'even chance bets' like red/black, odd/even etc.
When one side is losing the other side is winning, by structuring a money management system that takes advantage of that, and that wins on both sides at the same time, (hint a staggered progression for both sides, but not the same for each) you'll have a very awesome system indeed. (Pretty close to the grail really). This info will guide you in the right direction simon.

P.S. we can all learn from one another, I learned what you described had a name, "Parrondo's Paradox".



POST 2:
It depends on how think and use your imagination. 'Differential Betting' ? I would say there would have to be many different variations and they would probably run to infinity. So with that in mind, some variations may have been proven losers as you say, but until all have been tested and proven that way, to make a sweeping statement to say, you thought they were proven to be losers, IS NOT CORRECT.

If you think you can, you will achieve anything, and if you think you can't, you're right also. It just depends on what you believe. I BELEIVE if you persist long enough you will solve any challenge.

I gave many clues in my previous post, to guide his thinking in the right direction to help solve simon's problem. It's now up to simon to apply and test, until he comes to a favourable outcome. Was it Edison who tested 1000 different ways till he hit upon the solution and Colonel Sanders who got 1000+ no's till he got a yes and then became a Millionare late in his life with his recipe. You know I've been studying Roulette since 2001, sometimes it takes time, too many people want the answer now, (instant gratification) without doing the work to get it.

Cheese, don't be like others who give up so easily, or listen to hearsay and believe it as truth until you have analysed, researched and questioned it as far as its validity and prove it to be TRUE, then you can speak with authority on the matter.

You know cheese it has been proven, to master any skill or subject you must put 10,000 hours in!
If you spend 1hr a day for 27 years+ you will reach your 10,000 hours, if you put in 8 hours a day, you'll reach it in just over 3 years.

It makes sense, a University student who's determined to do well will achieve great results in the 3 years that it takes to do his/her Uni degree. I know I am already over my 10,000 hours in studying Roulette and that's why I replied to simon, in that, I recognised his frustration in trying to solve something that looked (and is) solvable.
If he approaches it with the info I have given him, applying his imagination and brain power to the problem I believe he will solve it. It just depends on whether you're willing to pay the price TO ACHIEVE SUCCESS.

[reddwarf]

Jahh, so? Do you say that you have a winning system using parrondo? Or do you say that because Rocky said roulette could be beaten using parrondo this must be it?

1.
What is important for Parrondo to apply: there must be a positive expectation game, then by alternating between 2 losing games and a winning game, overall you can win... There is no positive expectation game within roulette, at least not that I know of.

2.
Rocky basically states that by playing both sides of the coin basically leads to a winning system: he actually stated that it is possible to create a system that wins on both sides at the same time!

Think about it: "both sides at the same time"...

reddwarf

[amk]

I am just putting the info out there reddwarf.......

See were it can take us. It seems that you have drawn your conclusions. I have a strong suspicion that there are players out there who have made this work for them.

Maybe we can to.........

[Tomla021]

I have played around with this with friends,,, No success so far and hard to wrap your mind around the concept and find the right bets. That being said  I do think there is something here.

[reddwarf]

Hi amk,

Just read the information about parrondo you can find on the web (here, here and here for example). The basic element is, that there always must be a positive expectation game.

in the basic setup there are 3 games, game A, a loosing game, and game B1 and B2. B2 is a winning game, B1 a loosing game. We decide to play game B1 or B2, depending on past results. We decide between A and B based either on random input, or we use a so called word describing the sequence (ABAB, AABAAB etc).

Again, there is no positive expectation game within roulette that I'm aware of. If you can show me one, than you have solved the roulette riddle, and you do not have to use parrondo, just play that game!

Do I believe roulette can be beaten? I do not know, so investigating it might be useful, but I do know that Parrondo is useless (again, there is no positive expectation game within roulette, and if there is you play this game so you do not need parrondo at all)

reddwarf

[marivo]

Every time we are in plus we restart the play. 

[Tomla021]

Iv'e always thought That Iceman was trying to get to a P Paradox in his as how shall we say unusual way:)

[Bayes]

Again, there is no positive expectation game within roulette that I'm aware of. If you can show me one, than you have solved the roulette riddle, and you do not have to use parrondo, just play that game!

Agreed, I'm not sure why there is a such a fuss about Parrondo, and it isn't a paradox at all. As reddwarf points out, not all games in PP can be losing, it's necessary that at least one bet gives a positive expectation.

Take the example from wikipedia:

A second example of Parrondo's paradox is drawn from the field of gambling. Consider playing two games, Game A and Game B with the following rules. For convenience, define C_t to be our capital at time t, immediately before we play a game.

   
• Winning a game earns us $1 and losing requires us to surrender $1. It follows that C_{t + 1} = C_t + 1 if we win at step t and C_{t + 1} = C_t âˆ' 1 if we lose at step t.
• In Game A, we toss a biased coin, Coin 1, with probability of winning . If , this is clearly a losing game in the long run.
• In Game B, we first determine if our capital is a multiple of some integer M. If it is, we toss a biased coin, Coin 2, with probability of winning . If it is not, we toss another biased coin, Coin 3, with probability of winning . The role of modulo M provides the periodicity as in the ratchet teeth.

Notice that in step 1 it says that the payoff is even money (+1 on a win, -1 on a loss). But in step 3, P₃ (the probability of winning) is a little less than 3/4. This is equivalent to a roulette bet of 27 numbers (roughly), because 27/37 ~ 3/4. Now, if any casino paid out even money on this bet, they wouldn't be in business for long. 

So, if this bet is available, WHY mess around mixing it up with other bets which just dilute the edge? Just play the advantage bet!

[reddwarf]

Hi AMK,

To humor you, i created a system, you can try to play with it:

Basics:
Game A: bet on the previous half, when previous number is zero, bet on high
game B1: bet on the previous line, when previous number is zero bet on 1
game B2: bet on previous two dozens, when 1 or more previous numbers are 0, bet on dozen 1

Game play:
we use the word AABB, in other words, we start with game A twice, then we choose B1 or B2 twice, then we play game A twice again etc.

Decision B1/B2:
We start with bankroll1= zero
we calculate if the bankroll1 can be divided by 4, if so, we play game B1, else B2

Now we have something new: money management:
We know that we do not have a winning proposition, so we simulate one:
we create 2 bankrolls, bankroll1 and bankroll2

whenever we play A, this result is added to bankroll 1
whenever we play B1 or B2, we add the result+1 to bankroll1 and substract 1 unit from bankroll2

however we also need a weak progression now:
we start with 1 unit
tif bankroll2 is positive, we play with 1 unit
when negative: -bankroll2 divided by 3 and rounded up to the nearest integer

however, we reset the progression whenever it reaches more than 100 + plus, after 38 spins we stop and reset the game, no matter what.

you can play with this, also try betting the inverse of the above, this will really amaze you 


reddwarf

(Just to show that I'm not only negative...)

[Bayes]

Wiki also says:

Simple finance textbook models of security returns have been used to prove that individual investments with negative median long-term returns may be easily combined into diversified portfolios with positive median long-term returns.^[10] Similarly, a model that is often used to illustrate optimal betting rules has been used to prove that splitting bets between multiple games can turn a negative median long-term return into a positive one. ^[11]

So although the Parrondo bet requires a winning game, there is some merit (my opinion) in choosing a diversified "portfolio" of roulette bets, and playing them in some kind of sequence (or simultaneously). There is in fact, mathematical proof that diversification reduces the variance, and if you can do that, you're halfway there. I can't prove any of this, but it's my preferred way of playing.

[reddwarf]

I added an example and a nice teaser,

just go play with it and check if it is useful...

reddwarf

PS in the table, the normal and the inverse are non cummulative!!!
PPS sorry, made small mistake: the word is AABB, and  of course, whenever we play B, only 1 unit is substrated, not 2 (mistake in the table), I added a new table

PPPS oops small mistake, I removed the teaser, WRONG!! and I updated the table

[reddwarf]

please note you can play with any of the above mentioned settings...

have much fun!

[reddwarf]

Hi Bayes,

This is related to volatility pumping, really interesting! But also here there is nothing magical going on...

[Gizmotron]

What makes this work for long stretches is that it takes a very complex segment of spins to kill it. This losing  segment is also a moving target.

You can take 20 - 40 very complex patterns and rotate their use randomly after each win. It's  harder to hit a moving target. The point is to attempt avoiding the killer sequences that can kill any one of these 20 - 40 complex patterns. On their own these patterns are already difficult to hit with the killer sequence. By not using them back to back it makes it way more difficult to match  up for a loss. Obviously a progression is the best way to use  this moving target method.

[GLC]

What makes this work for long stretches is that it takes a very complex segment of spins to kill it. This losing  segment is also a moving target.

You can take 20 - 40 very complex patterns and rotate their use randomly after each win. It's  harder to hit a moving target. The point is to attempt avoiding the killer sequences that can kill any one of these 20 - 40 complex patterns. On their own these patterns are already difficult to hit with the killer sequence. By not using them back to back it makes it way more difficult to match  up for a loss. Obviously a progression is the best way to use  this moving target method.

This statement by Giz is akin to the statement I made a few months back that it's harder to lose if you skip spins rather than play continuously.  Let's say you have 512 units and you want to see how many times you can win an attack before hitting a 10 streak loss.

If we choose a random sequence of Reds and Blacks say RBBRBRRRRB or we could use RRRRRRRRRR (any sequence has the same odds of repeating as any other) and we begin betting at random intervals, we can play for the rest of our lives and not pick an entry point that begins these exact 10 results.  Remember, after each win we wait for 1 or more spins before jumping back in for another attack.

Whereas, you would be hard pressed to bet continuously for very long before running into this exact sequence of spins.

If you had to bet your life on one or the other, don't you think random entry points would be the better choice?  I do!

Sorry if this is getting too far off the topic, AMK.  Feel free to delete.