Talk:Parrondo's paradox

The math second illustrative example
Note that the probability of game B is not (2/3)(3/4) + (1/3)(1/10) - ε, which is 16/30 - ε and might suggest that B is actually a winning game.

"Harmer and Abbott[1] show via simulation that if M = 3 and ε = 0.005, Game B is an almost surely losing game as well." I should like to point out that simulation cannot show that such a statement is true; it may well strongly suggest that Game B is almost surely losing but the only way to prove it is to, well, prove it. Surely a more accurate wording would be "Harmer and Abbott[1] simulate Game B with M = 3 and ε = 0.005 and the results strongly suggest that this is an almost surely losing game as well." If one wants a proof then (as Harmer and Abbott[1] say) one needs to look at "Parrondo’s Paradoxical Games and the Discrete Brownian Ratchet, Proceedings of Upon’99, The Second International Conference on Unsolved Problems of Noise and Fluctuations, University of Adelaide, July 12-16, 1999, eds. D.A. Abbott and L.B. Kish, American Institute of Physics, Melville, New York 511 (2000) 189–200." —Preceding unsigned comment added by 128.243.220.22 (talk) 10:58, 16 February 2009 (UTC)

Note that Harmer and Abbott[1] actually has a confusing mistake in it, where, in the caption to Figure 1, it states "... coin 3 has a poor probability of winning, so B is a losing game." Coin 3 actually has an excellent chance of winning. Luckily, the main text of Harmer and Abbott[1] mentions in passing that Coin 3 is played a "little more often" than coin 2, which is the key to the math. What makes B a losing game is the steady state probability of using each coin, as specified in the main article for this topic. One might guess that the probability of using Coin 3 was 2/3, which is not true.

Problem of evil
I removed the following paragraph from the article:


 * Parrondo's paradox can interestingly be expanded as an objection to the problem of evil. It is true by Parrondo's paradox that sequential negative events can result in a positive outcome, suggesting that the problem of evil may ignore such possibilities. Parrondo's paradox effectively allows every negative event to eventually have a positive outcome. Empirically, President Clinton's approval ratings rose above pre-scandal levels after his admission of his sex scandal with Monica Lewinsky. Both his sexual action and his admission could be seen as losing strategies regarding presidential approval ratings, but the American public saw his apology as an honorable deed, fulfilling Parrondo's Paradox.

First, I'm worried about whether it is orignal research. It needs to be sourced if it is to be re-introduced. Even if sourced, I think that they will make the article harder (rather than easier) to understand, because it introduces a confusion. Parrondo's paradox is not paradoxical because of the simple addage "to wrongs don't make a right", it is rather more complex. --best, kevin [kzollman][talk] 07:59, 16 April 2006 (UTC)
 * I fully support what you did. I have not been able to keep update with the happenings of the page and saw the problem just now when you edited the talk page. Even I feel that the paragraph is Original Research. Parrando's Paradox should not be used to correlate events when no such justification exists. I don't know what to do with "agriculture" as it too is Original Research. There hasn't been any mathematical modelling of the phenomenon to establish a causation. Even if its true, the events are correlated, but causation is yet to be proved. -Ambuj Saxena (talk) 08:11, 16 April 2006 (UTC)

How is your challange to the way he put it valid? Many sources mention it. He put it in his own terms but they are in line with published sources. Not OR. Can you show a published source for your challange? Is there a published challange to mentioning two wrongs make a right in this context? If not your challange is OR. Those kinds of invalid challanges to every nit picking fact causes citations for articles to be longer than the articles. Most citations represent a response to a challange based in ignorance not one in compliance with wiki policy.

98.164.64.68 (talk) 07:04, 31 May 2019 (UTC)

External Links & References
The link Parrondo's Paradox Game at http://seneca.fis.ucm.es/parr/GAMES/ doesn't work --Mrebus 05:17, 8 November 2006 (UTC)


 * Try http://seneca.fis.ucm.es/parr/GAMES/index.htm

More critical sources are needed
Many academic circles do not think this paradox is actually worth anything. For example the example that Parrondo gives is rather... hand picked to prove a point. Game B is actually +ve expectation. Parradno says "a naive (and wrong) argument is as follows: coin 3 is used 1/3 of the time, whereas coin 2 is used 2/3 of the time" thus Game B is possitive expectation. But Parrondo then goes onto say that because the amount of money you have effects how game B plays, the it does end up having negetive expectation. But this is completely fallacy. If playing the game depends on the amount of money you have, then plays of the game are not indepedant events, but dependant upon one-another. Thus you cannot slimply play Game B multiple times, you are infact playing 1 round of a game that is not yet complete and has a positive expected value. Notice his game B is so rediculous that no such game exists in real life. Infact there isn't really any expample that exists in real life that can support this paradox, because the paradox is circular reasoning, he claims two negetive make a positive, when in reality there exists a negetive and a positive all along.

Stating the paradox
The article says:
 * Given two games, each with a higher probability of losing than winning, it is possible to construct a winning strategy by playing the games alternately.

it seems to me that it is not appropriate to say "each with a higher probability of losing than winning" because one of the games is allowed to have a probability of winning that in some case can be greater than the probability of losing.--Pokipsy76 (talk) 21:58, 18 February 2008 (UTC)

Quantum Communication: when 0 + 0 is not equal to 0
If communication channels that Fail (carry 0 content), when working together in pairs could actually communicate a single bit of information. Is this an example of a Parrondo's Paradox?

http://arxivblog.com/?p=554 —Preceding unsigned comment added by Rbenech (talk • contribs) 20:24, 2 January 2009 (UTC)

Statistical observations of the 'paradox'
When running a statistical test which returns number of played games under various conditions one realizes that all the 'paradox' does is change the ratio of played B1 and B2 games, which wins the 'B' game and offsets the small 'A' game loss. Logically, if the winning game is played more often, the return is positive. In this case (game 'B1'=9%, 'B2'=74% winning chance), playing the 'B' game alone produces 39% 'B1' games and 61% 'B2' games which is unfavorable to chances and the 'B' game finishes at loss. However when injecting almost neutral 'A' game, the ratio of 'B' games changes, so for example in the 'ABBAB' sequence 'B2' is played 72% of time (of 'B' games) which provides positive outcome.

I will leave it to mathematicians to make the proof of it, but no wonders here.

Besides and above all, the returns in the 'B' games are not proportional to chances, in which case the total return would be as expected (loss) regardless of the frequency and/or sequences of the played games. For the above examples the return for individual games should be roughly: +49/-51 for the 'A' game; +89/-10 for 'B1' and +24/-76 for 'B2' game, which would put 'the paradox' where it belongs.

It is just amazing that such stuff can be a subject of academic researches. --activeco


 * I doubt that it is. The article has a long reading list, but I wonder how many of the authors there take this "paradox" seriously. Maproom (talk) 22:32, 10 August 2011 (UTC)

Needs an animation showing how the alternating rachet ramp makes things go up
Would make the concept much easier to grasp. --TiagoTiago (talk) 02:00, 22 November 2011 (UTC)


 * The way it's written it's simply nonsense. Why should some marbles move to the valley towards A, up-slope and over a steeper edge, and none towards B? --Thrissel (talk) 22:38, 9 February 2012 (UTC)

Another coin-tossing example
Let us consider the following two games. Our start capital is an integer amount of Euros (€). The rules: It is easy to see that both games are losing games, with an average loss of 1€ per game, if played in a random sequence. The sequences (CCCCC...) and (DDDDD...) are even worse. But the sequence (CDCDCD...) wins!
 * 1) Coin 1 is a (highly) biased coin that always makes us win. Coin 2 is a (highly) biased coin that always makes us lose.
 * 2) Winning a game earns us 1€ and losing requires us to surrender 2€.
 * 3) In Game C, we first determine if our capital is an even number. If it is, we toss Coin 1. If it is not, we toss Coin 2.
 * 4) In Game D, we first determine if our capital is an even number. If it is, we toss Coin 2. If it is not, we toss Coin 1.

We see that it is essential for the example that the earnings depend on the current capital. And that the current capital depends on which games were played before - in a very sophisticated way in the A and B example of the Article, and in a simple way here (odd = C before, even = D before). --Peter Buch (talk) 12:52, 6 March 2012 (UTC)

The sawtooth setup doesn't give equal probabilities
I have a problem with the statement: "Now consider the second case where we have a saw-tooth-like region between them. Here also, the marbles will roll towards either ends with equal probability"

This case is analagous to a sawtooth shaped potential surface in physics with an oscillating force applied, which is known as a "rocking ratchet". As suggested by the name, it leads to preferential motion in one direction. In this case, towards B. So the second case here is actually a losing game even before the whole setup is tilted, see the diagram and explanation on page two of this article:

IEEE Transactions on Applied Superconductivity 19 3698 — Preceding unsigned comment added by 130.130.37.84 (talk) 03:24, 22 May 2012 (UTC)

A Simplified Example
"Playing Game B exclusively is also a losing strategy, since you will lose three out of every four times you play...."

Really? Schnaz (talk) 18:51, 22 November 2012 (UTC)


 * Yep. Try it with any starting number. Say, $113. $113 is not a multiple of 5, so you lose $6, reducing you to $107. $107 fails, so you lose again and go to $101. $101 fails, so you lose again and go to $95. At $95, you win $8 because $95 is a multiple of 5, so you increase your bank to $103. So far, that's 3 losses, and 1 win. Continuing to play with $103 in the bank...


 * $103 (lose)... $97 (lose)... $91 (lose)... $85 (win)... $93 (lose)... $87... (lose)... $81 (lose)... $75 (win)... $83...


 * So you lose 3 out of every 4 games. -Hatster301 (talk) 21:39, 22 November 2012 (UTC)


 * Are we talking about the same thing? I thought game B has even/odd criteria, not modulo-5. --Schnaz (talk) 17:00, 10 April 2017 (UTC)

Pretty inaccessible article for most people
Having read this twice I am, as the learned judge once said, "none the wiser". Unfortunately I am not even, as counsel retorted "No, just better informed".

What on earth does "There exist pairs of games, each with a higher probability of losing than winning, for which it is possible to construct a winning strategy by playing the games alternately." mean? It only makes any sense if you already know what the paradox is about. Read it cold (as I did) and its gobbledygook. Its a perfect example of the techies paradox - the summary is only understandable if you've already read the detail. (I made that up BTW)

Update: In fairness, having read it a third time prior to this edit, the light bulb does go on when reading the "simplified example" although it's still not obvious that there are any real life examples. (I think the "application" section basically says we haven't found one.)

I'm not qualified to edit this but I really do think sticking the simplified example at the top, re-writing the lede and perhaps simplifying the language in the non-technical paragraph would make the article more accessible. 212.74.5.11 (talk) 08:04, 1 July 2015 (UTC)