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Parrondo's Paradox

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Re: Parrondo's Paradox

#21

Post by nigamanth »

croutons wrote: post #20

I don’t really understand how this is a paradox, but it’s definitely surprising and non intuitive. It seems like if you have 2 games A and B, the second you start playing them together you’ve effectively created a new game C, which is a game of A and B combined.

> Is Parrondo's paradox really a "paradox"? This question is sometimes asked by mathematicians, whereas physicists usually don't worry about such things. The first thing to point out is that "Parrondo's paradox" is just a name, just like the "Braess's paradox" or "Simpson's paradox." Secondly, as is the case with most of these named paradoxes they are all really apparent paradoxes. People drop the word "apparent" in these cases as it is a mouthful, and it is obvious anyway. So no one claims these are paradoxes in the strict sense. In the wide sense, a paradox is simply something that is counterintuitive. Parrondo's games certainly are counterintuitive—at least until you have intensively studied them for a few months. The truth is we still keep finding new surprising things to delight us, as we research these games. I have had one mathematician complain that the games always were obvious to him and hence we should not use the word "paradox." He is either a genius or never really understood it in the first place. In either case, it is not worth arguing with people like that.

Re: Parrondo's Paradox

#22

Post by croutons »

simplicitea wrote: post #10

This seems like such a pointless semantic flex to me... In this case has the game not become Game A + Game B ? It's just a larger game with a distinct winning strategy because the ruleset is expanded right? What's the significance?

Agree completely

Re: Parrondo's Paradox

#23

Post by CamperBob2 »

croutons wrote: post #20

I don’t really understand how this is a paradox, but it’s definitely surprising and non intuitive. It seems like if you have 2 games A and B, the second you start playing them together you’ve effectively created a new game C, which is a game of A and B combined.

Exactly. Of course you can rig up a set of game rules that lead to a specified outcome under specified conditions. This paradox just boils down to a game rule that says "Alternately play these two subgames." I don't get it.

Re: Parrondo's Paradox

#24

Post by majormajor »

simplicitea wrote: post #10

This seems like such a pointless semantic flex to me... In this case has the game not become Game A + Game B ? It's just a larger game with a distinct winning strategy because the ruleset is expanded right? What's the significance?

Probability - and how you need to reason about independent vs dependent events - is poorly understood generally.

Let's try to make it HN-relevant by asking:

can two things that both AB tested positively in independent one-at-a-time testing possibly backfire if you launch both of them?

Re: Parrondo's Paradox

#25

Post by sdenton4 »

simplicitea wrote: post #10

This seems like such a pointless semantic flex to me... In this case has the game not become Game A + Game B ? It's just a larger game with a distinct winning strategy because the ruleset is expanded right? What's the significance?

I think a closer-to-real example is the problem of playing a collection of blackjack tables. All the games are the same, but sometimes the state of the decks (ie, which cards have been discarded) will lead to better odds of winning. If you know the state of the decks at each table, you can always choose to play the table with the best odds of winning. This type of strategy has been used to win piles of money in Vegas, FWIW, though it leads to ejection if you're caught.

This is similar to the 'ratchet' examples in the wikipedia page - you play the game with the best odds, and use one game to 'cool off' until you're in the right state to win the second game again. The games in the wikipedia article are kinda unsatisfying, though - there's too much dependence on player state.

Re: Parrondo's Paradox

#26

Post by boomboomsubban »

maxk42 wrote: post #4
bluedays wrote: post #2

Started reading the examples and my eyes glazed over. Someone have a better example?

Further down the article there's a simpler example: https://en.wikipedia.org/wiki/Parrondo%27s_paradox#A_simplif...

And now somebody edited it to put the simple example first.

I was really confused how anyone could glaze over with such a concise description, but they saw something different than I did.

Re: Parrondo's Paradox

#27

Post by vivegi »

If you take two mutually independent events and somehow introduce a dependence between the two, then the events are no longer mutually independent and therefore by law of conditional probability, you can influence the probability of the outcome of the combination.

Corollary: If you take two mutually dependent events and somehow break the dependence between the two, then the events are no longer dependent and therefore by law of conditional probability and law of independent events, you can influence the probability of the outcome of the combination.

A practical example of the corollary would be password re-entry user interfaces during account registration.

The reason while re-entering the password the second time, we are not shown what we typed earlier is to make the reentry independent of the previous entry. Otherwise, we may look at what was typed earlier and subconsciously type the same thing -- which would be bad while we are doing account registration.

Re: Parrondo's Paradox

#28

Post by hgsgm »

sdenton4 wrote: post #25
simplicitea wrote: post #10

This seems like such a pointless semantic flex to me... In this case has the game not become Game A + Game B ? It's just a larger game with a distinct winning strategy because the ruleset is expanded right? What's the significance?

I think a closer-to-real example is the problem of playing a collection of blackjack tables. All the games are the same, but sometimes the state of the decks (ie, which cards have been discarded) will lead to better odds of winning. If you know the state of the decks at each table, you can always choose to play the table with the best odds of winning. This type of strategy has been used to win piles of money in Vegas…

Market timing in the stock market (if you have a little insider info), and card counting in lotteries, are historical examples.

Re: Parrondo's Paradox

#29

Post by hgsgm »

duxup wrote: post #3
bluedays wrote: post #2

Started reading the examples and my eyes glazed over. Someone have a better example?

Sometimes Wikipedia reads like it is written by that math teacher who “just gets math” and teaches in a way that the only people who will understand … are people who already do. Granted maybe this article is good and just beyond me, but it is disappointing how much Wikipedia is like that.

It's a reference encyclopedia, not a text book, for better or for worse.

Re: Parrondo's Paradox

#30

Post by hgsgm »

croutons wrote: post #20

I don’t really understand how this is a paradox, but it’s definitely surprising and non intuitive. It seems like if you have 2 games A and B, the second you start playing them together you’ve effectively created a new game C, which is a game of A and B combined.

> I don’t really understand how this is a paradox,

You do:

> but it’s definitely surprising and non intuitive.

That's a common definition of a paradox: "a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true."

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