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Parrondo's Paradox

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Re: Parrondo's Paradox

#31

Post by hgsgm »

tristanj wrote: post #5

I've always found this paradox interesting, as it was discovered fairly recently (1996) compared to other paradoxes in math.

It's because the paradox relies on an unintuitive "mistake in your homework" premise that defines things in an unhelpful way. ( Game A+B+Rule C has different outcomes from Game A and Game B is obvious. You have to mistakenly hide Game C from your mind in order to make a paradox. It's a word game, mis-describing what is happening before doing it.

The resolution is "stop hitting yourself".

Re: Parrondo's Paradox

#32

Post by hgsgm »

keithplayer wrote: post #19
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 the HN relevant use case would be looking at this from the opposite side. You've designed 2 games (or algorithms) and both result in a winning state. But when they are used alternately, they lead to worse outcomes. A made up, possibly bad example that's using similar 'rules': Start with: 1 large fixed size data structure and 1 cache Algorithm A: Checks as it is iterating whether the cache is full. If not, it…

It's a mathematician discovering why we have integration tests.

Re: Parrondo's Paradox

#33

Post by jetunsaure »

yellowstuff wrote: post #12
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?

Yeah, this seems pointless. Here's an example of the paradox: 1) Hitting both nails and screws with a hammer is a losing game. 2) Screwing both nails and screws with a screwdriver is a losing game. Paradox alert! If you hammer the nails and screw the screws you've transformed two losing games into a winning game!

Or:

1) Wearing shorts and sandals all year round is a losing game (in this part of the world); you will freeze to death in the winter.

2) Wearing your warmest clothing all year round is a losing game; you will overheat in the summer.

This is a paradox, because the population of Canada should be zero. But wait! What if you just dress appropriately for the season?

Re: Parrondo's Paradox

#34

Post by nomind »

Life itself is a loosing game:-)

We die at the end and all we've accumulated doesn't worth a thing. Game over.

But paradoxically, by being alive, playfull and involved in playing the loosing game of life we win... moment after moment.

Re: Parrondo's Paradox

#35

Post by rustybolt »

It sounds counterintuitive, but it's not that hard to come up with an example.

Suppose you have a game where your score is A*B. The strategy to only increase A or only increase B are losing ones, but combining them gives a winning strategy.

Re: Parrondo's Paradox

#36

Post by playingalong »

vivegi wrote: post #27

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 therefor…

I think you are missing a "not" in your first paragraph. "You cannot"

Re: Parrondo's Paradox

#37

Post by [deleted] »

playingalong wrote: post #36
vivegi wrote: post #27

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 therefor…

I think you are missing a "not" in your first paragraph. "You cannot"

[deleted]

Re: Parrondo's Paradox

#38

Post by seanhunter »

I often wondered whether some old-school poker players are actually unintentionally doing a variant of this. If you analyze the play of someone like Daniel Negranu from a game theoretic perspective it's clear that lots of the things he does are just bad (blind limps, check in the dark on the flop etc)[1] but taken together over more than one hand they create situations which are positive ev by widening the ranges they might have in a particular spot and therefore increasing the advantage of information asymmetry (they know exactly what they have whereas the opponent only knows a now very wide range they could have).

[1] By which I mean these are strategies that are strictly dominated in the game-theory sense.

Re: Parrondo's Paradox

#39

Post by bmacho »

hgsgm wrote: post #29
duxup wrote: post #3

Earlier quoted context omitted.

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.

In my experience almost in every topic it is way better textbook than any textbook. Simply because Wikipedia has the right scope, and the right amount of content. Wikipedia can, and almost always do talk about anything in math in 3 different levels, and tell everything related (including history) about everything. Textbooks can't do that.

To be said, this article is not graspable at first for me either. There is the "even simpler example"[0], but I am not even sure if it is a right example (different games can share a state, the amount of money), or just an analogy.

[0] : https://en.wikipedia.org/wiki/Parrondo's_paradox#The_simple_...

Re: Parrondo's Paradox

#40

Post by bmacho »

boomboomsubban wrote: post #26
maxk42 wrote: post #4

Earlier quoted context omitted.

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.

Breaking our links, nice move!

Unrelated, but I always want to link permanent wiki articles, but there is no culture for it, and I am afraid it would annoy people because it is uncommon.

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