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Parrondo's Paradox: How two ugly parents can make a beautiful baby

datagenetics.com

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Re: Parrondo's Paradox: How two ugly parents can make a beautiful baby

#41

Post by lotharbot »

softbuilder wrote: post #38

Struggling with this one. Help me out: If I play roulette and bet black, red, red, black, red, red, etc., I'm going to win?

One way to think about it is that there are really three games: game A (a slight loser), and games which I'll call BL (losing) and BW (winning). If you win a couple rounds of BW, the casino changes you to playing BL for a round. But if you don't play BL and instead go play A for a round, then when you come back to the table you'll be back to game BW. So you use game A, a slight loser, to avoid BL, a bad loser.

Playing only A is a slightly losing strategy. Playing a mix of BW and BL is a losing strategy, because BL is so harsh. But if you play BW mixed with A, you combine big wins with small losses, and therefore come out ahead.

This doesn't work in roulette because, no matter what color you play, it's a slight loser. Black and red are both examples of game A, so no matter how you mix them you're just playing AAAAAAAA.

Re: Parrondo's Paradox: How two ugly parents can make a beautiful baby

#42

Post by hcarvalhoalves »

"The key to understanding this paradox is that the two games are not independent."

Well... can it really be called a paradox then? It's more of a classical failure at defining the problem since the probability distribution of B definitely depends on A - the description is just more convoluted, but it's not a contradiction.

Re: Parrondo's Paradox: How two ugly parents can make a beautiful baby

#43

Post by kschults »

lotharbot wrote: post #41
softbuilder wrote: post #38

Struggling with this one. Help me out: If I play roulette and bet black, red, red, black, red, red, etc., I'm going to win?

One way to think about it is that there are really three games: game A (a slight loser), and games which I'll call BL (losing) and BW (winning). If you win a couple rounds of BW, the casino changes you to playing BL for a round. But if you don't play BL and instead go play A for a round, then when you come back to the table you'll be back to game BW. So you use game A, a slight loser, to avoid BL, a bad loser. Playin…

That's an excellent explanation of what's actually going on in this situation. Thank you.

Re: Parrondo's Paradox: How two ugly parents can make a beautiful baby

#44

Post by unreal37 »

pastaking wrote: post #39

I read the article and understood what he's saying - but how exactly do two ugly parents make a beautiful baby?

They don't. But two losing games (the parents) can be combined to make a winning strategy (the beautiful baby).

(I read the whole article til the end waiting to see what this had to do with genetics. It doesn't.)

Re: Parrondo's Paradox: How two ugly parents can make a beautiful baby

#45

Post by yeahboats »

brilee wrote: post #25
brilee wrote: post #23

Uh... Something's fishy with the first graph of the 'drunken man's walk'. It's well known that the random walk veers away from the zero-line at a rate sqrt(N), where N is number of flips. Normalized by the number of flips, the random walk converges to the zero-line at the rate 1/sqrt(N). The graph does neither, so I'm not quite sure how it was generated...

Oops, I misinterpreted how the graph was generated... but the complaint still holds. The averaging of a million trials will cut the amplitude of the fluctuations by a factor of 1000, but the sqrt(N) effect should still be visible. (Note that if you multiply the Y-axis by sqrt(million) = 1000, then you get a scale of about 20, which is approx sqrt(500))

I'm not very good at this stuff, but I don't see anything wrong with the graph. It hovers around 0. A Brownian motion starting which starts at 0, will, at time T be normally distributed with mean 0 and variance T.

http://en.wikipedia.org/wiki/File:Random_Walk_example.svg

Some of them go up, some go down, but all will cross 0 infinitely many times, and all the paths averaged will equal 0.

Re: Parrondo's Paradox: How two ugly parents can make a beautiful baby

#46

Post by Scriptor »

viggity wrote: post #29

I was expecting something more along the lines of actual genetics, in which case two ugly parents make stunning children all the time. It is called hybrid vigor. The overwhelming amount of our produce is bred this way. They will inbreed corn like made so that it is 100% homozygous, but do it in five different pools. The resulting offspring of any two inbreds from two different pools is amazing. Inbred corn plants are…

And if the parents aren't homozygous it could be attributed to recessive genes. Same reason why two brunettes can have a blond child.

Re: Parrondo's Paradox: How two ugly parents can make a beautiful baby

#47

Post by softbuilder »

lotharbot wrote: post #41
softbuilder wrote: post #38

Struggling with this one. Help me out: If I play roulette and bet black, red, red, black, red, red, etc., I'm going to win?

One way to think about it is that there are really three games: game A (a slight loser), and games which I'll call BL (losing) and BW (winning). If you win a couple rounds of BW, the casino changes you to playing BL for a round. But if you don't play BL and instead go play A for a round, then when you come back to the table you'll be back to game BW. So you use game A, a slight loser, to avoid BL, a bad loser. Playin…

I think I understand now. Thank you!

Re: Parrondo's Paradox: How two ugly parents can make a beautiful baby

#48

Post by Scriptor »

viggity wrote: post #29

I was expecting something more along the lines of actual genetics, in which case two ugly parents make stunning children all the time. It is called hybrid vigor. The overwhelming amount of our produce is bred this way. They will inbreed corn like made so that it is 100% homozygous, but do it in five different pools. The resulting offspring of any two inbreds from two different pools is amazing. Inbred corn plants are…

And if the parents aren't homozygous it could be attributed to recessive genes. Same reason why two brown-haired parents can have a blond child.

Re: Parrondo's Paradox: How two ugly parents can make a beautiful baby

#49

Post by unreal37 »

Imagine if instead of Game B being dependent on your cash balance, let's say Game B is blackjack and your chances of winning depend on the number of 10s/face cards that have already been played.

If the collective number of 10s/face cards already played is If the collective number of 10s/face cards already played is >= 35%, you have a negative chance of winning. You switch to roulette until the balance of 10s/faces works back in your favor.

I think that could be a winning strategy when playing blackjack and roulette together. LOL

Edited to add: I think the author's point is that there are games where you can calculate your chances of winning "this hand" even though your chances over time are negative, and you should avoid playing (switch to something where your chances are better) when your chances are low. Which is a bit of an obvious point for such a long article filled with graphs.

Re: Parrondo's Paradox: How two ugly parents can make a beautiful baby

#50

Post by unreal37 »

GavinB wrote: post #13

Isn't it a little sketchy to have one of the "games" be a game that takes into account outside information like your balanace? Here's another "paradox": Game A: You lose a dollar every time. Game B: If the last game you played was game A, you win a million dollars. Otherwise, you lose a dollar. AAAAAAA... loses, BBBBBBB... loses, but ABABABABA... makes you rich! Suddenly it doesn't seem so paradoxical to me.

Your balance isn't really outside information. In a game like Texas Holdem Poker, your balance is a key factor in how much you bet.

But if we change the game so that "if you flip more than two heads in a row, your chances of flipping a third head are only 10%; if you flip two tails in a row, your chances of flipping a third tail are 90%", the result is the same, the odds turn more negative over time than Game A and you should switch to A after two consecutive flips.

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