another paradox

Originally posted by Peakite
I'm a bit puzzled as to why the person being offered the deal considers themselves to have the advantage. To actually offer the deal, said stanger in all probability would have less than average in their wallet (it would be daft of him to intiate the deal with a huge amount of money in it).

Sorry for the lack of clarity. There are two other people besides you. One that is offering the game to the you and the stranger.

Originally posted by ark13
Sorry for the lack of clarity. There are two other people besides you. One that is offering the game to the you and the stranger.

Do I know how much money I have in my wallet?

In that case the issue arises because of confusion between winnings and odds to win.

The odds will be even since the person initiating the bet has no idea of how much either person has, so each has the same chance of having most money.

Because the winner is the one with least money, he'll always get more money in return than from a normal evens bet, but as the figure itself is irrelevant for the odds.

Originally posted by BigDoggProblem
Do I know how much money I have in my wallet?

Yes, but not how much the other guy has. And it doesn't necessarily have to be a realistic amount. That's not what this puzzle's about. Assume it's just as likely that he has 1 cent or 10000000000000 etc. dollars, as it is that they've a normal amount like $100. You have no idea.

Going back to the initial question, what is wrong with their reasoning?

ok i see two ways to look at this problem

1) if the amount that can exist in either wallet is over a finite range i.e from say £1 to £10 or any finite range, then the probability of winning is 1/2 as each outcome is equally probable

2) however if no range is defined (i.e no limit to the amount the wallet can contain, even taking into account negative values as IOUs) then probabilities have no meaning, what i mean is there has to be a range of allowed probabilities or else the probability of having a particular value in one wallet falls to zero, which makes no sense.

If one person has an amount of money there will be an infinately large probabilty that the second person has more, and also an infinite probability that they have less.


Looking at the problem from case 2 then their reasoning is flawed as trying to assign a probability to either outcome becomes paradoxical as infinities are undefinable. They can neither win nor lose and the paradox remains.


heh i did something not so disimilar today in statistical mechanics in regards to energy states for two systems in thermal contact, but thats physics and i don't want to bore you all

Originally posted by ark13
Suppose someone comes up to you and a stranger on the street and asks you if you want to play a game. He explains that the game is very simple; you and the stranger both take out your wallets. Whoever has the least money, gets to keep the contents of both wallets. Assuming you didn't suspect any kind of fraud or trickery, would you play the game?

You co ...[text shortened]... the same way. But they can't both have the advantage. So what's wrong with their reasoning?

I think the fault is that both people have based there logic on two people who don't know how much they have in their wallets, whereas these two dudes doo.

i'm guessing it is a matter of wether i'm willing to take a chance (to loose what i have in my wallet)

it is more than obvious that the other person doesn't have much money, otherwise he would not propose this deal.

furthermore, there is a situation(as others have stated) when i would loose for sure(the stranger must have no money)

so if there is a situation when i would loose for sure, the risk isn't justified

This stranger would surely have no money. Since I don't even have a wallet would I win his wallet?

More seriously, say there is a sum of money $n, where it is disadvantageous to play this game, because nobody else carries that much. Then people with that much wil not play, so people with $n-$0.01 will not have any prospect of winning, so they won't play... etc. So the only people who will play are people with $0.00

Originally posted by Bowmann
Have a go at "The Monty Hall Dilemma".

This was discussed ad nauseum at
http://www.redhotpawn.com/board/showthread.php?threadid=11542

Originally posted by THUDandBLUNDER
This was discussed ad nauseum at
http://www.redhotpawn.com/board/showthread.php?threadid=11542

Interesting.

A somewhat morbid variation however 🙁

Originally posted by Bowmann
Interesting.

A somewhat morbid variation however 🙁

You obviously did not read very far, as the topic changes to Monty Hall later.
Anyway, Monty Hall is very well-known.

what if they have the same amount in their wallets

Then they pool their money and gamble it all away before getting drunk to forget their problems. Eventually they find themselves homeless on the street eating out of dumpsters. One rainy evening as they are shuffling to the dumpster to find what could be their last dinner, they see a shadow push apart the mist. It is a man with a rusty pipe. They try to run but are too weak from malnorishment. They are cornered in the alley and the crazed man is slowly, painfully bearing down upon the poor strangers. Suddenly with a grunt he swings the pipe with a skull crashing force that knocks both homeless men to the ground. Please don't kill us they think in a daze. But it's too late. The last thought in their heads before the pipe comes crashing down and they lie lifeless on the ground is, why did you have to ask that question?

So that's what happens. Any more questions *panting*?

Originally posted by soulby
ok i see two ways to look at this problem

1) if the amount that can exist in either wallet is over a finite range i.e from say £1 to £10 or any finite range, then the probability of winning is 1/2 as each outcome is equally probable

2) ...[text shortened]... ermal contact, but thats physics and i don't want to bore you all

If one person has an amount of money there will be an infinately large probabilty that the second person has more, and also an infinite probability that they have less.

I think there's a fundamental flaw in your logic. It's impossible to have such a thing as an "infinite probability" - the sum of all probabilities must be equal to one, by definition. I think you mean that there are an infinite different amounts that someone could have in their wallet (let's assume the wallet can hold an infinitely large amount of cash). But the probability of choosing any particular amount would be infinitely small: if I could be bothered to do the maths, it would be possible to show that the sum of all probabilities equals one.

(Think about it logically: how on earth can you have an infinte probability that the stranger will have both more AND less than you have in your wallet?)

As with most logic puzzles, you need to make some basic assumptions, for example:

1. Both wallets contain an amount in cash >= £0.00. (Or dollars , Euros, whatever!) Amounts in any wallet go up in discreet amounts, i.e. 0.01, 0.02 etc.

2. There is some kind of probability distribution for the amount of cash held in anyone's wallet at any particular time. Poisson distribution may be a reasonable starting point in this case.

3. You cannot tell from looking at the stranger how wealthy or otherwise he may be.

4. You know exactly how much you have in your own wallet.

5. If both you and the stranger have identical amounts, you each keep your own money.

Examples scenarios:

You have exactly £0.00 in your wallet. You have nothing to lose, so of course it would make sense to take the gamble.

You have exactly £0.01 in your wallet. You have very little to lose, and a very high chance of winning, so again it would make sense to take the gamble.

There will be a median point (given the Poisson ditribution assumed above), whereby there will be an equal chance of the strangers wallet containing either more or less than your own. I think the crux of the problem lies here - you don't know what that median point is, unless you've done shed-loads of research beforehand. You could make an educated guess, of course. If you were a gambling man, you could also decide that you were willing to risk the £17.37 in your wallet, knowing you could make a bigger return, even if the chance of winning was less than 50%.

In order to answer the problem completely, I think we would need to know more information than we have available.

In the spirit in which the question was asked - obviously it is impossible for BOTH you and the stranger to have an advantage.

You could reason that, if I have more than the stranger, he'll win just what I have. But if he has more, I'll win more than I have. Therefore, the game favors me. And the stranger can reason the same way. But they can't both have the advantage. So what's wrong with their reasoning?

What's wrong with the reasoning? The statement "The game favours me" is wrong. It's akin to placing a bet on a horse and saying, "If the horse loses, the bookies will only win my stake. If the horse wins, I'll win more than I have. Therefore, the game favours me." It just isn't a logical deduction.

Has this puppy gone to bed now? 😉