[Guest]

a buyer likes a watch he sees. however, the seller wants 800 dollars for it, and the buyer wants to pay 500. a referee comes by and sees the problem. he makes the following bargain. he'll put 500 dollars under one of three cups. then shuffle. you then pick a cup, and put 500 dollars in that cup. the ref shuffles again then the seller picks a cup and puts the watch under that cup. then the buyer picks a cup and gets to keep whatever is in the cup. then the seller picks a cup and gets to keep whatever is inside. finally the ref gets the remaining cup. should the seller agree to play this game? should the buyer? is the ref really risking anything by making this bargain?

[Guest]

The seller should not play this game because in case he gets $500 cup, he looses the watch for $500 which is not what he wanted. The best case for him is to have his watch back (which he does before playing the game)and the worst case is to get loose $300 which he could get by selling it to someone else.

The buyer should play the game. He would either end up with the watch for $500 or get his money back. No risk for the buyer.

The refree (who gets either the $500 back or the watch) has nothing at stake (unless he likes the watch too and wants to buy it for $500).

Edited July 6, 2009 by DeeGee

[Guest]

The seller should not play this game because in case he gets $500 cup, he looses the watch for $500 which is not what he wanted. The best case for him is to have his watch back (which he does before playing the game)and the worst case is to get loose $300 which he could get by selling it to someone else.

The buyer should play the game. He would either end up with the watch for $500 or get his money back. No risk for the buyer.

The refree (who gets either the $500 back or the watch) has nothing at stake (unless he likes the watch too and wants to buy it for $500).

thats what I was going to put, but something does'nt seem right...

the ref shuffles the cup between each persons turn to add their contents..so that must mean that any one of them (besides the ref) could potentially add to a cup that already has something in it..if that's not the case, then it makes no sense to shuffle the cups until it comes time to 'pick n keep'

also if they could watch the ref shuffle, I could see a way the ref loses every time, and the buyer gets $1000 and the seller gets his watch back...then they are right back where they started..just the buyer doubled his money..there must be a reason it's in this forum..

Edited July 7, 2009 by James8421

[Guest]

There is a potential for each person to get nothing just as much as everything. Only the buyer should play the game, however. The buyer would be content to get $500 back and happy to get a watch or $1000 (or both), whereas the seller would be unhappy getting $500, content to get the watch back and only truely happy to get $1000. Assuming the ref does not want a watch, he would also only truely be happy getting $1000 back, content getting $500 back, and unhappy getting a watch (or nothing).

It comes down to the fact that all three would like more money, they would all be content to get back what they put in, but the buyer is the only one who would be gaining by getting the watch.

Edited July 7, 2009 by Austin CG

[Guest]

Everything here is left up to chance, from how it is worded it implies that more than one of the prizes could end up in the same cup. Both of the $500s could be placed in the same cup, because the referee places his item, shuffles, then the next prize is placed, and so on. Unfortunately for the referee his chance is the left overs; if this weren't the case he could profit the most out of the deal by keeping track of where each item is placed. All the prizes could end up in the same cup, and the first person could win it, or the referee could walk away with the spoils.

As far as who should play this, it is a risk for them all. If the referee's $500 gets into the same cup as someone else's spoils then there is a chance for him to loose his $500.

[Guest]

As phillip1882 said,

a buyer likes a watch he sees. however, the seller wants 800 dollars for it, and the buyer wants to pay 500. a referee comes by and sees the problem. he makes the following bargain. he'll put 500 dollars under one of three cups. then shuffle. you then pick a cup, and put 500 dollars in that cup. the ref shuffles again then the seller picks a cup and puts the watch under that cup. then the buyer picks a cup and gets to keep whatever is in the cup. then the seller picks a cup and gets to keep whatever is inside. finally the ref gets the remaining cup. should the seller agree to play this game? should the buyer? is the ref really risking anything by making this bargain?

Here are all the possible cup layouts.

1. all items. 2.nothing 3.nothing

1. $1,000 2.watch 3.nothing

1. $500 and watch 2.$500 3.nothing

1. $500 2.$500 3.watch

There are 8 items you can get in the possible cup layouts, and 4 useless cups. So buyer would have a %66.66 of getting something, if he does, the seller would have a %50 chance now that 4 possible things are gone. There would be a 4 out of 8 chance. If he gets something, there would only be %25 chance for the the ref so that would be bad for the ref. If the seller got nothing, then that eliminates the fourth possible layout. so then ref would have a 5 out of 6 chance, or more than an %83.3 chance of getting something, so that would make the ref's fate good. Now if the buyer gets nothing, the seller would then have more than an %83.3 chance of getting something. So the seller probably will get something. If he does, that only makes a %66.66 chance of getting something for the ref. If seller doesn't get anything, the ref. would have to get everything, so it's a %100 chance. let's multiply the fractions. The buyer of course has a %66.66 percent chance of getting something, the seller's chances are 4 eighths and 5 sixths. Now 24 out of 48 times 40 out of 48 equals 25 out of 60, 5 out of 12, which makes it about a %40 chance to get something. %40 times 2 equals %80. Then for the ref, of course there is a chance of getting all of it, %100 so you don't have to include it. 1 out of 4, 5 out of 6, and 2 out of 3. well 20 out of 24 divided by 4 equals 5 out of 24. well 15 out of 72 divided by 3 is 5 out of 72, 5 out of 72 times 2 is 10 out of 72, a 10 out of 72 chance. 5 out of 36. About 1 out of 7. So the ref would have about 14 out of 100. 14 times 4 is 56. so he has a %56 chance of getting something. It's best for buyer, which has the highest advantage of getting something, worst for seller, who has the lowest advantage. The ref. probably shouldn't do it because he doesn't have the HIGHEST advantage of getting something.

[Guest]

Actually, there is no difference in any of their probabilities to get anything. To be more clear, at the end of the final shuffle, no matter what is in any cup, they each have a 1/3 chance of obtaining whatever the best choice is, no matter the order. For all intensive purposes they can all simultaneously point to a cup and have whatever is in there. Because of this, the only thing left is to examine gain-loss ratio. The only disadvantage is to the seller. His gain-loss ratio is much lower than that of the other 2 people. He wants to sell for 800. He can gain only 200 by getting 1000, gains nothing from the watch, and loses 300 if he gets a cup with $500 (or loses 800 with an empty cup). The other two only lose 500 by picking an empty cup, otherwise they each can gain 300 (picking watch) or 500 (picking 1000). They all gain obviosly if they choose a cup with everything, but the seller gains only 1000, while the other 2 gain 1300 (watch + 500).

[Guest]

Minimums for each person: 0$

maximums for each person 1000$

there is a 33%( roughly ) chance that one cup is empty and can contain 1k. Furthermore, its only an 11% chance that any one person will receive that much based on a .333 * .333 probability. (pick one cup, which a third of the time might have 1k in it)

the watch cup will always have just a watch. the other two cups are either .5k and .5k or 0k and 1k.

minimum for each person therefore is a 11% chance of nothing, a 33% chance of the watch, an 11% chance of 1k, 44%? chance of .5k (not sure if thats figured out right)

point is, the seller has only an 11% chance of profiting. most of the time he'll get 500 dollars, sometimes he'll get his watch back and sometimes lose everything. only when he gets the right cup, which one third of the time might ahve 1k in it will he actually profit.

referee similary has an 11% chance of losing money. He stands also an 11% chance of gaining 1k, and a 33% chance of a watch (+300$) and some other high percent of gettin ghis return value. He would stand a good stance to make this bet. if anything he's making a side bet flipping a coin whether he hits the empty cup or the big cup, when 1/3 of the time they exist. everything else for him will be break even or better (most of the time its in that tier)

the buyer is in the same stance as the ref.

[Guest]

If my logic is correct, then this is really a poor example of a puzzle, cause others are reaching the same conclusion, but arriving there incorrectly (if I'm right).

From what I figured there are 18 unique end possibilities. ThisIsALie has all the possible combinations for what the cups contain, but whom gets what cup is where I arrived at 18 different possibilities. Each person has the same chance of getting the same possibility, so ON AVERAGE each person would get a $600 return on their 'investment'. The only person investing more than that is the seller, so he wouldn't want to play. The other two are only investing $500 so they WOULD want to play.