Non-Poker Probability Paradox

[TallBrad]

This isnt probablity per se, but its a pretty well known little math teaser. Drove me nuts several years ago the first time I heard it.

More fun can be found here -> http://www.jimloy.com/puzz/puzz.htm

Three people are eating at a restaurant. The waiter gives them the bill, which totals up to $30. The three people decide to share the expense equally ($10 each), rather than figure out how much each really owes. The waiter gives the bill and the $30 to the manager, who sees that they have been overcharged. The real amount should be $25. He gives the waiter five $1 bills to return to the customers, with the restaurant's apologies. But, the waiter is a dishonest man. He puts $2 in his pocket, and returns $3 to the customers. Now, each of the three customers has paid $9, for a total of $27. Add the $2 that the waiter has stolen, and you get $29. But, the original bill was $30. What happened to the missing dollar?

There is no missing dollar. The customers have $3, the waiter has $2 and the restuarant has $25. That totals $30.

[Dave B]

Or, you could say:

each person was -10, rest +30 = 0

after:
each person now -9, rest +25, waiter +2 = 0

The trick is when people try to add the -9s to the plus 2 and ignore the +25

[Cyberhwk]

If there is infinity unique points between 1 and 0 (i.e. 1.1, 1.01, 1.001, 1.0001, etc.), then it stands that there should also be infinity points between 1 & 2. But wouldn't there be 2 X Infinity points between 1 & 2?

I think you mean 0 and 2 here?

Can't be because infinity would have to be finite, which it is not by definition.

I have no idea what this statement means.

...and don't even get started about .999999999 equaling 1.

I think you mean .9 repeating here. For two numbers to be different, you need to be able to find a number in-between them. There is no number between .9 repeating and 1, therefore, they are the same number.

Yes.

What it means is...if there is infinity points between 0 and 1, then (you're correct that's a typo), there should be 2 X infinity points between 0 and 2. But , how can one have more than infinity? (Yeah, this one's kind of lame. Solution = infinity is a abstract concept, not a number).

Ahhhhhh...I know there's a proof but that's a good simple way to explain it, thanks.

[galderon]

What it means is...if there is infinity points between 0 and 1, then (you're correct that's a typo), there should be 2 X infinity points between 0 and 2. But , how can one have more than infinity? (Yeah, this one's kind of lame. Solution = infinity is a abstract concept, not a number).

Now you're getting into advanced infinity math! Well, for one thing, there are different kinds of infinity, but the two you describe aren't different. Infinity is kind of a number, but it doesn't behave the same way with regards to math. This is where your false paradox comes from (because Infinity * 2 = Infinity).

I could go on, but I won't, since we're really far from poker at this point.

[snoogins47]

Supposedly, the answer is mathematical, but it defies conventional logic.

Or, it doesn't defy any form of logic, it's just not intuitive to most people.

btw, supa, your first few posts were missing the point. The point isn't that your odds increase, that's pretty obvious: with one choice narrowed down, a completely random choice will fare better than when there were all three doors. The point is that switching your door selection is far and away a better strategy than sticking with your original choice.