Give me some good paradoxes

[HedonismBot]

First one for you gamblers: Parrondo's paradox

http://en.wikipedia.org/wiki/Parrondo%27s_Paradox

[diebitter]

This sentence is a lie.

[baumer]

Is your answer to this question no?

(Y/N) [img]/images/graemlins/cool.gif[/img]

[Borodog]

How to get a job without experience, and how to get experience without a job.

[FortunaMaximus]

Zeno's paradox.

Take a set distance, then halve it, repeat until your hair's glossy and shiny and has that TV commercial bounce.

You never get there, do you? But when you try it in a room, you're going to bang your head on the wall every time.

[bobman0330]

You're damned if you do, and you're damned if you don't.

[Borodog]

[ QUOTE ]
You're damned if you do, and you're damned if you don't.

[/ QUOTE ]

Ain't that the truth.

[atrifix]

http://en.wikipedia.org/wiki/Simpson's_paradox

[Borodog]

[ QUOTE ]
http://en.wikipedia.org/wiki/Simpson's_paradox

[/ QUOTE ]

This is probably my favorite real-world paradox.

As for the OP, the Twin Paradox and the Ladder & Barn Paradox (from special relativity).

[rollyourown]

Here is the paradox:
Sleeping Beauty is to be given on Sunday a drug that causes her to sleep. A fair coin will be tossed. If it lands tails, she will be awoken on monday, put back to sleep, and awoken again on tuesday, and then again put back to sleep to await prince charming's kiss. If the coin lands heads, she will be awoken only on tuesday and then again put to sleep to await charming. The sleeping drug has the secondary consequence of short term memory loss: Sleeping Beauty will not remember on tuesday any monday awakening that might have occured. At each awakening she is to be offered a gamble on the outcome of the coin toss, at 1:1 odds, she taking the affirmative on the proposition "the coin landed heads". On sunday afternoon, Sleeping Beauty clearly ought regard the chance of heads as .5, and so ought to regard each potential wager as fair. Upon being awoken, should she change her estimation of the probability the coin lands heads?
Options:
(1) No. The prior on heads was .5, no new information has been learned, so the updated probability ought to be .5.

(2) Yes. If she takes the probabilty of heads to be .5, she ought regard the wagers as fair; but if she accepts such wagers, her expectation is negative (since she will be offered the wager twice when the coin is tails, but only once when heads). Hence, she must revise her estimate of the probability the coin landed heads.
Solution below....





















Various philosophers and computer scientists have in all seriousness argued for 2, and thought they could learn something about probability from the case. They can't of course (the solution is related both to Parrondo's paradox and to value betting), but it is not obvious to non-gamblers. This is just one of the many situations in which fair odds come appart from the probability of winning. In value betting, this happens when we are a) in a must call situation, b) do not fear a raise, and c) judge that our opponent will more often call with a loosing hand than bet with a loosing hand. Optimal action no longer depends on the chance that we win a wager if contracted, depending instead on the chances (freqeuncies ) that we contract a wager under winning (or loosing) conditions. These two chances-- the chance of winning given a contract and the chance of contracting under winning conditions-- are only nicely distinguished and often equal, but not always.

Bruce