OT: Coin toss puzzle

[QuikSand]

Okay, we've already had some discussion about the recent "revelations" that perhaps tossing a coin isn't quite a perfectly fair 50/50 event, after all.

See:
http://dynamic2.gamespy.com/~fof/forums/showthread.php?t=22422

That sets up a puzzle (I offered it in that thread, but it fizzled), based on this notion.

Assume you have a coin that is unfair - it isn't 50/50 to land on either of its two sides. How can you use that coin to resolve a 50/50 situation in a completely fair method?

[CraigSca]

Okay, we've already had some discussion about the recent "revelations" that perhaps tossing a coin isn't quite a perfectly fair 50/50 event, after all.

See:
http://dynamic2.gamespy.com/~fof/forums/showthread.php?t=22422

That sets up a puzzle (I offered it in that thread, but it fizzled), based on this notion.

Assume you have a coin that is unfair - it isn't 50/50 to land on either of its two sides. How can you use that coin to resolve a 50/50 situation in a completely fair method?


Hmmm...my guess is, if you allow the persons involved to come to a mutual decision as to who gets heads or tails, that would make it truly 50/50.

[QuikSand]

Let's leave people and psychology out of this... what I want is for you, in an empty room with nothing but "a man... a table... a chair... a glass of water..." (sorry... got sidetracked with an homage to Spalding Grey)

Empty room - you and the unfair coin. Find a way to use that coin to create a perfectly random 50/50 outcome.

[digamma]

Have one person place the coin in one of his hands and have the other person guess which hand it is in.

[Insert 2/3 or retarded ass pirate joke here.]

[digamma]

Dola...

If there is no second person, my answer is invalid.

[Retarded ass pirate joke still stands.]

[albionmoonlight]

My post from the other thread:

This one has been in the back of my head for a while.

Let's say that you have a coin which lands on heads more than tails by some amount. If I were to say that we will each flip the coin once and 1.) if I get heads and you get tails, then I win; 2.) if you get heads and I get tails, then you win; and 3.) if we each get the same thing then we re-flip.

Is it as easy as that?<!-- / message -->

[albionmoonlight]

dola:

If it is just me, then the above logic still works. Flip the coin twice. If you get H-T, then that's one outcome. If you get T-H, then that's another outcome. If you get H-H or T-T, then you reflip until you get H-T or T-H.

[thealmighty]

Flip the coin 10,000 times (room is empty, what else you got to do in there :) ) to determine the actual (within reason) percent chance to get a head or tail. Now flip the coin as many times as needed to determine an outcome based on the true % chance just determined.

Ex: If you find, after the 10k flips, that heads comes up 53%, flip 100 times. If you get less than 53 heads, you lose. More, you win; 53 exactly, try again.

[EagleFan]

Flip the cion once and if it's heads and you wanted it to be tails because you have already picked tails, then call your agent and file a suit agains the league in an attempt to void the last coin flip.

Actually, the one flip per person idea sounds like a good answer, but this depends on if it's just one person or two. Of course, if it's just one person in a room trying to do this, that person needs to get a new hobby.

[albionmoonlight]

Bump to see if there are any holes in my answer.

[Celeval]

Albion:

Assuming a heavily invalid coin - 70% H, 30% T:

Four possible outcomes:

H-H : .7 * .7 = 49%
H-T : .7 * .3 = 21%
T-H : .3 * .7 = 21%
T-T : .3 * .3 = 09%

Looks right to me.

[QuikSand]

Yes, albionmoonlight - that's the answer that I had in mind. Keep flipping until you get HT or TH back to back... and settle the 50/50 proposition based on which one shows up first. No matter how unfair the coin is, this ends up being a perfect 50/50.

[albionmoonlight]

It took me way longer than I care to admit to come up with that answer.