[Guest]

2 players want to decide a game by the toss of a coin. However, they are given a coin and told that the coin is biased. But, they do not know what is the probability of head (or tails) coming up. (In a biased coin, heads and tails do not have equal probability of coming up)

How can they make a fair game using this coin? (fair game meaning that each player has equal chance of winning)

Hint: Its not a trick question where you find flaws in the wording of the question.

[Guest]

throw coin 100 times get average head/tails outcome use that in game or make game where they both throw coin and have to come up with the same outcome?

Edited May 25, 2009 by evilsteve70

[Guest]

Well, they will toss the coin alternatively and head come will be the success. So both of them will have equal chance of winning.

Detail:

They decided in advance that head come will be success.

1. First person A toss the coin and if head come B win else A win.

2. Then B toss the coin and if head come A win else B win.

This would lead them to play fair game.

[Guest]

throw coin 100 times get average head/tails outcome use that in game or make game where they both throw coin and have to come up with the same outcome?

Even with 100 (or for that matter a 1000 tosses) you cant be sure about the probability of heads or tails

Edited May 25, 2009 by DeeGee

[Guest]

Well, they will toss the coin alternatively and head come will be the success. So both of them will have equal chance of winning.

Detail:

They decided in advance that head come will be success.

1. First person A toss the coin and if head come B win else A win.

2. Then B toss the coin and if head come A win else B win.

This would lead them to play fair game.

There can be only 1 winner. They are not playing a best of 3 or 5 game.

[Guest]

HT (heads tails) player 1 wins, TH (tails heads) player 2 wins. Any other outcome (HH or TT), they re-toss.

[Guest]

Even with 100 (or for that matter a 1000 tosses) you cant be sure about the probability of heads or tails

thats why i said "average" then there is the second half of my statement which would be fair

[Guest]

The necessity of flipping is not mentioned. I suggest they see which one can throw the coin so it lands closest to the wall (or other object).

[Guest]

Do it as if a sudden death penalty shoot out. Decide heads win: 1st player throws gets a heads if player two then gets a tails playing one wins if not they go untill tails comes up. (unless both get tails then rethrow)

(that or realise both sides are heads lol)

[Guest]

thats why i said "average" then there is the second half of my statement which would be fair

For your second half, what should be the outcome? Even if you predecide on a certain outcome, it would still not be a fair game as the person tossing the coin first would have a higher probability of winning.

[Guest]

you flip a fair coin to decided who gets heads or tails then the probability is .5P(biasedheads)+.5P(biasedtails) which is for each person equal

must sleep

[Guest]

must sleep

you flip a fair coin to decided who gets heads or tails then the probability is .5P(biasedheads)+.5P(biasedtails) which is for each person equal

You have only one coin (which is biased)... besides if you had the unbiased coin, you could play the game with that coin only.

[Guest]

you dont know which way it is biased so flip and call in air. technically if your calling is random its fair and any leaning to calling one side is just as likely to hurt someone as help them so from a statistics stand point and prediction stand point it is fair

[Guest]

For your second half, what should be the outcome? Even if you predecide on a certain outcome, it would still not be a fair game as the person tossing the coin first would have a higher probability of winning.

who the hell would play with a biased coiin anyway id just get another coin---you dont have to pe decide the outcome just match te first players outcome

Edited May 25, 2009 by evilsteve70

[Guest]

how about a nice game of rock, paper, scissors

[Guest]

Given that neither player has any knowledge on how the coin is biased, having one player flip the coin and the other call it out yields still a 50/50 outcome.

Otherwise, if that's somehow against the rules, draw a microscopic arrow on both sides of the coin. Give each player one half of the room (north vs. south). Flip, and whichever direction is pointed wins.

[Pickett]

This is the same as a riddle I posted not too long ago...see my answer (and others) here