Two men find an old gold coin and want to have a coin toss with it to decide who gets it. The only problem is the coin is heavier on one side so it comes up heads more than tails. What is a fair way for the men to toss the coin and decide who gets the coin?
The answer is to simply flip the coin once, but make sure you catch it without letting it bounce.
The question makes the assertion that a weighted coin will be biased, but that only happens if the coin is allowed to bounce and/or spin (on a surface). For a flipped/caught coin, there is no significant bias.
The law of conservation of angular momentum tells us that once the coin is in the air, it spins at a nearly constant rate (slowing down very slightly due to air resistance). At any rate of spin, it spends half the time with heads facing up and half the time with heads facing down, so when it lands, the two sides are equally likely (with minor corrections due to the nonzero thickness of the edge of the coin).
[This] explains why weighting the coin has no effect here (unless, of course, the coin is so light that it floats like a feather): a lopsided coin spins around an axis that passes through its center of gravity, and although the axis does not go through the geometrical center of the coin, there is no difference in the way the biased and symmetric coins spin about their axes.
Each person tosses the coin 3 times, whoever gets more heads wins, if tie then do it again. If ties keep occurring then toss it 5 times or more to decide
each person tosses it once whoever gets tail wins. If tie or no one gets tail then each person tosses it again until someone wins.
Each man "tosses" the coin. Whoever "tossed" it the farthest (or closest to a fixed point) gets to keep it (assuming they don't lose it in the process). This will eliminate any bias introduced by the coin.
NOTE: When I initially posted my answer it was tagged as a 'riddle' so I was playing off the semantics of 'coin toss' to literally mean 'to toss a coin'. If that absolutely bothers you that is fine, but if you are going to down vote at least be courteous enough to leave a comment as to why.
oooh we could use the same rules as NHL shoot outs! in hockey, the goaltender has a statistical advantage over the shooting player, but since each team takes turn shooting agaisnt the opponent's goalie, the overall result of the shoot out is unaffected by the statistical advantage of the goalie.
Each team names three shooters. If the game remains tied after the three shooters are done, teams continue shooting in "sudden death" mode. The game cannot end until each team has taken the same number of shots.
so, let's say that Heads = save and Tails = goal. the players simply take turn flipping the coin as if they were playing hockey shoot outs.