Coin toss puzzle
February 5, 2013 14 Comments
This is intended as a counter-example to the view, such as Savage’s, that uncertainty can, in practice, be treated as numeric probability.
You have a coin that you know is fair. A known trickster (me?) shows you what looks like an ordinary coin and offers you a choice of the following bets:
- You both toss your own coins. You win if they match, otherwise they win.
- They toss their coin while you call ‘heads’ or ‘tails’.
Do you have any preference between the two bets? Why? And …
In each case, what is the probability that their coin will come up heads?
In (1) suppose that you can arrange things so that the trickster cannot tell how your coin will land in time to influence their coin, so that the probability of a match is definitely 0.5, with no uncertainty. The situation in (2) can be similar, except that your call replaces the toss of a fair coin.
Other uncertainty puzzles .