HEADS OR TAILS.
(
Money Puzzles)
Crooks, an inveterate gambler, at Goodwood recently said to a friend,
"I'll bet you half the money in my pocket on the toss of a coin--heads I
win, tails I lose." The coin was tossed and the money handed over. He
repeated the offer again and again, each time betting half the money
then in his possession. We are not told how long the game went on, or
how many times the coin was tossed, but this we know, that the number of
times that Crooks lost was exactly equal to the number of times that he
won. Now, did he gain or lose by this little venture?
Answer:
Crooks must have lost, and the longer he went on the more he would lose.
In two tosses he would be left with three-quarters of his money, in four
tosses with nine-sixteenths of his money, in six tosses with
twenty-seven sixty-fourths of his money, and so on. The order of the
wins and losses makes no difference, so long as their number is in the
end equal.
