Mathematical Recreations; April 1998; Scientific American Magazine; by Stewart; 3 Page(s)

Suppose I keep tossing a fair coin-- one for which heads and tails are equally likely, each having probability 1/2--and maintain a running count of how many times each turns up. If at some stage I have tossed 100 more heads than tails, is there any tendency for tails to "catch up" in future tosses? Some people talk of a law of averages, based on the intuition that tosses of a fair coin ought to even out ultimately. Others assert that coins have no "memory"-- so the probability of heads or tails always remains 1/2--and deduce that there is no tendency whatsoever for the numbers to even out.

The same issues arise in diverse circumstances. If airplane crashes happen on average once every four months and three months have passed without one, should you expect one soon?