This can be generalized: Suppose one has experienced a sequence of

*n*increases; what are the odds against the next reading being higher still? Among the

*n*+2 numbers then in hand, there are (

*n*+2)! equiprobable permutations, but of these, only

*n*+2 begin with an increasing sequence of n+1 numbers, corresponding to the

*n*+2 ways of leaving out one of the

*n*+2; and of those, only one has the

*n*+2nd larger than the rest. So the odds against a further increase are

*n*+1 to 1. Each increase makes a further increase modestly less probable.

It surprises me that this result is independent of the distribution. In a hasty effort, I did not succeed in finding it in Feller or on the Web.