Since we're multiplying by 3 and adding 1 only if n is odd, i.e. for some n = 2k + 1, the result will be even 100% of the time, i.e. 3n + 1 = 3(2k + 1) + 1 = 6k + 4 = 2(3k + 2). Since this result is even, we'll immediately divide by 2 and we've gone from n = 2k + 1 to 3k + 2, a larger number. Of course this number could be even or odd but it's not immediately obvious that we'll ever encounter a number smaller than n.