“The upshot is that for a finite set of coin tosses, the sequences we intuitively feel to be less random are precisely the ones that are least likely to occur.

“The upshot is that for a finite set of coin tosses, the sequences we intuitively feel to be less random are precisely the ones that are least likely to occur. Imagine a sliding window that can only “see” four coin tosses at a time (roughly the size of our memory capacity) while going through a series of results – say from 20 coin tosses. The mathematics show that the contents of that window will hold “HHHT” more often than “HHHH” (“H” and “T” stands for for heads and tails). That’s why we think tails will come after three heads in a row when tossing a coin – demonstrating that humans do make sensible use of the information we observe. If we had unlimited memory, however, we would think differently.” This doesn’t make sense. You don’t need to be able to remember even one coin toss in order to understand that each coin toss is an independent event.