| If you take a run of three coins, T or H, you get only so many ways to make runs. TTT, HHH, THT, THH, HTT, HTH, HHT, or TTH. Out of 8 combinations, you get 2 which are three in a row i.e. 1/4, either head or tail. This is non intuitive to most people, as they would think that the odds against are the same for both heads and tails and this prevents either a head or a tail run from showing up more than one in 8 times, as either face "has the same chance". But the complete distribution shows that two faces have double the chance of achieving at least one run in any trial. A trial run of fair coins has one chance in 16 of achieving 5 heads or 5 tails in any run of 5 coins! In 16 coin tosses, there are 11 runs of 5!. I just flipped a coin 30 times, I got one run of 4, several runs of three, and one run of 5!. Try it. |
