A man announces that he has tossed a coin that has landed head side up 19 times in a row. Knowing that the probability of tossing a coin head side up 20 times in a row is 1 out of 1048576, will head or tail be a better bet on the twentieth toss of the coin, or do you think the odds is the same for either?

It makes no difference in terms of probability to bet the twentieth toss on head or tail if the coin was made such that its weight is even. The result of the first 19 tosses has no bearing on what will come out of the next toss.

But given the highly unlikely result of tossing a coin 19 times in a row on the head side (the chance is 1 out of 524288), it is reasonable to suspect that the weight of the coin is biased to one side. In this case, head is definitely the better bet.