 Even a perfectly fair coin in an odd number of flips will never result in exactly the same number of heads and of tails. When the coin is fair and the number of flips is even, an outcome perfectly balanced between heads and tails is not guaranteed either. So, even on the assumption that the probability of the coin’s coming up heads does not change over the course of the trials, we need to be cautious. A larger number of flips might make us more confident that the ratio we have seen is close to the “actual” value, but there is no finite number of flips after which we can say that the observed ratio is exactly right. We will never make an infinite number of flips either, and in actual cases a large finite number of flips might so erode the coin as to bias the coin and discredit the result. Notwithstanding these limitations on an actual series of trials one can imagine an infinite series of trials and define a notion of probability with respect to it. This raises its own difficulty, namely that ratios are not defined for infinite collections. They would be defined, however, for any finite initial segment of such an infinite series, thus giving a sequence of ratios. If this sequence of ratios settles down on a limit, the probability of the coin showing a head given that it has been flipped can be defined as the limit of the ratio of heads to total flips as the number of flips goes to infinity.