Ignoring punctuation, spacing, and capitalization, a monkey typing letters uniformly at random has a chance of one in 26 of correctly typing the first letter of Hamlet. It has a chance of one in 676 (26 × 26) of typing the first two letters. Because the probability shrinks exponentially, at 20 letters it already has only a chance of one in 26^20 = 19,928,148,895,209,409,152,340,197,376 (almost 2 x 10^28) roughly equivalent to the probability of buying 4 lottery tickets consecutively and winning the jackpot each time. In the case of the entire text of Hamlet, the probabilities are so vanishingly small they can barely be conceived in human terms. Say the text of Hamlet contains 130,000 letters (it is actually more, even stripped of punctuation), then there is a probability of one in 3.4 × 10^183,946 to get the text right at the first trial. The average number of letters that needs to be typed until the text appears is also 3.4 × 10^183,946
For comparison purposes, there are only about 3 × 10^79 hydrogen atoms in the observable universe and only 4.3 × 10^17 seconds have elapsed since the Big Bang. Even if the observable universe were filled with monkeys typing for all time, their total probability to produce a single instance of Hamlet would still be less than one in 10^183,800. As Kittel and Kroemer put it, "The probability of Hamlet is therefore zero in any operational sense of an event…", and the statement that the monkeys must eventually succeed "gives a misleading conclusion about very, very large numbers."