Monkeys typing Shakespeare or even just the word "Hamlet"

It is frequently stated in books and articles on probability that if a succession of monkeys were set before a typewriter with limitless paper, eventually the complete works of Shakespeare would be repeated by chance.

If there are 50 keys on the typewriter, the probability of the monkey getting Shakespeare correct is raised to the power of the number of characters (letters and spaces) in Shakespeare plus the adjustments of the typewriter needed for capitals and punctuation. On this basis the chance of the monkey typing the word 'Hamlet' correctly is one in 15,625,000,000, so to quote the probability of him typing the complete works involves a large number indeed.

The Bridge hand of thirteen spades

The chance of being dealt 13 spades in a bridge hand is one in 635,013,559,600. A man dealt such a hand would be staggered, and anybody seeing the hand dealt would immediately expect (probably correctly) some sort of trickery. Yet when we realise that the number of bridge hands dealt since the game was invented is doubtless many times the large number quoted, it would be surprising if a hand of 13 spades had never been dealt legitimately


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