# The Infinite Monkey Theorem 3

2009-02-16

My Canadian concubine put on a production of *Words, Words, Words*, which features a take on the Infinite Monkey Theorem. Infinity is a shitload of monkeys, so I crunched some numbers for her:

Assuming the monkeys are using an old-style 52-key typewriter, the chances of them typing *tiffany* with the first seven strokes:

```
1 monkey(s): 0%
10 monkey(s): 0%
100 monkey(s): 0%
1000 monkey(s): 0%
10000 monkey(s): 0%
100000 monkey(s): 0%
1000000 monkey(s): 0%
10000000 monkey(s): 0.001%
100000000 monkey(s): 0.01%
1000000000 monkey(s): 0.097%
10000000000 monkey(s): 0.968%
100000000000 monkey(s): 9.269%
1000000000000 monkey(s): 62.193%
10000000000000 monkey(s): 99.994%
100000000000000 monkey(s): 100%
```

It doesn't really become inevitable until you get a quadrillion monkeys. Logistically, that's just a nightmare, so a better approach would be to smear banana on the T, I, F, A, N, and Y keys. The number of monkeys required then becomes:

```
1 monkey(s): 0%
10 monkey(s): 0.001%
100 monkey(s): 0.012%
1000 monkey(s): 0.121%
10000 monkey(s): 1.207%
100000 monkey(s): 11.434%
1000000 monkey(s): 70.307%
10000000 monkey(s): 99.999%
100000000 monkey(s): 100%
```

With the banana goo, you'd only need 100 million monkeys, and perhaps 25 million bananas.