Everything Is Predictable by Tom Chivers

Author:Tom Chivers
Language: eng
Format: epub
Publisher: Atria/One Signal Publishers
Published: 2024-05-07T00:00:00+00:00

ON DESCRIBING PROBABILITIES AS ODDS

If we think about probabilities in terms of odds, rather than percentages or a number between zero and one, the reason to avoid ones and zeros becomes clearer. You get odds by taking the probability and dividing it by 1 minus the probability. If something is probability 0.9, then you take 0.9 and divide it by 1 minus 0.9, or 0.1. So it’s 0.9/0.1 = 9. Your odds are, therefore, 9:1. If it’s 0.5, then your odds are 0.5/0.5, or 1, so they’re 1:1.

When you use probabilities, a probability of one looks much the same as a probability of 0.9 or 0.5—it’s just one more number. But when you use odds, it’s clearly very different. A probability of 0.999999 in odds is 999999:1, but a probability of 1 equals infinity to 1. Infinity isn’t a real number, and you can’t use it in sums like a real number. (To steal a line from Yudkowsky again: “People sometimes say something like, ‘5 + infinity = infinity,’ because if you start at 5 and keep counting up without ever stopping, you’ll get higher and higher numbers without limit. But it doesn’t follow from this that ‘infinity − infinity = 5.’ ”11)

Odds have another advantage, which is that they show the real differences between seemingly similar probabilities. The difference between 0.99 and 0.999 in probability looks small—smaller than the difference between 0.5 and 0.51—but in odds, it’s the difference between 99:1 and 999:1.

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