If you break an outcome up into 6 or more stages and multiply out all the probabilities to get a tiny number, then there’s at least a 90% chance that you’ve severely underestimated the true odds. Why?
Well, estimating probabilities is hard, but let’s say you’re really good at it. So for the first probability in your sequence, you have a full 90% chance of not underestimating. The next probability is conditional on the first one. This is harder to reason about, so your chance of not underestimating drops to 80%. Estimating probabilities that are conditional on more events gets harder and harder the more events there are, so the subsequent probabilities go: 70%, 60%, 55%, 50%. If we multiply all these out, that’s only an 8% chance that you managed to build a correct model!
To put it another way:
If you break an outcome up into 6 or more stages and multiply out all the probabilities to get a tiny number, then there’s at least a 90% chance that you’ve severely underestimated the true odds. Why?
Well, estimating probabilities is hard, but let’s say you’re really good at it. So for the first probability in your sequence, you have a full 90% chance of not underestimating. The next probability is conditional on the first one. This is harder to reason about, so your chance of not underestimating drops to 80%. Estimating probabilities that are conditional on more events gets harder and harder the more events there are, so the subsequent probabilities go: 70%, 60%, 55%, 50%. If we multiply all these out, that’s only an 8% chance that you managed to build a correct model!