Comment by zamadatix
7 hours ago
Which is precisely what I'm responding about above. 93% actually collapses much slower than 90% since the rate of reduction is based on that of all of the previous rounds, not just the current chance. E.g., this is the difference between 14 rounds before an expected failure instead of 10. An extra 4 rounds deep at the same error rate is a big step forward despite a small change in the base percentages. Add just few more percentage points again and you've more than doubled the depth.
I.e. it's precisely when you look at these chained that the difference is actually very large. It's really only the 1st turn or two of prompts where the difference seems negligable.
How are you running that math and what are you consider to be "expected failure"? If even 30% of your runs go into the garbage, that sounds horrifically unreliable, and both 7 and 10% failure rates hit those margins in less than 5 iterations.
Not to mention that the deeper your iterations, the more money burned on garbage before you realize that data in turned to garbage out turned to garbage in somewhere in the chain.
I'm taking 0.90^n and 0.93^n and seeing 0.93 does more than the initial 3% better over time, which preciesly saves you from things like spending tokens on garbage by this larger factor. You're free to pick whatever target reliabilities from that. E.g. you can maintain above 80% accuracy over 3 turns rather than 2 or 50% over 6 turns instead of 3 or you can pick another percentage point and see how the depth to expected error/expected error at depth numbers are much better than 3% and how another 3% actually doubles accuracy because this is all non-linear.
There's also the matter of "90% compared to what". If it was 90% per attempt compared to a calculator then I'd just use a calculator. If it was 90% per attempt for something I have a 10% chance of getting right per attempt then it's not really so bad. OTOH if it's 90% per attempt at keeping my car in the lane then it's obviously quite bad. I.e. there isn't one "reliable percentage" to target which is why I'm comparing the curve instead of just the most stringent things I can think of in isolation.
Completely agree that error tolerance depends on what it is that we're doing. Some things demand no errors at all, some things have a cost to attempt, some things you can't pre-evaluate for correctness if you don't already have the prerequisite knowledge and you only get one chance. Not everything is software where we can conjure 50 more end-to-end tests to ward off demons. When it's not a harmless throwaway weekend project, 7% is already a huge error rate before you ever think of feeding it back into itself.