Shots and standard error

A run is repeated: each repetition is a shot, each shot returns one bitstring. From N shots you estimate a ratio p with a standard error of about √(p(1−p)/N). At p = 0.5 that is 0.5/√N.

0.0079 standard error on a ratio near 0.5 · three standard errors:

Four times the shots halve the error bar. That is why the accuracy target in a job sets the shots: 1,000 for a quick read, 4,000 for the record setting, 10,000 for the tightest bars — and why machine time scales with it.

The record rule uses three standard errors: a lead is counted as a lab-grade win only when it clears three SE. The product rule reports ahead or not ahead without a threshold and prints the SE next to it, so you can apply any rule you like.