[gbear605]

Doesn’t it depend on what you mean by guarantee? The test can’t get 100% certainty, since theoretically you could be flipping a coin each time and miraculously getting it right, for 1000 times in a row. The chance of that is minuscule (1/2^1000), but it’s nonzero. So we’d have to define a cutoff point for guaranteed. The one used generally in many sciences is 1/20 chance (p = 0.05), so that seems like a plausible one, and with that cutoff, I think you’d need five questions passed in a row (1/2^5 = 1/32). Generally, if you want a chance of p, you need log2(1/p) questions in a row passed correctly. However, that only works if your only options are random guessing and having learned the heuristic. If you sorta know the heuristic (eg. right 2/3 of the time), then you’d get the 5 questions right ~13% ((2/3)^5) of the time, which isn’t inside the p = 0.05 range. So you also need to define a range around your heuristic, like knowing it X of the time. Then you’d need log(1/p)/log(1/X) questions. For example, if you wanted to be the same as the heuristic 19/20 times and you wanted to pass the p = 0.05 threshold, you’d need log(1/0.05)/log(1/(19/20)) ~= 59 questions.

[mark-r]

There were more than two possible answers to choose from on each page, so the odds of being right were considerably lower.