Crackerjack

Originally posted by Aetherael
in fact, try to calculate a 99.99% confidence level using computational ratios and i think even intuition would tell you that your answer is way off base.

Out of interest - my approach (which I believe to be correct) gives 37 for this.

Originally posted by mtthw
Out of interest - my approach (which I believe to be correct) gives 37 for this.

I get the same answer, 37 boxes to be at least 99.99% sure. Good jorb! 😀

Originally posted by Aetherael

when it came time to compute the 90% answer, using a little bit of hazy logic and a misapplication of your computed numbers, you added 6 to your PREVIOUS answer of 50%, rather than to the 4 boxes associated with a 12.5% confidence level. so you achieved the correct answer of 13 boxes, though your method (when computed accurately) should have given you an answer of 10 boxes.

I added the two together precisely because the question is non-linear. As you get more accuracy, the amount of boxes does not initially increase in a linear fashion so you need to build upon your previous answers.

What i find interesting is the correlation between the following:

50% equals 7 boxes
90% equals 13 boxes
99.99% equals 37 boxes

A 40% increase in accuracy from 50-90 results in you only needing 6 additional boxes, but a further 9.99% from 90 results in you needing and additional 24 boxes.

That's 4 times as many boxes to get what amounts to an extra 10% versus an extra 40%

What's really really interesting is that to go from 99.99% to 99.999% you just add nine boxes...to go from 99.999 to 99.9999% you just add nine more boxes etc etc

Anyone of you non-linear boys care to explain?

Originally posted by uzless
I added the two together precisely because the question is non-linear. As you get more accuracy, the amount of boxes does not initially increase in a linear fashion so you need to build upon your previous answers.

What i find interesting is the correlation between the following:

50% equals 7 boxes
90% equals 13 boxes
99.99% equals 37 boxes
...[text shortened]... .9999% you just add nine more boxes etc etc

Anyone of you non-linear boys care to explain?

I'll have a go at that. The asymptotic behaviour is like a power law.

Using my notation from above, for a large enough number of boxes:

P(n, 1) << P(n, 2) << P(n, 3) << P(n, 4)

So as an approximation we can write:

P(n, 1) = P(n, 2) = 0
P(n, 3) = a (where a << 1)
P(n, 4) = 1 - a

Then
P(n + 1, 4) = (1 - a) + a/4 = 1 - 3a/4
P(n + 2, 4) = 1 - (3/4)^2.a
etc.


And (3/4)^8 is very close to 0.1. So roughly every 8 boxes you move up an order of magnitude in your confidence.

99.9 -> 29
99.99 -> 37
99.999 -> 45
99.9999 -> 53
99.99999 -> 61
99.999999 -> 69 etc