Members of the Forum -
I had a blind-tasting last night where we sampled five different wines.
After two rounds of tasting the wines in the same order, we had a round
where we sampled them in a random, unknown order. Afterwards, we tried to
guess which wines from the random order corresponded to their original
numbering. On average, we were able to do this only once each.
Not knowing how this shakes out by chance, I did the following to simulate
comparing pairs of random permutations of five items to see how our results
compared to random selection.
?~5 NB. 5-permutation
0 4 3 1 2
$rs=. ?~2 1000$5 NB. 1000 pairs of 5-permutations
2 1000 5
0{=/rs NB. Look at the first comparison
1 0 0 0 0
0{"2 rs NB. and permutation pair.
1 0 4 3 2
1 3 2 0 4
+/,=/rs NB. How many total matches?
992 NB. Average of 1.
So, our ability to recognize the wines we'd just tasted twice is no better
than random. It occurred to us that perhaps five is too many to distinguish
and maybe we should taste only two at a time if we do this again.
So, what would be the random match if we did this with only two wines?
+/,=/?~2 1000$2
986
Huh? It's the same: about one on average. Try this for other permutation
lengths....
+/,=/?~2 1000$3
992
+/,=/?~2 1000$10
982
Try larger sample size too.
+/,=/?~2 10000$5
9886
+/,=/?~2 10000$10
10185
+/,=/?~2 10000$20
10058
+/,=/?~2 10000$100
10049
No matter what size the permutation, the average chance of a match is about
one. This seems counter-intuitive to me. Am I doing something wrong in my J
code or is this one of those well-known theorems of statistics about which
I'm completely ignorant?
You decide.
Regards,
Devon McCormick
^me^ at acm.
org is my
preferred e-mail
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