The hidden pattern of Freecell

zudensternen

I play a lot of Freecell games which I "beat" — get all 52 cards — but don't make the top 10. I've noticed a pattern to the scores of those games, and it revolves around what may be the overall average score:

The #10 player on average completes the game in 1 minute 10 seconds. (Averaged over a large number of games, each of which has been played a sufficiently large number of times, say > 150.)

Here's the pattern:

If the #10 player is at or right around 1:10, then my own number of seconds (s) slower than that player will be about equal to my number of places (p) out of the 10th position.

If the #10 player finishes slower than 1:10, then my s will be greater than p.

If the #10 player finishes faster than 1:10, then my s will be less than p.

The larger the divergence of the #10 player from 1:10, the larger will be the difference between my s and p (in whichever direction).

Here it is in quasi-mathematical notation:

midpoint = 1:10

s = my # of seconds out of 10th
p = my # of places out of 10th

time @ 10th place —

[ << midpoint: ] s > p

[ ~= midpoint: ] s ~= p

[ >> midpoint: ] s > p

The attached shows one game in which the #10 player beat 1:10 by a lot.

Just thought I'd post in case anyone else finds this of interest. Play on.