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#1

I would have to think someone has done this before, but I have run all the non-trivial isomorphically distinct PLL cases in Cube Explorer to come up with the real optimal PLL move counts for all 288 PLL cases. I summarize the results below, total cases and broken down by the standard 14 PLL cases (including PLL skip case).

This works out to an average of approximately 11.642 moves. Note that Helmstetter's site (http://www.ai.univ-paris8.fr/~bh/cube/) gives an average of 11.21 moves. Why is his figure lower? Because Helmstetter only uses the best case within each PLL category, and doesn't compensate for the fact that a given alg will require an "AUF" 75% of the time. That means his average should be as much as 11.96 to properly account for AUFs. By considering optimal algs for each of the "AUF" cases, the real average comes down to 11.64.

(Note: Because of certain symmetrical PLL's, properly using the proper angle or mirror for an alg can reduce the AUF percentage slightly, so I would say that the 11.96 figure that I stated is slightly too high, but would still be higher than 11.64.)

Code:

```
Optimal PLL (FTM) - All 288 cases
Moves All Skip A E F G H J N R T U V Y Z
----- --- ---- - - - - - - - - - - - - -
0f* 1 1
1f* 3 3
9f* 18 8 2 8
10f* 82 24 2 24 8 24
11f* 16 8 8
12f* 40 32 8
13f* 84 12 32 4 24 12
14f* 40 4 4 4 8 16 4
15f* 4 4
--- -- -- -- -- -- -- -- -- -- -- -- -- -- --
Total 288 4 32 8 16 64 4 32 8 32 16 32 16 16 8
```

(Note: Because of certain symmetrical PLL's, properly using the proper angle or mirror for an alg can reduce the AUF percentage slightly, so I would say that the 11.96 figure that I stated is slightly too high, but would still be higher than 11.64.)