Hey everyone,
I have a new LL strategy for centers first people to propose and
analyze in this post. I am trying to come up with new ways to handle
the parities on a 4x4, and am requesting we put our brains to this task.
Here is the idea, to only have the double parity (meaning do an alg to
fix the orientation parity, then do an alg later in the solve to fix
the permutation parity) 1/8 the time instead of 1/4. To do this break
the orientation parity cases into 2 groups.
1 oriented LL edge:
Do either the parity alg or double parity alg leaving a 50-50 chance
to also have PLL parity so to encounter double parity here is a 1/8
chance overall.
3 oriented LL edges:
Do a COLL alg, now recognizing whether the 3x3 edge groups have the
same parity as the corners is very easy. So if you have double parity
do the double parity fix pure version, if not do the regular parity
fix pure version.
So that means only 1/8 the time you do 2 algs. Now don't get excited
yet, this method stinks.
Here are the times for each LL strategy (for me). I did an average of
each alg.
permutation parity fix:
02.34, 02.24, 02.63, (03.28), 02.44, 02.73, 02.68, 02.23, 02.43,
02.90, 02.79, (02.11) = 2.54 average
orientation parity (speedsolve version - double parity alg):
04.94, 04.47, 05.34, 04.91, 04.65, 05.03, 04.42, 04.45, (04.18),
(05.52), 04.97, 05.29 = 4.85 average
double parity alg pure version:
06.23, 07.56, (06.02), 08.10, 06.50, (08.24), 08.02, 06.71, 07.64,
07.33, 06.42, 06.24 = 7.07 average
orientation-parity-only alg pure version
06.06, (05.98), 06.79, 06.75, 06.77, 06.38, (08.66), 06.51, 06.41,
06.66, 07.40, 07.60 = 6.73 average
So here is the analysis of the extra time spent on average just fixing
parities:
Conventional method with 1/4 double parity:
0.25*0 + 0.25*2.54 + 0.25*4.85 + 0.25*(2.54+4.85) = 3.70 seconds on
average to fix parities.
-----
and with the new 1/8 double parity method
0.25*0 + 0.25*2.54 + 0.125*(4.85+2.54) + 0.125*(4.85) + 0.125*(7.07) +
0.125*(6.73) = 3.89 seconds on average spent fixing parities.
Also solving with the new way I have to do COLL vs. OLL 1/8 the time
which is probably 1 second longer. So 1/8 second overall. Making the
3.89 actually 4.02 seconds.
In order to make this faster than the conventional approach I would
need to solve the pure version double parity alg (x) and the pure
version orientation-parity-only alg (y) in:
3.70 = 0.25*0 + 0.25*2.54 + 0.125*(4.85+2.54) + 0.125*(4.85) +
0.125*(x) + 0.125*(y) + 0.125
2.94 = 0.125*(12.24 + x + y)
11.28 seconds = x + y
Which means the sum of both pure alg versions has to be 11.28 seconds
or less.
We can assume that x can be no faster than 4.85 and y can be no faster
than 5.55 which is my average for the speed solve
orientation-parity-only alg (again this analysis is done with my
times, since those are the only available to me right now).
05.82, 05.38, 05.11, 05.82, 05.54, 05.58, (04.75), (06.07), 05.57,
05.52, 05.74, 05.39 = 5.55 seconds
So that means there is only a give room of about 0.8 or 0.4 seconds
per alg. Meaning that my pure version double parity alg can only be
0.4 slower than my speed solve version and same for the
orientation-only-parity algs. I don't think that's possible for me.
So in conclusion again, this method stinks.
But can we somehow reduce the 1/4 chance to do both parities and, for
me, take 7.39 doing nothing but fixing parities. I mean come on that
amount of time is ridiculous. Added on to a solve that would
otherwise have been 55 seconds means that 11.91% of the solve is
fixing parities. Fixing parities. That's ridiculous, we shouldn't
have the standard accept that as ok.
Can we take anything from this and form a different, better strategy?
Any ideas? My only idea so far is to use the COLL case when you have
orientation parity to guess the corner permutation and then compare it
to the edge permutation. I think that is fairly thought intensive
though, so the amount of decision time required could actually make
that strategy take more time fixing parities on average. Alright,
well I'm trying to think of something new, anyone else have ideas?
Also, should the centers first method be scrapped entirely in favor of
a cage method? That would allow me flexibility to fix the orientation
parity (the only one!) and also commutators are very easy to come up
with on the fly once you have practice and experience with them. So
with mastery it seems to me that maybe a cage method is a better
choice in the long run than a centers first method.
Fixing parity sucks, but the fact that the edge permutation is
completely independent of the rest of the cube (!) is what makes the
4x4 so cool in my opinion :-D
Chris
P.S. If you actually made it to the end of this post congratulations.
I know it's long, but I want to come up with a better way to handle
the 4x4 parities. Even if it only saves 0.5 second on average, that's
still time saved. Thanks for your time spent reading.
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