A move count metric is used to quantify the number of moves of an algorithm.
Note, that the same sequence of moves can have different move counts depending on the metric used.
Metrics are often tailored to specific purposes and puzzles and can tell about the efficiency of an algorithm.
Example: Move count of a Pyraminx algorithm
| MU
| ML
| TR'
| TU'
| TB'
| TL
| TU
| TB'
| TL'
| TR'
| R'
| B'
|
|
| 1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
= 12 btm |
| 1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
= 12 ltm |
| 2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
= 14 ftm |
Definition: The Block-Turn Metric (btm) counts
any turn of a continuous block of slices (outer or inner slices or outer or inner block of slices)
on a single axis by the same directed angle as 1 turn.
Slice moves: Turns of outer inner or slices count as 1 turn.
Pyramid rotations: Whole-pyramid rotations are considered as 0 turns.
Purpose: The standard metric for big pyramids (4x4x4 and up).
It provides a more accurate, intuitive, and 'natural' measure of efficiency on larger puzzles
compared to strict face-turn metrics.
It measures the amount of move tokens used.
Example: Move count of a Pyraminx algorithm
| MU
| TR
| TL'
| MU
| TR'
| TL'
| TB
| TL'
| TB'
|
|
| 1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
= 9 btm |
| 1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
= 9 ltm |
| 2 |
1 |
1 |
2 |
1 |
1 |
1 |
1 |
1 |
= 11 ftm |
Definition: The Layer-Turn Metric (ltm) or Slice-Turn Metric (stm) counts
any turn of any single layer (outer or inner slice) by any angle as one move.
Slice moves: Turns of outer or inner slices count as 1 turn.
Therefor a middle-slice move counts as 1 turn, not 2 as in Face-Turn Metric (ftm).
Pyramid rotations: Whole-pyramid rotations are considered as 0 turns.
Purpose: This metric for 3x3x3 pyramids is used for algorithms with middle-layer movements.
The metric measures the amount of layer turns used.
Example: Move count of a Pyraminx algorithm
| B
| TL
| MR'
| MU'
| (
| ML
| TR'
| TU'
| )2
|
|
| 1 |
1 |
1 |
1 |
|
1 |
1 |
1 |
|
= 10 btm |
| 1 |
1 |
1 |
1 |
|
1 |
1 |
1 |
|
= 10 ltm |
| 1 |
1 |
2 |
2 |
|
2 |
1 |
1 |
|
= 14 ftm |
Definition: The Face-Turn Metric (ftm) or Half-Turn Metric (htm) counts
any face turn, by any angle (120 degrees) as 1 turn.
Slice moves: Outer slice moves counts as 2 turns.
Inner slices, like the middle-slice move counts as 2 turns,
because it is interpreted as two outer layer moves.
Pyramid rotations: Whole-pyramid rotations are considered as 0 turns.
Purpose: The standard metric for corner twist algorithms on 3x3x3 pyramids.
Example: A Rubik's Cube algorithm that is optimal in two metrics
CD' · D2 F2 R B2 MD B2 L D2 L2 U2 · R' L' · U2 (13* ltm, 14* ftm, 22 qtm)
Optimal algorithms in a metric are marked with an * asterisk after the move count.
Algorithms can be optimal in one or more metrics simultaneously.
It is not always possible to find optimal algorithms.
Even with a 4x4x4 cube, the number of possible combinations can become too large for today's computers.
Bandelow, Christoph
Inside Rubik’s Cube and Beyond
120 pp. Birkhäuser Boston, 1982.
ISBN 978-0-8176-3078-2
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