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 Rubik's Cube algorithm
| CD'
| R'
| D'
| F
| MD2
| F2
| MD'
| F
| D
| R
| U'
| SR2
| D
|
|
| 0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
= 12 btm |
| 0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
1 |
= 13 ltm |
| 0 |
1 |
1 |
1 |
2 |
1 |
2 |
1 |
1 |
1 |
1 |
2 |
1 |
= 15 ftm |
| 0 |
1 |
1 |
1 |
4 |
2 |
2 |
1 |
1 |
1 |
1 |
4 |
1 |
= 20 qtm |
Definition: The Block-Turn Metric (btm) counts
any turn of a continuous block of slices (outer or inner slice or outer or inner block of slices)
on a single axis by the same directed angle as 1 turn.
Slice moves: Turns of outer or inner slices count as 1 turn.
Cube rotations: Whole-cube rotations are considered as 0 turns.
Purpose: The standard metric for big cubes (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.
Variant: The Block Quarter-Turn Metric (bqtm) counts
90° block turns as 1 turn, but 180° block turns as 2 turns.
Example: Move count of a Rubik's Cube algorithm
| CF2
| L2
| B2
| D'
| MF2
| U
| R'
| MD'
| R'
| B2
| R
| MD
| R'
|
|
| 0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
= 12 btm |
| 0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
= 12 ltm |
| 0 |
1 |
1 |
1 |
2 |
1 |
1 |
2 |
1 |
1 |
1 |
2 |
1 |
= 15 ftm |
| 0 |
2 |
2 |
1 |
4 |
1 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
= 20 qtm |
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).
Cube rotations: Whole-cube rotations are considered as 0 turns.
Purpose: This metric for 3x3x3 cubes is used for algorithms with middle-layer movements,
since Face-Turn Metric (ftm) and Quarter-Turn Metric (qtm) are supposed to relay on face moves only.
The metric measures the amount of layer turns used.
Example: Move count of a Rubik's Cube algorithm
| CF
| B'
| SR
| D
| L2
| U'
| MF'
| U'
| F'
| SR2
| F
| L2
| U2
|
|
| 0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
= 12 btm |
| 0 |
1 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
1 |
1 |
1 |
= 14 ltm |
| 0 |
1 |
2 |
1 |
1 |
1 |
2 |
1 |
1 |
2 |
1 |
1 |
1 |
= 15 ftm |
| 0 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
1 |
4 |
1 |
2 |
2 |
= 20 qtm |
Definition: The Face-Turn Metric (ftm) or Half-Turn Metric (htm) counts
any face turn, by any angle (90 or 180 degrees) as 1 turn.
Slice moves: Outer slice moves counts as 2 turns, since the centers are assumed to be fixed.
Inner slices, like the middle-slice move counts as 2 turns,
because it is interpreted as two outer face moves.
Cube rotations: Whole-cube rotations are considered as 0 turns.
Purpose: The most standard metric for face twist algorithms on 3x3x3 and 2x2x2 cubes.
Example: Move count of a Rubik's Cube algorithm
| CD
| R
| SU
| L2
| D'
| SR2
| D2
| F
| MD'
| F'
| D'
| F2
| L'
|
|
| 0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
= 12 btm |
| 0 |
1 |
2 |
1 |
1 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
= 14 ltm |
| 0 |
1 |
2 |
1 |
1 |
2 |
1 |
1 |
2 |
1 |
1 |
1 |
1 |
= 15 ftm |
| 0 |
1 |
2 |
2 |
1 |
4 |
2 |
1 |
2 |
1 |
1 |
2 |
1 |
= 20 qtm |
Definition: The Quarter-Turn Metric (qtm) counts
any face turn, by any 90 degree angle as 1 turn.
Slice moves: Slice moves can count as either 2 turns (if it is a 90° turn) or
4 turns (if it is a 180° turn), since the centers are assumed to be fixed.
Outer slice moves counts as either 2 turns (if it is a 90° turn) or
4 turns (if it is a 180° turn), since the centers are assumed to be fixed.
90° inner slices, like a middle-slice move counts as 2 turns,
because it is interpreted as two outer face moves.
A 180° middle-slice move counts as 4 turns,
because it is interpreted as 4 outer face moves.
Cube rotations: Whole-cube rotations are considered as 0 turns.
Purpose: Standard, more strict metric for face twist algorithms on 3x3x3 and 2x2x2 cubes.
It measures the amount of 90° twists used.
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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