Cluster Counting | Mental Shifting Flashcards
Basic Idea
It would be nice if every time you needed a pip count, the board would consist of clusters as previously described. Unfortunately, that doesn’t happen. Fortunately, these easy-to-count clusters are relatively simple to form by mentally moving the checkers where you want them.
One-way mental shifting involves moving the checkers forward to key points or reference positions and then adding the forward movement to the value of the key points or reference positions.
Black can be easily counted in three clusters: 40 (eight 5’s) + 33 (RP4 + 3 pips) + 64 (three 20’s + 4) = 137.
Divide White’s checkers into three clusters: 44 (5-prime + 4 pips forward, 2 each from the 7-point to the 5-point) + 33 (three 10’s + 3 pips from 13 to 10) + 44 (two 20’s + 4) = 121.
Black = 137. White = 121.
Note that two of White’s checkers were shifted to White’s 5-point which is occupied by Black’s checkers. When shifting one player’s checkers, the other player’s checker position can be ignored.
Two-way mental shifting differs from one-way mental shifting in that checkers are shifted either forward or backward to key points or reference positions and then compensating shifts are made in the opposite direction on the same side of the board, or in the same direction on opposite sides of the board.
Black’s spare checkers on the 6- and 8- points are on the same side of the board. By shifting them one pip in opposite directions to the 7-point, a 5-prime is formed. Black’s position can easily be counted in two clusters: 70 (5-prime) + 65 (five 13’s) = 135.
White’s spare checkers on the 8- and 13-points are on opposite sides of the board. By shifting them in the same direction, in this case left-to-right, a 5-prime is formed (RP1) and RP7 is also formed. White’s position can then be counted in three clusters: 60 + 40 + 42 (two 20’s + 2) = 142.
Black = 135. White = 142.
It should be noted that there are often several cluster counting choices available. For instance, in Black’s position above, instead of forming a 5-prime, you could have shifted the two 9-point checkers to the 8-point and compensated by shifting the two 5-point checkers to the 6-point to form RP3. This cluster is also 70 pips.
