Every pairs tournament movement has three basic components: the boards, the tables and the pairs. The tables are a trivial component as they are stationary. In a Mitchell movement, the pairs comprise two components, the N-S pairs and the E-W pairs.
Therefore the four components of a Mitchell movement are N-S pairs, E-W pairs, boards and tables.
The number of tables equals the number of N-S pairs equals the number of E-W pairs.
The number of boards is a multiple of the number of tables. It is also possible for N-S pairs to equal E-W pairs minus 1 or E-W pairs plus 1 (the half table movement).
The object of the Mitchell movement is for all the N-S pairs to meet all the E-W pairs while all pairs play all the boards.
Except for a slight modification with an even number of tables, this is achieved by one component remaining stationary (together with the tables), while another component moves up one table and the final component moves down one table.
The normal procedure is for the N-S pairs to remain stationary, the E-W pairs to move up one table, and the boards to move down one table.
The advantage of moving the boards, instead of their remaining stationary, is that there is less movement of people around the room at change time.
With the boards stationary and both groups of pairs moving, the advantages are that the boards will never be misplaced, and the pair numbers (both N-S and E-W) are in sequence and errors are obvious in entering pair numbers.
Too much movement during the change tends to spoil the event. On the other hand, if a movement is using more than one room, then keeping the boards stationary is highly recommended (also see "switch Mitchell").
As it is quite clear that no pair meets another pair sitting in the same direction, there will be two winners. Mathematically, this does produce the ideal situation: each pair being compared with the same set of pairs on each board and all pairs playing all boards. This movement is then said to have perfect comparisons.
The following schedules will help clarify these points.
This is the very simple case of a three table Mitchell. The N-S and E-W pairs are shown, for example, as 2-3 respectively. The board set 1 indicates a set of boards numbered 1 through 8 or 1 through 9 etc., depending on the number of boards in the movement (24 and 27 in these two cases).
Table 1 2 3
Round 1 1-1 2-2 3-3
Board set 1 2 3
Round 2 1-3 2-1 3-2
Board set 2 3 1
Round 3 1-2 2-3 3-1
Board set 3 1 2
