Editing Handicapping in Go (section)

==Small board handicaps==
Small [[go equipment#Equipment|boards]] are often used for novice players (double-digit kyu players) just learning to play Go, or for quick games. As the fewer moves made when playing on smaller boards gives White fewer chances to overcome the advantage conferred by the handicap, smaller handicaps are used on smaller [[Go equipment#Equipment|Go boards]] (most commonly 13×13 and 9×9).<ref>See [http://senseis.xmp.net/?HandicapsForSmallerBoardSizes page at Sensei's Library for a fuller discussion]</ref>

The per-rank handicap is therefore reduced, by a scaling factor. Various estimates have been given for the factor that applies to 13×13, in the range 2.5 up to 4; and on grounds both theoretical and experimental (small-board tournament play). The evidence is that 2.5 is more realistic than 4, for clock games. The corresponding factor for a 9×9 board is not easy to understand, and the change for each stone added is very large.

One theoretical approach is according to the distribution of the number of moves made in a game on a board of a given size relative to the number made on a 19×19 board. Using estimates that a 19×19 game will last about 250-300 moves, a 13×13 game about 95-120 moves, and a 9×9 game about 40-50 moves, a quadratic formula for the ratio of the mean number of plays may apply. Arguing that White catches up by means of Black's 'small errors', so that White's deficit drifts at a constant rate, it makes sense to take the ratio of game lengths as scaling factor.<ref>Psychologically speaking, Black (the pupil) probably sees blunders as more important in a loss; but White (the teacher) is more aware of getting into the game by means of Black's inefficiencies.</ref>

Each full stone of handicap on a 13×13 board is in any case probably equivalent to about 2.5 to 3 ranks, and each full stone on a 9×9 board is equivalent to about 6 ranks. For example, if the appropriate handicap is 9 (i.e., 8.5) stones on a 19×19 board, the handicap between those two players is reduced to 4 (because 3.5 × 2.5 = 8.75) stones on a 13x13 board  and 2 (1.5 × 6 = 9) stones on a 9×9 board. A 5 (i.e., 4.5) stone handicap on a 9×9 board is accordingly equivalent to a handicap of 27 or 28 stones on a 19×19 board.

These figures are not a consensus, but have wide support. They can be used to give rankings, by converting 13×13 handicaps back to rank difference.