(互先, 互い先) Tagai-sen, (literally 'alternate first') is a Japanese go term describing conditions of play in which neither player takes a handicap.
1) In a series of tagai-sen games the players would alternate in playing the black stones. Usually, after one player achieved a lead of 4 wins over the other, or some other threshold, the handicap shifted to sen-ai-sen. A game which if lost would result in a shift in the handicap is called a kadoban. For more information on professional handicaps in the days before komi go, see Match Handicap System.
2) After komi was generally introduced in late 1940s, games with standard komi (that is, no handicap) also came to be called tagai-sen. One notable exception was the Oteai (rank promotion tournament in Japan), where tagai-sen meant 1) above until the tournament's end in 2003.