Sen-ai-sen (先相先, senaisen?) describes the handicap of taking Black (making the first move) in two games out of every three. This was the smallest handicap possible between two players in the era before the introduction of komi.
This is the crucial level from the point of view of promotions under the handicap system. To prove one is under-ranked, one should play a match against a player of one rank above. To break even under sen-ai-sen means to win (for example) 65% of games with Black, and 20% of games with White; or two games out of three with Black, and one game in six with White. A steady player, under the old style of opening, would aim to win games with Black more frequently; a less consistent but more aggressive player would expect better success in claiming some wins with White with ambitious strategies to cause confusion on the board.
Read more about this topic: Professional Go Handicaps