You should restring your racket after about 50 games. Waiting for the strings to break is not recommended as this is considered an extreme case of wear and the string will probably have lost its tension and elasticity long before breakage occurs.
The 50 game rule works out to be the same number of restrings a year as games you play a week. e.g. if you play three time a week, then you need three restrings a year.