In February and May 1973, experimental forms of the mathematics game EQUATIONS were used in two seventh-grade classes which had been participating twice a week in EQUATIONS tournaments since the previous September. The purpose of the experimental games was to gain information as to the kinds of mathematical ideas players choose to concern themselves with during the course of playing EQUATIONS. The study addressed two questions: (1) What is the change in the proportion of games in which simpler solutions are extinguished before the more advanced solutions? and (2) What is the change in the proportion of students correctly using solutions with more advanced concepts to sustain the burden of proof? The analysis indicated that as students acquired more advanced mathematical concepts they were willing to apply them in the classroom tournament setting. An increase also occurred in the proportion of players correctly using the more advanced concepts when previous plays of the game allowed it. (Author/JBW)