Which statistical test you propose to assess whether there is significant effect of specified categorical variable (s) on a categorical outcome?

I have a table that I am trying to analyse.

GAME    COMP win
BBall   N   Y
FBall   N   Y
FBall   N   Y
BBall   N   Y
FBall   Y   Y
FBall   N   Y
BBall   Y   Y
FBall   Y   N
BBall   N   Y
FBall   N   Y

John plays football and baseball under competitive and non-competitive conditions.
He wants to know which he is better at.

• What is a good statistical test to determine which game he is better at? I think Chi-Square test. Does that make sense?
• Are there some useful visual charts that can be used to show this?
• Also, an informative chart to show wins vary by game or competitiveness?