What testing strategy should I use to test tournament algorithm

I have a tournament algorithm that generate trees depending on several factors, like:

• hasPreliminary
• how much player can pass preliminary
• tournamentType ( singleElim, doubleElim, Playoff, etc )
• etc.

My question is about testing strategy ?

Should I test all combinations? this would mean each factor I had would have a significant impact on the tests duration

Should I test only a limited set of combination ? If so, I would not be sure it passes all the cases

Should I test all cases? For example, odd, pair, primal number, etc...

Should I test statically? Defining the result in all case? But for each factor I add, static result will be bigger and bigger

What should be the best trade-off to test such system?