I haven't read the comments yet, so apologies if this has already been said or addressed:

If I am watching others debate, and my attention is restricted to the arguments the opponents are presenting, then my using the "one strong argument" approach may not be a bad thing.

I'm assuming that weak arguments are easy to come by and can be constructed for any position, but strong arguments are rare.

In this situation I would expect anybody who has a strong argument to use it, to the exclusion of weaker ones: if A and B both have access to 50 weak arguments, and A also has access to 1 strong argument, then I would expect the debate to come out looking like (50weak) vs. (1strong) - even though the underlying balance would be more like (50weak) vs. (50weak + 1strong).

(By "having access to" an argument, I mean to include both someone's knowing an argument, and someone's having the potential to construct or come across an argument with relatively little effort.)