OH MY GOSH I VERSED MIKE KLEIN IN 3 CHECK

Well, apart from the fact that (in my opinion) white has a forced win in 3-check, and Klein was playing white, I didn't expect you to win.

The main idea in 3-check is to try and get checks in combinations. Hence, it's really important to activate your pieces very well, and having more space is very valuable, since it gives you more mobility for you, and increases your attacking chances. I'd say that, if there's one thing in 3-check that matters most, it's getting a strong pawn structure that restricts the opponent's pieces. 

Notice how Mike had this pawn structure, extremely active pieces, to the point where you couldn't get any rooks out or castle. At the cost of a pawn, this was well worth it. 

And there's also a saying the 3-check: "One check is not a big deal" - If you can get a very active, good position, then giving up one check often is fine... as long as you increase your ability to get checks in combinations later on.

I hope this makes some sense - I'm not the most familiar with 3-check, although I have some general idea of how to play it. 

Best of luck!