pedestrian: Ok, update: I found this site where you can create an account and play:
http://www.playok.com/en/makruk/

I played a couple of quick games. It works this way: When all pawns are gone or promoted, you're presented with the option to start counting (I don't know if this applies to both players. I was behind in material). When one player is down to a bare king, the counting starts over - but this time it's automated.

Fencer: The way I read the rules, yes. Keep in mind that I don't know this game any better that you do, though. I'm just trying to make sense of it, same as you.

Fencer: The point of counting is to obtain a draw. Counting is voluntary. Stopping to count is voluntary too (in case you change your mind and don't want a draw anymore). This much seems to be clear.

Couldn't you simply interpret the rules like this: Whoever starts counting, thinks he's at a disadvantage. That means that theoretically, both players could count if they wanted to - but they would probably both be happy with a draw in this case!