>Oh, and one more thing: The commentators refer to the situation as, say, "1 and 2", the TV dirsplay showing "1-2". Now I understand the 2nd no. to be the no. of strikes but what's the 1st? No. of good balls?
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>How does this increment?
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>How high can it go? (No. of good "balls" that the batter hasn't had a swipe at? Therefore he's allowed 3?)
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>The batter is allowed only 3 swipes at the ball. Is there a limit to the no. of duff pitches that can be made?
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The count is expressed as balls-strikes. So 1-2 means one ball and two strikes. One or the other increments on each pitch (with one exception to be discussed in a moment). If it gets to 4 balls, that is a base on balls and the runner gets to go to first base without a play. Any runner already on first advances to second and any other runner without an empty base behind him also moves up.

There are two kinds of strikes: swinging strikes and called strikes. A swinging strike is when you swing and miss or hit the ball foul. A called strike is when you don't swing but the umpire determines that the pitch crossed the plate in the "strike zone." The strike zone is the width of the plate and from the knees up to the torso. I think if you read the official rules the top of the strike zone is defined as the middle of the chest but it has crept down over the years and nowadays you won't usually get a called strike on anything much above the waist. There is a saying that every umpire has his own strike zone (vertically -- they all agree on the width of the plate), and that's fairly accurate. It sounds wacky but as long as the ump is consistent and calls them the same for both teams, players will understand where the strike zone is that day and it isn't a big problem. Of course, they will still argue balls and strikes. (So much so that there is a rule managers can't come out onto the field to argue balls and strikes).

You probably already picked this up but a ball is a pitch the batter doesn't swing at and the umpire rules was outside the strike zone.

The exception I mentioned above is that you can't strike out on a foul ball. The third strike has to be either a swing and a miss or a called strike. As you probably saw, the umpire will usually call the third strike with great theatricality. Umps are supposed to be unobtrusive but most of them are hams.

I'm glad you like baseball! It's like chess in that the basics are fairly simple but there are endless nuances and strategies. I was shocked the other day when Charles Hankey, an otherwise intelligent guy, said baseball bores him. I may have to meet Charles for a game sometime and enlighten him ;-)