Ok, let's just look at one row, because it's equivalent, and do out all the math.
First, say you picked a jack. There is a 2/3 chance of this happening. Then Monty reveals a card. 1/2 the time, you reshuffle. 1/2 the time, he reveals the other jack, and you switch to win. So you win 1/3 of the time here, and reshuffle 1/3 of the time.
Then, suppose you pick a queen instead. There is a 1/3 chance of this happening. Every single time, you lose. So there is a 1/3 chance of you losing
Doc Al, the problem with your 100 card example is that if he picks 98 jacks in a row, it's probably because he was picking out of a pile of 99 jacks, and you had the queen the entire time (actually, half the time that's true)
