A nagging question

I already know that I enjoy playing deuce, and that I have the potential to be very good at it. However, I have a question about deuce that's been bugging me for a while; I need to find out what the answer is. It's not just idle curiosity, either; the answer could very well change my playing strategy. The question is simply this: when all the 52 cards in the deck have been dealt out, but there are still draw requests remaining, where do the additional cards come from?

A little explanation is in order here. Even though there are only 6 seats at a deuce table, instead of the 9 at a hold'em table, if enough of the seats are filled, and enough players stay in the hand, and enough players keep drawing enough cards, the 52 cards in the deck will be exhausted before all the drawing rounds have been completed. As an example, suppose all six seats have active players. That means that 6 x 5, or 30 cards, must be dealt out before the first drawing round. Let's further suppose that each player draws 3 cards in the first drawing round, 2 in the second, and 1 in the third. That's an additional 6 * (3 + 2 + 1), or 36 cards to be dealt out. That means the total number of cards which must be dealt out in that particular scenario is 30 + 36, or 66 cards. But there are only 52 cards in a deck. Where are the extra 14 cards coming from?

I can only think of two ways to supply those extra cards, and neither one of them is entirely satisfactory.

1. start out with more than 52 cards. The best way to do this is to start out with 2 decks, shuffled together. The problem with this solution is that players can easily get hands containing 2 of the same card (both denomination and suit), and that makes the game both look and feel rigged and crooked.

2. supply the extra cards from previous discards. The problem with this solution is that the later you are in the drawing order, the more likely it is that you'll eventually receive some of this "backwash". Almost by definition, you don't want to be receiving previous discards, since it's highly likely they'll be high denomination cards which can't possibly improve your hand. In all other poker variants, having the dealer button is either a neutral proposition or a decided advantage; if the extra cards in deuce are supplied from previous discards, having the dealer button is a decided disadvantage, since you're dead last in the drawing order. That inconsistency, if indeed it exists, is offensive to a poker purist (and you must surely know I consider myself one of them :-).

I wrote a utility which reads the PokerStars hand history files of deuce hands and calculates the number of cards dealt out in each; I ran it on last night's hand histories, and found that fully 10 of the 22 hands I played went into what we can call "extra card territory". So it's actually very important to know the answer to this nagging question. For now, I'll assume that solution #2 is the one being used, and fold early and often whenever I have the dealer button at a full table :-)

During current 2-7 Triple Draw session you were dealt 22 hands
Pots won if drawing - 4 of 18 (22%)
Pots won at showdown - 4 of 8 (50%)
Pots won without showdown - 0

delta: $2,350
balance: $2,033,705