[MarkGritter]

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Sklansky says you make money every time your opponents do something they wouldn't do if they knew your hand, not that you always do what you would if you knew your opponents' hands.

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His statement of the FToP starts with "Every time you play a hand differently from the way you would have played it if you could see all your opponent's cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose." The situation is dual, so if my opponents lose by playing other than they would with knowledge of my hand, I must lose by playing other than I would with perfect information.

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The draw order matters tremendously, even with only two players. Let's simplify the problem to focus on the essential mathematics. Suppose we played one-card lowball using only the Spades. Each of us gets one card, and I know yours, but you don't know mine. Each of us has one chance to throw our card away and get another. After that, the lower card wins the pot.

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I was actually thinking of the case where all players had perfect information, not the asymmetrical case. I'm sorry I didn't make that clear.

Your example is a good one to think about. Is there a case where position will affect the draw?

Suppose we just have 5 cards, 2-6.

A 2 will never draw. A 6 must always draw.

A 3 will lose to a 2. Against a 4, 5, or 6 it should not draw, since the opponent is only going to hit the 2 1/3 of the time, and the 3 wins otherwise.

A 4 must draw vs. a 5 or 6. If the 4 stands pat he is likely to be outdrawn 2/3 of the time. Similarly, a 5 cannot stand pat against a 6 or he is sure to lose when the 6 draws.

So, in this toy game at least, there is no case where the decision to draw depends on position or not. But I cannot prove why this is the case.

The reason I think the full lowball game is more interesting is that the distribution of cards in the deck might make it so that pat/draw or draw/pat pairs are more advantageous to one player than to another.