[MarkGritter]

Here is a 2-7 lowball hand that partially answers my question.

Player A has 2c 3c 4c 5s Ts
Player B has 2s 3s 4s 5c Tc
Player C has 2h 3h 4h 5d Td
Qd is a dead card.

Now, if all three players stand pat the pot is split 3 ways. (0.333 equity each.)

If just one of the players breaks he increases his equity to 0.343 (according to pokenum) while the others drop to 0.329.

But, if two players break then their equity is 0.290, while the player pat with a T has equity 0.420.

Thus it is advantageous to be either the only player to break or the only player to stand pat.

If the 1st player discards, the 2nd player cannot discard. If he does, the 3rd player will stand pat and gain nearly 9% equity from going last. If the 2nd player does not discard, the 3rd player cannot discard either, or he gives the 2nd player an advantage. Thus if the 1st player discards, the other two players must stand pat (unless they can act in collusion) and the 1st player gains a 1% edge.

If the 1st player stands pat, the 2nd player can gain the 1% edge by discarding.

In this case, there is an advantage to going first because it puts the other two players in a position which neither can exploit (unless they collude.)

So, position does matter with three players.