Theory quiz: Optimal freeroll play

I started thinking about a situation today, and after figuring it out (I think), I thought it’d be fun to make a little quiz out of it. This is one of those theoretical situations that you’ll never encounter at a poker table, but might train your poker thinking a little. It will also show how extremely powerful the freeroll is. Another reason that you should do it is that I want to find out if there are flaws in my reasoning. Ok, so here’s the situation:

The game is No-limit Hold ‘em

Player1 has the 9d8d
Player2 has the 9h8h

The flop is 5h-6h-7s

The size of the pot is 100

Each player knows what the other player is holding, and will assume that his opponent will be using optimal strategy. To simplify things a bit, we will round off the odds of hitting the flush to exactly 2:1 on the flop and 4:1 on the turn.

What should each player do if

1. The effective stack sizes are <100?

2. The effective stack sizes are 100-199?

3. The effective stack sizes are 200-700?

4. The effective stack sizes are >700?

If you feel like it, you can add what the players should do on the turn.

Hopefully this thread will generate some discussion. I’ll post my answers when I feel that either enough players have answered or the thread is starting to die out, but there is some interest in what I think is the optimal play. It would be really great if someone could put together a simple mathematical explanation a la Sklansky, since I suck at that

I remember reading a situation like this on here a while back. The guy who was freerolling shoved and the other folded.
If you flopped the straight with no re-draw you want to play it as cheap as possible and hope he doesn't hit. If you have the re-draw then value town it and hope he follows, and you hit the river