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The text for Stinking Cloud says

Effect: The burst creates a zone of poisonous vapor that blocks line of sight until the end of your next turn....

Does that mean that even at the inside edge of a Stinking Cloud creatures have total concealment?

Can a creature on the inside edge make an opportunity attack against a creature on the outside edge or vice versa?

Can a creature in a Stinking Cloud make an opportunity attack at all, unless they have some sort of special vision?

Does a creature on the inside have partial or total concealment from someone on the outside edge of the Stinking Cloud ?

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Does that mean that even at the inside edge of a stinking cloud creatures have total concealment?

Yes - typically the area of effect represent the area of maximum concentration of the gas. You can visualize it as tenuous tendrils of gases in the squares of the outer edge.

Can a creature on the inside edge make an opportunity attack against a creature on the outside edge or vice versa?

No - the Stinking Cloud blocks LOS, once in the target is completely enveloped by the gas obscuring it from other targets.

Can a creature in a stinking cloud make an opportunity attack at all, unless they have some sort of special vision?

No - there is no LOS and thus no opportunity attacks available. Same situation if the two were on square on opposite sides of a wall.

Does a creature on the inside have partial or total concealment from someone on the outside edge of the stinking cloud?

Yes - again the inside edge of the stinking cloud represents where the gas completely takes effect. As a referee you can add color by describing tenuous trails of gas beyond the edge of the gas but they are not concerntrated enough to have an effect.

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With the new Playtest Arcanist they have revised the zone to be "heavily obscured."

The damage in the Effect can now occur at the end of a creature’s turn, not at the start, and a creature can take the damage only once per turn. Changes the zone damage to a static amount instead of a damage roll. The zone is heavily obscured.

Thus, Yes A creature can, though they will take a hit penalty from being heavily obscured.

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Line of sight and Line of Effect are different. Not having line of sight does not prevent most powers and attacks from occurring. One thing that it does prevent, is Opportunity attacks though!

This spell, and a couple others are problematic in that they do not completely answer questions like yours. It seems they are trying to create a set of special rules just for that power. My preference would be to recast them into normal defined game terms so that we can all understand the edge cases.

I would rule that the zone creates an area of total concealment. Rules governing that are on p220-1 of the Rules Compendium.

In short your to hit modifier depends on how much concealment the defender has. The concealment value of the square the attacker is in does not matter.

  • If the defender is in an adjacent totally concealed square, take -2 to all attacks
  • If the defender is in a non-adjacent totally concealed square, take -5 to all attacks

You could also rule that each defender in the zone is effectively invisible. In that case, all attacks against it would take -5.

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I believe it's worded the way it is so that you can't shoot an arrow at a target on the far side of a cloud. By definition anyone in or blocked by the cloud has total concealment because they are "invisible, in a totally obscured square, or in a heavily obscured square and not adjacent to you." Because LoS is broken, they are "totally obscured", even to people in melee with them. –  AceCalhoon Dec 6 '10 at 17:54
    
This also means that someone attacking OUT of the cloud has to deal with the penalty as well... Because their targets are "totally obscured" (i.e. they can't see them). –  AceCalhoon Dec 6 '10 at 18:09
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