My opponent has a 3/3 and he blocks my Nova Chaser. In response to the 7 damage trampling through can I then fling the Nova Chaser with Brion Stoutarm for 17 damage?
No. All damage is dealt simultaneously and then State Based Actions are checked. In this case, the Nova Chaser has 3 damage marked on it so it will die before you get priority to activate Brion's ability.
No. Combat damage does not use the stack (and hasn't for a very long time now), so it can't be responded to. Instead, it is a turn based at the very beginning of the combat damage step, that no player can interrupt, you can only do things afterwards in that step.
However, if your Nova Chaser has first strike or double strike, then it would deal comnat damage in the first combat damage step, while your opponent's creature would only get to deal its combat damage in the second one (so not at all in this scenario, since it should be dead at that time). That gives you a window (the whole of the first combat damage step) to fling your Chaser, if the 3/3 somehow survived and is still in combat to kill your creature (indestructible, damage prevention, etc.).
Ok thanks. Follow up question. Can I cast Phyrexian Dreadnought and then fling it with Brion Stoutarm immediately?
Yes. You can respond to the Dreadnought's enter-the-battlefield ability with Brion's ability to "fling" it before it gets sacrificed to itself.
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Ok thanks. Follow up question. Can I cast Phyrexian Dreadnought and then fling it with Brion Stoutarm immediately?
Yes, you can do this. Dreadnought's ability does use the stack and can be responded to. If you choose to do this, you can still sac other creatures but, if you choose not to, the Dreadnought will not be around to be sacrificed so nothing happens.
Ok thanks. Follow up question. Can I cast Phyrexian Dreadnought and then fling it with Brion Stoutarm immediately?
Yes, you can fling it in response to the trigger. When that one finally resolves, you can simply choose to not sacrifice any creatures, and the punishment for that will be irrelevant for you since the Dreadnought is already gone, so nothing happens.
However, if your Nova Chaser has first strike or double strike, then it would deal comnat damage in the first combat damage step, while your opponent's creature would only get to deal its combat damage in the second one (so not at all in this scenario, since it should be dead at that time). That gives you a window (the whole of the first combat damage step) to fling your Chaser, if the 3/3 somehow survived and is still in combat to kill your creature (indestructible, damage prevention, etc.).
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)
Yes, you can fling it in response to the trigger. When that one finally resolves, you can simply choose to not sacrifice any creatures, and the punishment for that will be irrelevant for you since the Dreadnought is already gone, so nothing happens.
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)