stack resolving?

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Hey i was wondering how the stack resolving thing works. My friend says that the stack resolves all at once which means that you can't do anything in response to the resolve. For example, if theres a grizzly bears, they cast safe passage, then I cast lightning bolt and in response they cast cloudshift. Can i let the cloudshift resolve and then cast another lightning bolt to target the grizzly bears before the safe passage and other lightning bolt resolves? Also as it resolves does order matter? 

For example, if they start with an Archaeomancer, deadeye navigator and <a href="http://gatherer.wizards.com/Pages/Card/Details.aspx?multiverseid=240096" rel="nofollow">Restoration Angel</a> where restoration angel and deadeye navigator are paired. So what happens is they cast safe passage in response to an irrelevant creature, in response I cast lightning bolt on archaeomancer, then they bounce restoration angel with the paired ability, I tap two mountains to deal 2 damage to it (through Koth's emblem), they use bounce ability again with restoration angel, tap 2 mountains, ability again. I said that he can't do that because after he uses the ability once they are no longer paired, and also as it resolves the bounce ability is targetting a different creature since the bounced creature is a new target. His argument was that since it resolves all at once it doesnt matter. 

Can someone please explain the ruling for those two situations? I'm sorry that there pretty wordy. Thanks for any help in advance. 

koth of the hammer 
yes, you get priority after each spell/ability on the stack resolves
your scenarios work and you got it right

I think the "stack resolves all at once" is from YuGiOh
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how does the stack work with the second situation? would it be safe passage, lightning bolt, restoration angel leaves play, restoration angel returns to play, archaeomancer leaves play, archaeomancer returns to play and etc? so if i tap two mountains as restoration angel leaves play then archaeomancer would die? or is it just as I said above which means that the archaeomancer would live as the angel's bounce ability was last , and then all spells afterwards would be targetting the older version of the same card? or are they not allowed to play the same ability twice on the stack?
From my understanding if I cast lightning bolt on a grizzly bear and then they cast vines of vastwood on the bear, it survives and I can't redirect the damage to another target say another grizzly bear. 

Thanks!
Your second example is very confusing, so I won't address it. Instead, I'll tell you how the stack works.

At the start of each step/phase, the active player gets priority and can play as many spells or abilities in a row as he or she wants on top of each other (they don't resolve). Once he passes (doesn't play something), the next player gets priority and may play any number of spells/abilities. This continues until all players pass in succession.

When all players pass, the top item of the stack resolves, then the active player gains priority again.

If nothing is left on the stack, you go to the next step or phase. 

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okay so what im trying to understand is this. if you use deadeye navigator skill with restoration angel (leaves play and returns to play, and with restoration angels ability, targetting archaeomancer) how does this look like on the stack?
will it work like which of the following situations?
1) restoration angel is exiled (through deadeye navigator skill) --> restoration angel returns to play --> restoration angel ability triggers targetting archaeomancer --> archaeomancer leaves play --> archaeomancer returns to play --> archaeomancers skill triggers targetting spell in graveyard. 
 2) restoration angel leaves and returns to play targetting archaeomancer --> archaeomancer leaves and returns to play targetting spell in graveyard
3) something else

Another new question is if they have 2 grizzly bears, i target a grizzly bears with a lightning bolt and in response they cast vines of vastwood. the grizzly bears i targeted would survive since it is no longer a valid target correct? Also I can't change targets for lightning bolt while the spell is resolving. for example i cant change the target of lightning bolt to the other grizzly bear after vines of vastwood has resolved. therefore in a sense the vines of vastwood has nullified the effect of lightning bolt. Is this correct? 

 
Your second example is very confusing, so I won't address it. Instead, I'll tell you how the stack works.

At the start of each step/phase, the active player gets priority and can play as many spells or abilities in a row as he or she wants on top of each other (they don't resolve). Once he passes (doesn't play something), the next player gets priority and may play any number of spells/abilities. This continues until all players pass in succession.

When all players pass, the top item of the stack resolves, then the active player gains priority again.

If nothing is left on the stack, and both players pass priority you go to the next step or phase.



Edit: bold.

And yes, that is what vines does, and that is why I love it. Your lightning bolt will fizzle (fail to resolve, and is put in the graveyard) on resolution because it's target is illegal. Same thing would happen if the bears were removed some other way.
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yeah okay I thought so but wasn't 100% sure, thanks!
also how does deadeye navigator restoration angel and archaeomancer interact and look like on the stack?
so starting with restoration angel and deadeye navigator on the field and already paired and archaeomancer also on the field.
if I use restoration angel's paired skill from deadeye navigator and then since restoration enters the battlefield, I target archaeomancer which leaves and enters the battlefield, allowing me to pick an instant or sorcery from my graveyard. I understand that this works but I don't understand how it looks like on the stack. If someone can explain to me how this looks like on the stack it would be very helpful. Thanks 
also how does deadeye navigator restoration angel and archaeomancer interact and look like on the stack?
so starting with restoration angel and deadeye navigator on the field and already paired and archaeomancer also on the field.
if I use restoration angel's paired skill from deadeye navigator and then since restoration enters the battlefield, I target archaeomancer which leaves and enters the battlefield, allowing me to pick an instant or sorcery from my graveyard. I understand that this works but I don't understand how it looks like on the stack. If someone can explain to me how this looks like on the stack it would be very helpful. Thanks 



1: You activate restoration angel's ability (from the deadeye) and place "Exile this creature, then return it..." on the stack.
2: You pass priority, opponent passes priority.
3: Angel's ability (from deadeye)resolves. Angel is exiled and then returned.
4: Restoration Angel's "When restoration angel enters..." ability triggers and deadeyes souldbond ability trigger (Whenever another creature enters the battlefield under your control, if you control both that creature and this one and both are unpaired, you may pair that creature with this creature for as long as both remain creatures on the battlefield under your control) and are put on the stack and you declare archaeomancer as your target of Restoration Angel's triggered ability. Since they trigger at the same time you get to choose which order these are placed on the stack. In this case it is irrelevant. But, just for clarity let's specify that the soulbond trigger goes on top of the stack, and restoration's "when ... enters" is second, and last on the stack.
5: You and opponent both pass priority.
6: Soulbond ability resolves and they are paired. Restoration angel's ability is still on the stack.
7: You and opponent pass priority.
8: Restoration's "when ... enters" resolves and Archaeo is exiled and then returned to play.
9: Archeao's ability triggers and is put on the stack. You declare an instant card in your graveyard as your target.
10: You and opponent both pass priority.
11: Archaeo's ability resolves and is put in your hand.

Sounds right, I'm kinda tired though, let me double check.
That looks better now.
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thanks that explains alot. So from what I understand, if I cast lightning bolt on archaeo in response to step 4 then it will die and not be saved. they can not use the deadeye's ability as it is not soulbound to anything and restoration angel's ability is still on the stack as well. Therefore archaeo dies.
Once again thanks for that detailed explanation 
Correct, and no problem.
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I think the "stack resolves all at once" is from YuGiOh

It actually comes from Magic itself, but was changed more than 13 years ago.

P.S. YuGiOh comes directly from Magic: they copied Magic and (drastically) lowered the difficulty level... 
Magic itself looks suspiciously similar to the older Mille Bornes game, aside from the Dungeons&Dragons theme. 

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From Milles Bornes:
«The premise of Mille Bornes is that the players are in a road race(1). Each race—or hand—is usually 700 miles (or kilometers) long,(...) Mille Bornes is played with a special deck of cards(2). There are hazard, remedy, safety, and distance cards(3). Each hazard is corrected by a corresponding remedy, and is actually prevented(4) from happening in the first place by a corresponding safety...» 
 
Translation to Magic:
1) Road Race = life points, race for zero 
2) Special deck of cards!!!
3) Hazard, remedy, safety, and distance cards = Terror, Counterspell, Healing Salve and Lightning Bolt
4) Prevented!!! 

The major ideas Garfield invented are the mana system and the open-ended possibilities of new cards.