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I didn't say 'not possible' I said improbable. And while I won't call you a liar, some of the results you are quoting are statically very, very improbable.
Again, I've personally witnessed a player who *twice* summoned and bound/invoked Force 12 spirits. All without burning Edge. Now, let's say he goes for it a third time, and this time blows the roll. Should he be banned from burning Edge to succeed at a task he's already accomplished?
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As to the cheesyness of the GM burning edge to negate a players burn, come-on. The player is blatently twisting the rules in order to summon a spirit way more powerful then his character could normaly have. Whats more, a force 12 spirit is a incredibly powerful being, on par with a dragon or even a great dragoon.
That's kind-of the GM cheese I'm referring to. You're blatantly favoring the spirit, and twisting the spirit of the rules to make the game go the way you want. A force 12 spirit is decidedly not on par with a Great Dragon; Buttercup is more than Force 12, and she was beaten by Dunkelzahn.
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The waiting game is a logical alternative, I grant you. But remember that a bound spirit is forced to obey and prevented from overt attack or refusal of directions. If the GM plays an ornery, troublesome spirit looking for a chance to stick it to the Man, there is lots of opportunity for fun role-play and interaction on the part of player and GM. There is also lots of opportunity for the kind of cheese you decry.
There are fewer opportunities for GM cheese, though. Sure, twisting it's orders is fair game, but realistically it'll be up to the roleplay between the summoner and spirit. In my case, the player actually did a fair job of interacting with the spirits, and had Spirit Affinity with their type as well. They had fewer reasons to rebel than, say, a lower-force spirit who he's got a Bane against.
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Ie, if you need 15 hits, and you have 15 dice, no problem, but if you need 16 hits, and only have 15 dice, yes it would be possible to do it with edge, but i'd say that it isn't probable, so no burning edge to buy it.
The issue here is that any roll that you might burn Edge on, you probably will have already spent Edge as well. So, you have the theoretically unlimited success problem again. Also, what happens if they burn Edge just because they're close, or because they really want to go from a marginal success to a Critical one?
For example, let's say you need 16 successes, and you have 15 dice with Edge. You roll and get 14 successes-- not enough, but only just. So, you burn an Edge. By your rule, you can't do that, even though you only needs 2 more successes.
Or what happens if the player successfully summons the spirit, with 1 net success. That gives him one service; but he decides that's not enough, and burns an Edge to gain 4 services out of it. What happens then?
The fact is, it's impossible to draw a statistical line between the possible and the impossible. Luckily, there is a clear line in this case: Assuming Magic 6, you cannot burn Edge to get a Force 13 spirit, no matter what.