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If your dice pool is ever reduced to zero or fewer dice, you can still make a "chance roll."

A chance roll gives me one die. If I spend willpower on that roll, does it bump me up to four dice? Or do I start from whatever pool ended up giving me the chance die to begin with and then add three?

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You add three dice to your original pool, not to the chance die.

From the section on Willpower, p. 132:

Willpower should be spent and three dice are added to your dice pool before all penalties for your roll have been applied. So, form your pool, add all bonuses — including your three dice from Willpower — and then subtract all penalties. Yes, that means if penalties are sufficiently extreme, you could be reduced to a chance roll even if you have spent Willpower for three extra dice.

(Emphasis mine.)

In fact, the example in the book involves just this situation and concludes, "You must make a chance roll for your character to succeed, even though you spent Willpower on the task."

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