I am writing a paper for a conference. I have finished the paper, but I must review some experimental results and this requires some additional days.
How can I find out the probability that the submission deadline will be extended?
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Just look at past editions and see if there was indeed an extension. If they always do it, there will be another one; if they never extend, there is no reason to believe they will start this year.
If they don't, you could always give a shot to a polite email to the organizers and explain your situation. Perhaps you can submit a tentative proposal, with the uncertain data, and submit a refined version later (provided it doesn't change much).