I'm sure there's a way to get an exact answer to the odds of a tie using
the laws of combination and the assumption of each vote's being the toss of
a coin.  However, I suggest a recursive way to an APPROXIMATE answer.

First, use a Gaussian distribution (close enough to binomial to work with a
sample that size) to figure out the odds of all the votes coming within,
say, 128 of each other.  Put that number aside.

Now, for election results lying within 128 votes, use the Gaussian
distribution to figure out the MEAN difference.  The mean should coincide
with the mode for a distribution like this.

Next figure out the odds of exactly that number of heads in 128 coin
tosses.

Finally multiply those odds by the odds from the previous calculation.  The
result will overestimate the odds against, but if my thinking's right, it
won't be by much.

In Your Sly Tribe,
Robert
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