Analyzing a Voting System (Math Geeks Please Help!)

[hmkpoker]

I'm testing a theory about the US voting system and I'd like a little help devising a formula to tell me the likelihood that one vote will make or break the election.

The assumptions are that there are n number of participating voters, two candidates A and B, and all voters will vote with a 50-50 likelihood of either candidate. What is the formula to determine the likelihood that the same number will show up for both sides?

There is probably going to be a resolution problem, because for even numbers a vote count of n/2 on either side yields, and ((n/2) +/- 1) depicts voting situations where one vote did make a difference...but for odd numbers, the countable outcomes would be ((n/2) +/- .5) with no stalemate.

Can anyone figure out a simple formula for this?