"Living in a part of the US that skews VERY heavily towards one party, I especially vote in primary elections, which are where it's actually determined which congresscritter or senator we'll be sending to Washington or the state capital."
This is exactly the case in NYC, which is heavily Democratic: the winner of the Democratic primary is the most likely winner of the general election (where they sometimes even run unopposed). In the recent primary in my district, the vote for City Council member was won by a margin of a few hundred votes, since the voter turnouts for primaries are pretty sparse compared with the general election. One person's vote really makes a difference in this situation.
You mean, a few hundred people's votes really make a difference in this situation.
Voting has a bit of a free-rider problem. To a first approximation, one vote never makes a difference; but an attitude that voting doesn't make a difference (especially when unevenly distributed) definitely makes a difference.
This is exactly the case in NYC, which is heavily Democratic: the winner of the Democratic primary is the most likely winner of the general election (where they sometimes even run unopposed). In the recent primary in my district, the vote for City Council member was won by a margin of a few hundred votes, since the voter turnouts for primaries are pretty sparse compared with the general election. One person's vote really makes a difference in this situation.