It Depends on What You Mean by "Matter"
There are a couple of ways in which you can think about whether your vote will "matter" or not. First, you can ask whether your vote will be decisive, which means that the election would have gone the other way had you not voted or had you voted differently. If the election is decided by more than two votes, then your vote is not decisive. If candidate Jack Johnson wins by three votes over candidate John Jackson, then your vote was irrelevant to the outcome. Suppose you voted for Jack Johnson. Had you stayed home, Johnson still would have won by a single vote. Had you voted for John Jackson, this would subtract one from Johnson's total and added one to Jackson's total, in which case Johnson still would have won by a single vote. The probability that your vote will be decisive falls rapidly the larger the polity gets. If you're a member of the Supreme Court, then there is a pretty good chance that your vote can be decisive. If you are one of tens of millions of voters in a federal election, the probability that your vote will change the outcome is so low that you can safely assume it will be zero. I voted in a local election a few weeks ago; the same people would have won and lost and the same measures would have passed or failed had I bypassed the polling place in order to get home a little earlier. There is another sense in which you can interpret your vote as having "mattered," and that is as a statement of your political preferences. I will have more to say on that later.
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I disagree.
Consider this, if a tree falls in a forest and no one is there to hear it, does it mean that the tree didn't fall?
Of course not!
Now consider this too, if an election is based on a count of 1 vote, which all are by the way, then how will you ever know that your vote wasn't that one your candidate needed? You can't, unless you're claiming Supreme Godhood!
Some where along the election process the pivotal point of 1 vote is passed, but on that road are all those votes being cast which tally up to that pivoting point. So what if 1,000,000 votes are cast afterword. Nobody knows when that pivotal point is reached until hours after it's actually been reached. So the weight of your vote isn't unknown to anyone but God.
Were I would agree is on your point of a vote being "decisive". Every vote is crucial, but only in a extremely close election or in the case of your example of a small polity like the Supreme Court, does a single vote become "decisive."
It's a basic statistical understanding that when you breach 30 data points, points beyond the 30 tend to not matter in the grand scheme of things. This is true in just about every aspect of life. Calculating present values of time periods greater than 30 are assumed to be an infinite perpetuity because the difference between the two is essentially zero. The same goes with the concept of voting in any election that breaches 30 voting members.
Your best chance to matter in an election, statistically, is in an election where you are voting in an election with two other individuals. If there is only one other voter, your vote doesn't count because it's either a stalemate or your candidate wins by default. For your vote to count in an election where there is only you and two other voter, the chances your vote will count comes in at 25% (assuming pure random chance, it only becomes worse with preferences involved). This means there is only a 25% chance that the other two voters will vote differently than one another (0.5^2). Now let's use 30 people, you being voter #30. .5%^29 = 1.86e-9. Basically, at 30 people, the statistical chance that your vote will count is zero. For a typical senate race , the calculation is .5%^5e6 requires a supercomputer to properly decimalize it, meaning it's millions of times more zero than you voting in a group of 30.
Additionally, there is a temporal factor involved. You literally have to be the last person to vote for yours to count. For the 30 voter initiative, on top of you having to hit the 1/536,870,912 chance that there will be a 15-14 vote, you personally have to be voter #30. Again, using random sampling, this makes the chances out at 1 in 16,106,127,360 that your vote actually counts. You have a better chance at striking the million dollar jackpot at Las Vegas than you do to make your vote count in an election over a single high school political science class. Expand that to 600,000 for a Congressman, 5 million for a Senator, or 130 million for President, and you get a number so long no word exists for it.
Your vote literally does not count.