I think that it's something like the posterior probability of OOFLam given my current existence -- if, the sharpshooter fallacy doesn't apply.
Why would you think the Texas sharpshooter fallacy wouldn't apply? You seem to think it's something you can just set aside if it becomes inconvenient to getting the answer you want. You haven't yet figured out that it's possible for you to be wrong.
The probability of your current existence matters only if it was supposed to be a certain thing and did or didn't turn out that way. Over a large number of trials, the law of large numbers dictates that the toss of a fair coin should approach a certain distribution. We know this because we know the physics of a fair coin. The probability of you coming out a certain way matters only if there is some way we can know what you were "supposed" to be like. Then and only then can you speak meaningfully about the probability of some outcome. The significance of where the bullet lands in in the Texas sharpshooter fallacy matters because of where it was supposed to land.
No, the toss of a fair coin is nothing like you trying to say you must be special because there were so many different possibilities.
Let's consider a variation on your example. Let's use smaller numbers. You have a fair nickel, and you toss it three times. How many possibilities for that outcome? 2
3 or 8. We use small numbers so that we can enumerate all 8 possible sequences: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. Let's say in your case it comes up TTT. "How remarkable!" you might say. "Three tails in a row!" Sure, you could talk about whether this was a fair coin. Why? Because TTT is more likely given a gimmicked coin versus a fair coin. And that's because we know that to gimmick a coin means to make it come out one way more often than the other.
But the question at hand is not the fairness of the coin. The question is whether the outcome TTT is legitimately remarkable. A moment's thought indicates it's remarkable only because you intuitively considered TTT special from the among the possibilities because it's all the same. TTT and HHH are
intuitively remarkable because your primate brain recognized a pattern. Statistically, neither TTT nor HHH is any more probable an outcome that HHT or THT.
That's how poker works. All the hands you could be dealt are equally probable. We primately choose patterns of them ahead of time that meet certain intuitive criteria, mostly because that helps us remember what the winning hands are. Ahead of the game, we identify them as the ones that have special significance for the game. You want to play fast and loose with the opposite intuition -- that if something merely arose out of a huge number of potential combinations, it must therefore be remarkable. And so you draw a chalk circle around it and say, "What a remarkable feat!"
