If more than 1% of the top 51% decide to try their luck at getting more after the captain is eliminated, then the captain dies.
Assumptions about the rationality of the participants can become
extremely complex. Mutual agent-modeling itself, which that is potentially an example of (depending on the assumptions), can actually go "infinitely" complex even in very simple cases:
In most messaging apps, when I send you a message, I can see whether you read it or not. It places a little "Read" next to the message I sent, like this:
That basically tells me whether you know what I wrote.
But the app could, although it doesn't, also proceed to tell you that I read the "Read" on the message; that is, it could tell you that
I know that
you read it, so that you know that I have seen that you have already read my message. Then it could go even further and tell me that you saw the message that indicated that I had seen that you had read my original message. Then it could tell you that I had seen that, and then me that you had seen that, and so on without end.
This shows how it is an actual "thing" to know that someone knows that you know that they know that you know that they know, etc. By that I mean, each of those endless possible steps are different. "I know that you know" is different from "I know that you know that I know," which is different still from "I know that you know that I know that you know." And so on. One might assume it's just some kind of toggling, like repeatedly multiplying a number by -1, but it isn't. Each successive state is unique and potentially represents a different set of possible real world implications. In everyday life we usually quickly stop caring or get too confused and forget before these can get nested all that deeply, but now...
Imagine a highly communicative environment where you are making very meaningful-feeling eye contact with someone in the moment, where you feel like you have a rather clear picture of their mental state, and they of yours. This is like a situation where the nesting is going very deep in super-fast iterations, possibly a very richly communicative situation where you might even call it a momentary "incredible connection."
That's another example, with nested iterations of modeling each other's modeling of each other's modeling of each other's mental state, etc... Akin to placing two mirrors opposite one another and seeing the nested pattern that forms and trails off into "infinity."
It is a tangent to remark that "infinity" or boundless possibility is praxeologically baked into human relationships, when there is an effort to concentrate on that nesting and the modeling is fairly accurate (during a makeout or vibing or very same-wavelength joking around or whatever).
In any case, modeling other people - at least during these kinds of interactions - is impossible in the sense that if they're trying to model you while you're trying to model them, you have to try to model their modeling of you while they're trying to model your modeling of them, and then their modeling of you modeling their modeling of them, etc. It's not just a trivial toggling, but an endless blossoming of intricacy.
So I don't think there is an unambiguously correct answer to the pirate puzzle as stated, due to way too much underspecification of assumptions, and I think that's exactly the aim.
But anyway, what of Paul Stzorc's response to Vitalik? Riskless counter-contracts. In general with PoS it seems to me that Vitalik and the other PoS people are falling into the "make the security model confusing enough that even really smart people can't understand it = good security" error. Sure, PoS doesn't seem confusing, but with things like stake-grinding plus an endless parade of more unfamiliar-to-security-researchers workarounds it optimizes for a security model that's difficult to poke holes in during debate, but that a motivated attacker could eventually figure out how to attack precisely because it's too opaque to know that what the attack vectors are so that they can be defended against.
