mmmmm… I don’t know. Let’s make things less confusing.
Firstly, put “the hedge fund” aside as none of this strictly comes from the actual hedge fund per se. Just say Numerai. Numerai has a treasury of NMR. It exists to pay us, not for Numerai to buy things. A few times though they have sold NMR (with a lockup period) to investors directly (people investing in the NMR token, not investing in the hedge fund). So it seems it doesn’t exist STRICTLY to pay us, but basically that is what it is there for.
Now, whats a burn? We use the term “burn” in two senses around here. One, the ordinary everyday “I burned today” or “I burned this round”. This first one has (almost) no meaning whatsoever since daily scores are just pretend anyway (except for one score a week for the round that resolves). The second one means the user actually lost some of their stake with a negative round. So that’s a real burn for the user – that stake is gone. They may earn enough later to make it back, but they well and truly lost it just like any other bet you might lose. So both of these are the first sense of the term – the user lost some of his stake and it is no longer theirs.
The second sense of “burn” is that the underlying NMR is destroyed forever – nobody ever gets to have it again and the total amount of NMR that exists in the world is now less. It is in this sense that I am talking about when I say “real” burns are rare – actual NMR being destroyed forever.
And so what’s happening generally when an individual burns is the first type – they lost it, but no NMR is lost from the world forever.
But I should have clarified further because the first scenario you posited when Numerai is out 100 from their treasury is not something that would happen even if real burns happened every week. If you lose NMR, nothing comes out of Numerai’s treasury, why would it? It is YOUR NMR that you lose when you burn, not Numerai’s. It was NMR you had acquired on the open market and staked. If it was really burned, then Numerai loses nothing and gains nothing – there is just less NMR in the world. Numerai only loses NMR when you win and they have to pay out, not when you lose. (Whether the burns are “real” or not doesn’t matter to that.) Which is why in theory if you lose and then completely cash out, that lost NMR should really be burned, because otherwise where is it? If it isn’t yours anymore and it isn’t destroyed, then somebody else must now have control over it, right? Except that’s not right – that shouldn’t happen, so it should be burned for real (and that’s all “being destroyed” means – it means the NMR is sent somewhere that nobody ever has access to). But possibly they are netting it out over all users or something and it still isn’t really burned as long as they are paying out in total. It is all to do with ETH contracts and I don’t understand it. So we need the technical explanation of what actually happens there from the team.
So to sum up, however burning occurs, it is always YOUR stake that burns and burns don’t cost Numerai anything except for the bad trades they might make from your crappy predictions that burned.