You need *at least* 26.9 bits. Since the boxes he talked about provide 2 bits each, you need 14 boxes to get *at least* 26.9 bits (13 boxes would only be 26 bits, not enough). 14 boxes happens to be 28 bits.
I'm not getting the same result... let's see if I have this right.
If you quit if the first coin is heads:
50%*75% death rate from quitting on heads, 50%*50% death rate from tails
If you never quit:
50% death rate from eventually getting tails (minus epsilon from branches where you never get tails)
These deathrates are fixed rather than a distribution, so switching to a logarithm isn't going to change which of them is larger.
I don't think the formula you link to is appropriate for this problem... it's dominated by the log(2^-n) factor, which fails to account for 50% of your possible branches being immune to death by tails. Similarly, your term for quitting damage fails to account for some of your branches already being dead when you quit. I propose this formula as more applicable.
In every case of the pirates game, the decision-maker assigns one coin to every pirate an even number of steps away from himself, and the rest of the coins to himself (with more gold than pirates, anyway; things can get weird with large numbers of pirates). See the Wikipedia article Kawoomba linked to for an explanation of why.
Seeing as how what I was saying was basically "let the poor starve", this ending seems strangely appropriate.
I'm trying to interpret this in a way that makes it true, but I can't make "AI researchers" a well-defined set in that case. There are plenty of people working on AI who aren't capable of creating a strong AI, but it's hard to know in advance exactly which few researchers are the exception.
I don't think we know yet which people will need to cooperate for FAI to succeed.
I've just made the unpleasant discovery that being downvoted to -4 makes it impossible to reply to those who replied to me (or to edit my comment). I'll state for the record that I disagree with that policy... and proceed to shut up.
[I've written two different responses to your comment. This one is more true to my state of mind when I wrote the comment you replied to.]
Consider this: a man gets a woman pregnant, the man leaves. The woman carries the child to birth, hands it over to an adoption agency. Raising the child to maturity is now someone else's problem, but it has those parents' genes. I do not want this to be a viable strategy. If some people choose this strategy, that only makes it more important to stop letting them cheat.
It's a lot of resources from the perspective of a single person, but I was thinking at a slightly larger scale. By "easy", I mean that manageable groups of people can do it repeatedly and be confident of success. Really, the fact that sentient minds can be valued in terms of resources at all is sufficient for my argument. (That value can then be ignored when assessing productivity, as it's a sunk cost.)
You seem to be looking in the wrong place with your "that people ought to earn every resource themselves" example - my opinion is that the people who have resources should not give those resources to people who won't make good use of them. That the people who lack resources will then have to earn them if they're to survive is an unavoidable consequence of that (and is my real goal here), but those aren't the people that I think ought to be changing things.
As for what strategies people actually follow, I think most people do what I'm saying they should do, on an individual level. Most people protect their resources, and share them only with those who they expect to be able to return the favor. On the group level, though, people lose track of how much things actually cost, and support things like welfare that help people regardless of whether they're worth the cost of keeping alive.
If you look in box B before deciding whether to choose box A, then you can force Omega to be wrong. That sounds like so much fun that I might choose it over the $1000.