Caplan and Yudkowsky bet at 1-1 odds whether humanity would be exterminated from the surface of the Earth by 2030. How it works is Caplan pays Yudkowsky $100 in 2017 (when the bet began). If humanity is still living on the surface on the Earth in 2030 then Yudkowsky owes Caplan $200 plus 5% annual interest. See here for details.
I don't think Yudkowsky was taking this bet seriously, which somewhat invalidates it, but let's pretend the bet was in good faith. Does the bet actually work?
Some people criticized the bet on the grounds that it relied on Yudkowsky's honesty and interest rates staying similar. I don't think either of these are an issue. The bet contains a clause to deal with interest rates going haywire and there's no way even a psychopathic machiavellian Yudkowsky would trash his public reputation for a mere CPI-adjusted $200. Moreover, accounting for interest rates is something all time-displaced bets need to deal with. It's just an annoying fact of quantitative finance.
There's a bigger problem with the Caplan-Yudkowsky bet. The bet only makes sense from the perspective of Caplan. There's no direct way for Yudkowsky to intentionally profit from it except indirectly, via financial derivatives, unless our annihilation becomes certain.
Consider the most conservative approach. Yudkowsky invests his $100 in the stock market at 5% annual interest for 13 years. There are two possible outcomes: Either the world ends or it doesn't. If the world ends, Yudkowsky gains exactly nothing from the bet, because he never spent the money. If the world doesn't end then Yudkowsky simply loses money. If Yudkowsky is to profit from the bet, then he must spend money before the world ends in 2030.
Suppose it's 2029. Yudkowsky is confident that the world will end on January 1, 2030. There's no reason to preserve capital, so he blows all of his money on cocaine, prostitutes and a cryogenic vault. If the world ends, then great! But if the world doesn't end then Caplan doesn't get paid back. Yudkowsky can't spend the money as long as there is a chance the world will survive.
In other words, Yudkowsky can only benefit from the $100 by going bankrupt. (Unless interest rates change. Caplan notes that "this is primarily a bet that annualized real interest rates stay below 5.5%". Which is true. But what's interesting is the "End-of-the-World" part, not the 5.5% interest rate.)
It's plausible that financial derivatives might work around this problem, but unless Yudkowsky is using them (unlikely for a bet this small) then this bet was just an indirect way of buying a genuine probability estimate from Bryan Caplan. The only way Yudkowsky can earn money from this bet is via unintended edge cases where he survives the apocalypse (e.g. by being off-planet). Or where our doom has become certain, but it hasn't happened yet, and where money value is still meaningful.
In the limit of high expectation of the world ending, the expected value loss if the world survives goes to zero, so we've now established that the bet can, in fact, work.
With respect to the actual values, given that the bet is for an amount of money small relative to expected income, I'd expect fairly linear effects where the expected utility cost* of doing extra work/spending less to accumulate $200 in the future is pretty close to twice the utility cost of having $100 more to spend now, such that if the chance of the world ending is greater than 50% it makes sense to make the bet.
(*ignoring discount rates, wage rate changes etc., which aren't the point)
Further edit: if the world is likely to end, yes Yudkowsky wins alpha.