Related to: Can Counterfactuals Be True?, Newcomb's Problem and Regret of Rationality.
Imagine that one day, Omega comes to you and says that it has just tossed a fair coin, and given that the coin came up tails, it decided to ask you to give it $100. Whatever you do in this situation, nothing else will happen differently in reality as a result. Naturally you don't want to give up your $100. But see, Omega tells you that if the coin came up heads instead of tails, it'd give you $10000, but only if you'd agree to give it $100 if the coin came up tails.
Omega can predict your decision in case it asked you to give it $100, even if that hasn't actually happened, it can compute the counterfactual truth. Omega is also known to be absolutely honest and trustworthy, no word-twisting, so the facts are really as it says, it really tossed a coin and really would've given you $10000.
From your current position, it seems absurd to give up your $100. Nothing good happens if you do that, the coin has already landed tails up, you'll never see the counterfactual $10000. But look at this situation from your point of view before Omega tossed the coin. There, you have two possible branches ahead of you, of equal probability. On one branch, you are asked to part with $100, and on the other branch, you are conditionally given $10000. If you decide to keep $100, the expected gain from this decision is $0: there is no exchange of money, you don't give Omega anything on the first branch, and as a result Omega doesn't give you anything on the second branch. If you decide to give $100 on the first branch, then Omega gives you $10000 on the second branch, so the expected gain from this decision is
-$100 * 0.5 + $10000 * 0.5 = $4950
So, this straightforward calculation tells that you ought to give up your $100. It looks like a good idea before the coin toss, but it starts to look like a bad idea after the coin came up tails. Had you known about the deal in advance, one possible course of action would be to set up a precommitment. You contract a third party, agreeing that you'll lose $1000 if you don't give $100 to Omega, in case it asks for that. In this case, you leave yourself no other choice.
But in this game, explicit precommitment is not an option: you didn't know about Omega's little game until the coin was already tossed and the outcome of the toss was given to you. The only thing that stands between Omega and your 100$ is your ritual of cognition. And so I ask you all: is the decision to give up $100 when you have no real benefit from it, only counterfactual benefit, an example of winning?
P.S. Let's assume that the coin is deterministic, that in the overwhelming measure of the MWI worlds it gives the same outcome. You don't care about a fraction that sees a different result, in all reality the result is that Omega won't even consider giving you $10000, it only asks for your $100. Also, the deal is unique, you won't see Omega ever again.
The problem only asks about what you would do in the failure case, and I think this obscures the fact that the relevant decision point is right now. If you would refuse to pay, that means that you are the type of person who would not have won had the coin flip turned out differently, either because you haven't considered the matter (and luckily turn out to be in the situation where your choice worked out better), or because you would renege on such a commitment when it occurred in reality.
However at this point, the coin flip hasn't been made. The globally optimal person to be right now is one that does precommit and doesn't renege. This person will come out behind in the hypothetical case as it requires we lock ourselves into the bad choice for that situation, but by being a person who would act "irrationally" at that point, they will outperform a non-committer/reneger on average.
What if there is no "on average", if the choice to give away the $100 is the only choice you are given in your life? There is no value in being the kind of person who globally optimizes because of the expectation to win on average. You only make this choice because it's what you are, not because you expect the reality on average to be the way you want it to be.