you only get to 50% probability of dying as the game continues, which is better than the 75% from quitting the game.
20% probability of losing $100 can be better than 10% probability of losing $100 dollars, if the 20% is independent but the 10% is correlated with other events (e.g., if you lose $100 in the 10% of states of the world where you are already poorest). (This is well known in investment theory where being uncorrelated with market risk is valuable for an asset.) Similarly, 50% probability of dying is not necessarily better than 75% probability of dying, if the 50% is correlated with other events (in this case, dying in other quantum branches), and the 75% is independent.
To be more specific, let's analyze the decision problem using UDT. Suppose every copy of you in every branch is facing the same problem, and all of their "original" coins are perfectly correlated (which makes sense since the "original" coin is supposed to be a stand-in for "the laws of physics are such that LHC would destroy Earth if some accident didn't intervene"). You're trying to choose between the strategies (A) "keep flipping until the game ends" and (B) "keep flipping until either the game ends or I get to 1000 heads, then quit".
A UDT agent might choose B over A because saving 1/4 * 2^-1000 of its copies is considered more valuable in the state where there are already very few copies of itself. Perhaps our intuitions for "anthropic evidence" should be translated into such preferences, in line with my previous suggestions?
(My answer is very similar to Benja's. I'm guessing that our perspective is not the easiest to understand, and it helps to have multiple explanations.)
Closely related to: How Many LHC Failures Is Too Many?
Consider the following thought experiment. At the start, an "original" coin is tossed, but not shown. If it was "tails", a gun is loaded, otherwise it's not. After that, you are offered a big number of rounds of decision, where in each one you can either quit the game, or toss a coin of your own. If your coin falls "tails", the gun gets triggered, and depending on how the original coin fell (whether the gun was loaded), you either get shot or not (if the gun doesn't fire, i.e. if the original coin was "heads", you are free to go). If your coin is "heads", you are all right for the round. If you quit the game, you will get shot at the exit with probability 75% independently of what was happening during the game (and of the original coin). The question is, should you keep playing or quit if you observe, say, 1000 "heads" in a row?
Intuitively, it seems as if 1000 "heads" is "anthropic evidence" for the original coin being "tails", that the long sequence of "heads" can only be explained by the fact that "tails" would have killed you. If you know that the original coin was "tails", then to keep playing is to face the certainty of eventually tossing "tails" and getting shot, which is worse than quitting, with only 75% chance of death. Thus, it seems preferable to quit.
On the other hand, each "heads" you observe doesn't distinguish the hypothetical where the original coin was "heads" from one where it was "tails". The first round can be modeled by a 4-element finite probability space consisting of options {HH, HT, TH, TT}, where HH and HT correspond to the original coin being "heads" and HH and TH to the coin-for-the-round being "heads". Observing "heads" is the event {HH, TH} that has the same 50% posterior probabilities for "heads" and "tails" of the original coin. Thus, each round that ends in "heads" doesn't change the knowledge about the original coin, even if there were 1000 rounds of this type. And since you only get shot if the original coin was "tails", you only get to 50% probability of dying as the game continues, which is better than the 75% from quitting the game.
(See also the comments by simon2 and Benja Fallenstein on the LHC post, and this thought experiment by Benja Fallenstein.)
The result of this exercise could be generalized by saying that counterfactual possibility of dying doesn't in itself influence the conclusions that can be drawn from observations that happened within the hypotheticals where one didn't die. Only if the possibility of dying influences the probability of observations that did take place, would it be possible to detect that possibility. For example, if in the above exercise, a loaded gun would cause the coin to become biased in a known way, only then would it be possible to detect the state of the gun (1000 "heads" would imply either that the gun is likely loaded, or that it's likely not).