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Running through this to check that my wetware handles it consistently.

Paying -100 if asked:

When the coin is flipped, one's probability branch splits into a 0.5 of oneself in the 'simulation' branch, 0.5 in the 'real' branch. For the 0.5 in the real branch, upon awaking a subjective 50% probability that on either of the two possible days, both of which will be woken on. So, 0.5 of the time waking in simulation, 0.25 waking in real 1, 0.25 waking in real 2.

0.5 x (260) + 0.25 x (-100) + 0.25 x (-100) = 80. However, this is the expected cash-balance change over the course of a single choice, and doesn't take into account that Omega is waking you multiple times for the worse choice.

An equation for relating choice made to expected gain/loss at the end of the experiment doesn't ask 'What is my expected loss according to which day in reality I might be waking up in?', but rather only 'What is my expected loss according to which branch of the coin toss I'm in?' 0.5 x (260) + 0.5 x (-100-100) = 30.

Another way of putting it: 0.5 x (260) + 0.25 x (-100(-100)) + 0.25 x (-100(-100)) = 30 (Given that making one choice in a 0.25 branch guarantees the same choice made, separated by a memory-partition; either you've already made the choice and don't remember it, or you're going to make the choice and won't remember this one, for a given choice that the expected gain/loss is being calculated for. The '-100' is the immediate choice that you will remember (or won't remember), the '(-100)' is the partition-separated choice that you don't remember (or will remember).)

--Trying to see what this looks like for an indefinite number of reality wakings: 0.5 * (260) + n x (1/n) x (1/2) x (-100 x n) = 130 - (50 x n), which of the form that might be expected.

(Edit: As with reddit, frustrating that line breaks behave differently in the commenting field and the posted comment.)

(For thoroughness, noting that the other approach was also wondered about a little earlier. Surface action is an alternative to look at if projectile-launching would definitely be ineffective, but if the projectile approach would in fact be better then there'd no reason not to focus on it instead.)

A fair point. On the subject of pulling vast quantities of energy from nowhere, does any one country currently possess the knowledge and materials to build a bomb that detonated on the surface could {split the Earth like a grape}/{smash the Earth like an egg}/{dramatic verb the Earth like a metaphorical noun}?

And yes, not something to try in practice with an inhabited location. Perhaps a computer model, at most... actually, there's a thought regarding morbid fascination. I wonder what would be necessary to provide a sufficiently-realistic (uninhabited) physical (computer) simulation of a planet's destruction when the user pulled meteors, momentum, explosives et cetera out of nowhere as it pleased. Even subtle things, like fiddling with orbits and watching the eventual collision and consequences... hm. Presumably/Hopefully someone has already thought of this at some point, and created such a thing.

Not directly related, but an easier question: Do we currently have the technology to launch projectiles out of Earth's atmosphere into a path such that, in a year's time or so, the planet smashes into them from the other direction and sustains significant damage?

(Ignoring questions of targeting specific points, just the question of whether it's possible to arrange that without the projectiles falling into the sun or just following us eternally without being struck or getting caught in our gravity well too soon... hmm, if we could somehow put it into an opposite orbit then it could hit us very strongly, but in terms of energy... hmmm. Ah, and in the first place there's the issue that even that probably wouldn't hit with energy comparable to that of a meteor, though I am not an astrophysicist. In any case, definitely not something to do, but (as noted) morbidly fascinating if it turned out to be fairly easy to pull off. Just the mental image of all the 'AUGH' faces... again, not something one would actually want to do. )

()

In practice, this seems to break down at a specific point: this can be outlined, for instance, with the hypothetical stipulation "...and possesses the technology or similar power to cross universe boundaries and appear visible before me in my room, and will do so in exactly ten seconds.".

As with the fallacy of a certain ontological argument, the imagination/definition of something does not make it existential, and even if a certain concept contains no apparent inherent logical impossibilities that still does not mean that there could/would exist a universe in which it could come to pass.

'All possible worlds' does not mean 'All imaginable worlds'. 'All possible people' does not mean 'All imaginable people'. Past a certain threshold of specificity, one goes from {general types of people who exist almost everywhere, universally speaking} to {specific types of people who only exist in the imaginations of people like you who exist almost everwhere, universally speaking}.

(As a general principle, for instance/incidentally, causality still needs to apply.)

Edit:

(Absent(?) thought after reading: one can imagine someone, through a brain-scanner or similar, controlling a robot remotely. One can utter, through the robot, "I'm not actually here.", where 'here' is where one is doing the uttering through the robot, and 'I' (specifically 'where I am') is the location of one's brain. The distinction between the claim 'I'm not actually here' and 'I'm not actually where I am' is notable. Ahh, the usefulness of technology. For belated communication, the part about intention is indeed significant, as with whether a diary is written in the present tense (time of writing) or in the past tense ('by the time you read this[ I will have]'...).) enjoyed the approach

To ask the main question that the first link brings to mind: What prevents a person from paying both a life insurance company and a longevity insurance company (possible the same company) relatively-small amounts of money each in exchange for either a relatively-large payout from the life insurance if the person dies early and a relatively-large payout from the longevity insurance if the person dies late?

To extend, what prevents a hypothetically large number of people to on average create this effect (even if each is disallowed from having both instead of just one or the other) and so creating a guaranteed total loss overall on the part of an insurance company?

To answer the earlier question, an alteration which halved the probability of failure would indeed change an exactly-0% probability of success into a 50% probability of success.

If one is choosing between lower increases for higher values, unchanged increases for higher values, and greater increases for higher values, then the first has the advantage of not quickly giving numbers over 100%. I note though that the opposite effect (such as hexing a foe?) would require halving the probability of success instead of doubling the probability of failure.

The effect you describe, whereby a single calculation can give large changes for medium values and small values for extreme values, is of interest to me: starting with (for instance) 5%, 50% and 95%, what exact procedure is taken to increase the log probability by log(2) and return modified percentages?

Edit: (A minor note that, from a gameplay standpoint, for things intended to have small probabilities one could just have very large failure-chance multipliers and so still have decreasing returns. Things decreed as effectively impossible would not be subject to dice rolling or similar in any case, and so need not be considered at length. In-game explanation for the function observed could be important; if it is desirable that progress begin slow, then speed up, then slow down again, rather than start fast and get progressively slower, then that is also reasonable.)

For what it's worth, I'm reminded of systems which handle modifiers (multiplicatively) according to the chance of failure:

## [quote]

For example, the first 20 INT increases magic accuracy from 80% to

(80% + (100% - 80%) * .01) = 80.2%

## not to 81%. Each 20 INT (and 10 WIS) adds 1% of the remaining distance between your current magic accuracy and 100%. It becomes increasingly harder (technically impossible) to reach 100% in any of these derived stats through primary attributes alone, but it can be done with the use of certain items.

[/quote]

A clearer example might be that of a bonus which halves your chance of failure changing 80% success likelihood to 90% success (20% failure to 10% failure), but another bonus of the same type changing that 90% success to 95% success (10% failure to 5% failure). Notable that one could combine the bonus first in calculation to get a quarter of 20% as 5% with no end change.