LessWrong 2.0 Reader

There is an important nuance that makes it ~n+4/5 for large n (instead of n+1), but I'd have to think a bit to remember what it was and give a nice little explanation. If you can decipher this comment thread, it's somewhat explained there: https://old.reddit.com/r/mathriddles/comments/17kuong/you_roll_a_die_until_you_get_n_1s_in_a_row/k7edj6l/

For me, "enjoying life" means "enjoying good things that happen in life", while everything in-between is neutral at best. Many people seem to put positive value on "in-between" space.

If I try to point out, some people enjoy just the fact of being embodied.

What I think will happen is things keep getting worse for at least a decade. At some point a critical mass of people will know at least one person whose life was ruined by gambling and then we get a (way over the top) backlash.

Gambling bans in general, strong regulation of even non-monetary video game gambling mechanics.

You see rumblings of this among gamers, who got exposed to gamba trash earlier than the general population.

Or we just embrace the darwinism aspect of it and it becomes one more cause of permanent cultural inequality.

150 or 151? I don't have a strong intuition. I'm inclined to trust your 150, but my intuition says that maybe 151 is right because 100+99/2+almost1 rounds up to 151. Would have to think about it.

(By the way, I'm not very good at math. I know high school math plus I took differential equations and linear algebra while studying mechanical engineering. But I don't remember any of it well and don't do engineering now or use math in my work. (I do like forecasting as a hobby and think about statistics and probability in that context a lot.) I wouldn't be able to follow your math in your post without a lot of effort, so I didn't try.)

Re the almost1 and a confusion I noticed when writing my previous comment:

Re my:

E.g. For four 100s: Ctrl+f "100,100,100,100" in your mind. Half the time it will be proceeded by an odd number for length 4, a quarter of the time it will be length 5, etc.

Since 1/2+1/4+1/8...=1, the above would seem to suggest that for four 100s in a row (or two 6s in a row) the expected number of rolls conditional on all even is 5 (or 3). But I saw from your post that it was more like 2.72, not 3, so what is wrong with the suggestion?

It doesn't matter whether you call your multiplier "probability" or "value" if it results in your decision to not care about low-measure branch. The only difference is that probability is supposed to be about knowledge, and Wallace's argument involving arbitrary assumption, not only physics, means it's not probability, but value - there is no reason to value knowledge of your low-measure instances less.

this makes decision theory and probably consequentialist ethics impossible in your framework

It doesn't? Nothing stops you from making decisions in a world where you are constantly splitting. You can try to maximize splits of good experiences or something. It just wouldn't be the same decisions you would make without knowledge of splits, but why new physical knowledge shouldn't change your decisions?

You have very strong intuition. A puzzle I was giving people before was "Round E[number of rolls until 100 6s in a row | all even] to the next integer" and the proof I had in mind for 101 was very close to your second paragraph. And when I friend of mine missed the "in a row" part and got 150, the resolution we came to (after many hours!) was similar to the rest of the argument you gave.

I read part of the paper. That there's a cultural difference north-south about honesty and willingness to break the rules matches my experience on the ground.

I'm not at all saying the experiences of a person in a low-weight world are less valuable than a person in a high-weight world. Just that when you are considering possible futures in a decision-theoretic framework you need to apply the weights (because weight is equivalent to probability). 

Wallace's useful achievement in this context is to show that there exists a set of axioms that makes this work, and this includes branch-indifference.

This is useful because makes clear the way in which the branch-counting approach you're suggesting is in conflict with decision theory. So I don't disagree that you can care about the number of your thin instances, but what I'm saying is in that case you need to accept that this makes decision theory and probably consequentialist ethics impossible in your framework.

My intuition was that B is bigger.

The justification was more or less the following: any time you roll until reaching two $6\text{s}$ in a row, you will have also hit your second 6 at or before then. So regardless what the conditions are, $A$ must be larger than $B$.

This seems obviously wrong. The conditions matter a lot. Without conditions that would be adequate to explain why it takes more rolls to get two 6s in a row than it does to get two 6s, but given the conditions that doesn't explain anything.

The way I think about it is that you are looking at a very long string of digits 1-6 and (for A) selecting the sequences of digits that end with two 6s in a row going backwards until just before you hit an odd number (which is not very far, since half of rolls are odd). If you ctrl+f "66" in your mind you might see that it's "36266" for a length of 4, but probably not. Half of your "66"s will be proceeded by an odd number, making half of the two-6s-in-a-row sequences length 2.

For people that didn't intuit that B is bigger, I wonder if you'd find it more intuitive if you imagine a D100 is used rather than a D6.

While two 100s in a row only happens once in 10,000 times, when they do happen they are almost always part of short sequences like "27,100,100" or "87,62,100,100" rather than "53,100,14,100,100".

On the other hand, when you ctrl+f for a single "100" in your mind and count backwards until you get another 100, you'll almost always encounter an odd number first before encountering another "100" and have to disregard the sequence. But occasionally the 100s will appear close together and by chance there won't be any odd numbers between them. So you might see "9,100,82,62,100" or "13,44,100,82,100" or "99,100,28,100" or "69,12,100,100".

Another way to make it more intuitive might be to imagine that you have to get several 100s in a row / several 100s rather than just two. E.g. For four 100s: Ctrl+f "100,100,100,100" in your mind. Half the time it will be proceeded by an odd number for length 4, a quarter of the time it will be length 5, etc. Now look for all of the times that four 100s appear without there being any odd numbers between them. Some of these will be "100,100,100,100", but far more will be "100,32,100,100,88,100" and similar. And half the time there will be an odd number immediately before, a quarter of the time it will be odd-then-even before, etc.

I have a friend with eidetic imagination who says that for her, there is literally no difference between seeing something and imagining it. Sometimes she's worried about losing track of reality if she were to imagine too much.