Vanilla_cabs

Karma: 723

Vanilla_cabs 4 May 2026 19:15 UTC
1 point
0
in reply to: justinpombrio’s comment on: Just Use Bayes: Sleeping Beauty and Monty Hall
I went to check Adam Elga’s paper. It’s very short, only 5 pages written with a big font. He does ask
When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads?
But he doesn’t mean that you (the person experimented upon) know that it’s your first awakening. Rather, it’s a way to single out Monday’s awakening for the sake of the reader. It’s obvious later in the paper:
If (upon first awakening) you were to learn that the toss outcome is Tails, that would amount to your learning that you are in either T1 or T2.
So the 2 versions of the problem on wikipedia are consistent. Still, if I was confused by the formulation of the first, I bet I’m not the only one.

Vanilla_cabs 4 May 2026 0:06 UTC
2 points
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in reply to: Steff’s comment on: Just Use Bayes: Sleeping Beauty and Monty Hall
I took a look at your table, and I have to say, it was a great variant. It took me a while to de-confuse my thoughts about it, and made me realize I wasn’t as comfortable with the SB problem as I thought.
Initially I was a bit uncertain what you meant by “round”, whether it was a wake-up event of a full iteration of the experiment. After rereading a few times, I became more certain that it was the latter.
So, you gain $30 if the coin lands heads and $6 + $6 = $12 if it lands tails. So your expectation of gain per iteration of the experiment is ¹⁄₂ * $30 + ¹⁄₂ * $12 = $21
There are 3 equally likely wake-up events, so the expectation of gain per wake-up event is ¹⁄₃ * $30 + ¹⁄₃ * $6 + ¹⁄₃ * $6 = $14
We can notice that there are on average 1.5 wake-up events per iteration, and $14 * 1.5 = $21, so that checks out.
Now, let’s say I experience a wake-up event. I believe that there is ¹⁄₃ chance that the coin landed heads. You think that my calculation for the expected gain per iteration will be ¹⁄₃ * $30 + ²⁄₃ * $6 = $14
However, I reason: if the coin landed tails, I won’t gain $6, I will gain $6 * 2, once for Monday and once for Tuesday. So my expected gain per iteration is ¹⁄₃ * $30 + ²⁄₃ * $6 * 2 = $18
That’s the point where I was confused. What did that $18 mean? What actually helped me figure it out was the betting scheme that you added in your post.
Sleeping Beauty is put to sleep like normal with only the usual information supplied to her about the original SB problem. When she awakes, there is a surprise message left for her:
You may agree to play the following game: If the coin had flipped Heads, your bank account will receive $30 right now. If the coin had flipped Tails, your bank account will receive $6 right now. However, once this round of experiment is over and you awake, you will pay $18 for having played this game. (If you are inconsistent between wakings about whether you agree to play the game, the game is considered defunct and all bank transfers will be reverted.)
This betting scheme is a based on a version of the SB problem where the Monday guess and the Tuesday guess are counted as a single one. So, Tuesday is unnecessary, so (see previous comment) it boils down to the trivial prediction of the result of a fair coin toss. $21 - $18 = $3 gain expectation.
Next I tried a few variations:
- if the bets are per wake-up (SB can bet once on Monday and another time on Tuesday), but SB is only paid for her current situation (if she bets on Monday she gains $6 and pay $18, same for Tuesday), then her gain expectation is 1/3($30 - $$6 - $18) = -$4. In other words, it’s $14 (average gain expectation per wake-up event) - $18 (cost to bet per wake-up event).
- if the bets are per wake-up, but SB is paid for both Monday and Tuesday when she bets on either Monday or Tuesday, then her gain expectation is 1/3($30 - $$12 - $18) = $0. So that’s what the $18 found with the thirder calculation meant: it’s the gain expectation, over the whole iteration, but knowing that she’s in a wake-up event. In hindsight, I should have guessed, because it naturally corresponds to the formulations where the thirder answer is correct. It is not meaningless: if you repeat the experiment a large number of times, and then tag each wake-up event with the profit that SB made during the iteration that included that event, then the average of tags will be $18. In other words, when SB’s Monday and Tuesday answers are not conflated in a single one, it does answer the question (to SB during a wake-up event): how much money do you expect to gain during this iteration? It’s not intuitive, but it checks out.
So, cool variation, but ultimately each interpretation finds the result that it expected.

Vanilla_cabs 2 May 2026 2:34 UTC
2 points
−1
in reply to: Steff’s comment on: Just Use Bayes: Sleeping Beauty and Monty Hall
I have read your blog post. You are aware of the traditional arguments for both sides. You also agree that halfers and thirders answer slightly different questions.
If you want to maximize the number of times you answer correctly, go Thirder.
If you want to maximize the number of flips you guess correctly, go Halver.
You even say yourself that the halfers answer a version of the problem where Tuesday doesn’t matter:
To test Beauty’s accuracy at guessing coin flips, we should see what she says for every Heads, and see what she says for every Tails. It doesn’t make sense to ask her the same question again for every Tails waking, because [...] we already know her answer.
And since Tuesday doesn’t matter, the whole protocol (sleeping, waking up, the amnesia) is unnecessary: it comes down to guessing the result of a fair coin toss. Which is my point: halfers answer a trivial version of the problem. Same for your “unfair coin” variant.
I’ll use what I read from you post to speculate a little, so feel free to correct me. If I had to guess, I think our disagreement might come from 2 points:
- the version of the SB problem that you favor is Adam Elga’s, which asks “When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads?” Which indeed has ¹⁄₂ as its unique answer, but is trivial.
- maybe you view the fair coin has having an intrinsic ¹⁄₂ chance of landing heads. I view that all probabilities are in a person’s head (nothing original, I just absorbed the standard Bayesian view as taught in the Sequences on LW, see https://www.lesswrong.com/posts/f6ZLxEWaankRZ2Crv/probability-is-in-the-mind for example). A probability expresses a state of knowledge at a given moment, not an intrinsic property of a physical object.
You said it yourself in your blog post when examining the thirder version:
The questions ask about degrees of belief.
I am guessing that to you, it’s an exception. To me, there is nothing else: all probabilities are degrees of belief.
I discovered the SB problem through the version deemed canonical by wikipedia, which is different from Elga’s:
Any time Sleeping Beauty is awakened and interviewed she will not be able to tell which day it is or whether she has been awakened before. During the interview Sleeping Beauty is asked: “What is your credence now for the proposition that the coin landed heads?”
In that version, each day is treated equally.
And to that version, my answer is: when SB wakes up, the coin has a ¹⁄₃ chance to have landed up heads. You can verify it simply (and you did in your post) by remarking that if you iterate the experiment a large number of times, ¹⁄₃ of the wake-up events happen after a heads toss.
I might be unfair, but I have noticed that, faced with such a version that does not trivially reduce to a coin toss, you and other halfers make this weird dance where you say that SB (waking up) ought to believe that the coin has a ¹⁄₃ chance to have come up heads, but really, really, in the real world the coin has a ¹⁄₂ chance to have come up heads. As if the point of forming beliefs wasn’t to accurately model the real world.
Adding a betting structure, at best, doesn’t change anything (at worst it can give wrong intuitions): the reason why betting ¹⁄₃ is the best (under a well-formed betting scheme) is because it is the actual probability.
You already know a lot about the arguments of the thirders. This here is just my point of view, but hopefully, it helps fill some of the gaps.

Vanilla_cabs 1 May 2026 18:49 UTC
2 points
0
in reply to: justinpombrio’s comment on: Just Use Bayes: Sleeping Beauty and Monty Hall
I agree with your point that the answer depends on the exact formulation of the question. But I think that the two questions that you submitted don’t work.
First, there’s no difference between them: the degree I ought believe that my guess will be correct if I guess Heads is the same as the degree I ought believe that the outcome of the toss is Heads (implied: knowing that I am in a wake-up event).
Second, if you preface your question with “when you are first awakened”, then the answer will always be ¹⁄₂ whatever comes next. The reason is that you ask to consider only Monday, and in that case the existence of Tuesday is irrelevant so it’s just Monday^heads VS Monday^tails.
It is hard finding a formulation that unambiguously yields ¹⁄₂ as an answer without being equally trivial. The reason is that the answer is always ¹⁄₃ as long as you consider the context of being in a wake-up event and take every answer into account separately. If you somehow group the answers into a single one or ignore all answers but one (by asking “when you are first awakened”, or by discarding all answers except one on a random day, etc.) then you get ¹⁄₂, but again trivially, making the existence of Tuesday and the induced amnesia completely pointless.

Vanilla_cabs 27 Apr 2026 4:13 UTC
1 point
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on: Primitive Perspectives and Sleeping Beauty
In the fission experiment, how do you know in advance that you will experience about ¹⁄₂ heads and ¹⁄₂ tails, if you have no method of determining which of the resulting clones you will be? After all, on average a random clone will have experienced ¹⁄₃ heads and ²⁄₃ tails, so you seem to know that you will be more likely to be in a subpart of all clones that experiences heads more often than average.

Vanilla_cabs 26 Apr 2026 21:04 UTC
1 point
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in reply to: dadadarren’s comment on: Anthropical Motte and Bailey in two versions of Sleeping Beauty
Here is a model that might interest halfers. You participate in this experiment: the experimenter tosses a fair coin, if Heads nothing happens, you sleep through the night uneventfully. If Tails they will split you in the middle into two halves, completing each half by cloning the missing part onto it. The procedure is accurate enough that the memory is preserved in both copies. Imagine yourself waking up the next morning: you can’t tell if anything happened to you, if either of your halves is the same physical piece yesterday, or if there is another physical copy in another room. But regardless, you can participate in the same experiment again. The same thing happens when you find yourself waking up the next day. and so on.....As this continues, you will count about an equal number of Heads and Tails in the experiments you have subjective experiences of...
Counting subjective experience does not necessarily lead to Thirderism.
Does your experiment really make a difference with the incubator experiment? I still think you will subjectively count witnessing about twice as many tails than heads. Say you run your experiment for a month, forcing all copies to undergo the coin toss and split in case of tails every day. Then at the end of the month you sample one copy at random. Well I think that copy will report seeing about twice as many tails than heads.
Intuitively, you’re more likely to end up being a copy who has seen more tails than heads. And I think that if you count total tails:total heads (totaled over all the clones), you’ll get around 2:1.
Just to check, I ran the following code that returns a ratio of total tails, ran it 20 times and it usually returned something between 0.6 and 0.7.
def experiment_day(clone):
tails = random.random() < 0.5
if tails:
return [clone + [“tails”], clone + [“tails”]]
else:
return [clone + [“heads”]]
def run_experiment(nb_days):
clone_pool = [[]]
for i in range(nb_days):
new_clone_pool = []
for a_clone in clone_pool:
new_clone_pool += experiment_day(a_clone)
clone_pool = new_clone_pool
return clone_pool
days = 30
final_clone_pool = run_experiment(days)
nb_tails = 0
nb_heads = 0
for a_clone in final_clone_pool:
nb_tails += a_clone.count(“tails”)
nb_heads += a_clone.count(“heads”)
print(“Proportion of tails %r” %(nb_tails/(nb_tails+nb_heads)))
Edit: formatting.

Vanilla_cabs 25 Apr 2026 21:30 UTC
1 point
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on: Anthropical Paradoxes are Paradoxes of Probability Theory
I didn’t fully understand OP’s argument, but I used a different approach that feels simpler and more intuitive to me.
First, I agree that there is no paradox: if, upon waking up in a green room, you are offered to bet $1:$1 on whether the coin came “heads”, then you should take the bet: after pooling your gains and losses, you and your clones will have gained (1/2 * 18 * 1$) - (1/2* 2 * $1) = $8. There is no paradox with this bet.
So what’s different in Eliezer’s bet? That a single bet is made for the entirety of the clones who wake up in a green room. When the coin comes “heads”, there might be 18 clones in green rooms, but there’s not 18 bets, only a single one.
To check my intuition, I kept Eliezer’s version, but simplified the bet structure: if you and your other clones in green rooms unanimously agree, I will give $1 to your collective of clones if the coin came “heads” and take $1 if it came “tails”. Well then it’s a fair bet, the expected value is (1/2 * $1) - (1/2 * $1) = $0.
The way I see it, since all clones will behave the same way, it is no different from asking a single one chosen at random among green rooms to decide.
Imagine the following variant: after waking up the clones, I pick one at random among those who are in a green room, and I offer that one to decide whether to pay all clones in green rooms $1 and take $3 from all clones in red rooms. I don’t contact any other clone.
Well now the gain in probability mass from waking up in a green room is exactly counterbalanced by the loss of probability mass of being chosen: you have 9 times more green rooms in the “heads” case than in the “tails” case, but a clone in a green room is 9 times less likely to be picked in the “heads” case than in the “tails” case. Accepting the bet in this variant gives the same general utility as in Eliezer’s.

Vanilla_cabs 21 Sep 2025 14:01 UTC
22 points
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on: The Company Man
Houellebecq visits Silicon Valley.

Vanilla_cabs 4 Jun 2024 12:00 UTC
4 points
1
in reply to: Eli Tyre’s comment on: Cheap food causes cooperative ethics
I’m not an expert, but assuming that by revolution you mean something close to “an attempt to change government through non-legal means”, then I agree with your points, but I’ll also note that revolt and revolution only partially overlap. Revolts are typically less organised and with more modest goals than a government overthrow. They are also mostly initiated and fueled by the resentment and desperation of a lower class.
My tentative model is “Starving peasants revolt. Kings don’t like revolts.” Not “Starving peasants lead successful revolutions.”
To take a modern day example that I have experience with, the yellow vest movement in France was a revolt from the working poor outside big cities because the rise in the gas price made their life impossible in a context where they needed cars to work and purchase essential goods. They were leaderless and actually opposed attempts at vertical organisation. In their early stages, they would have been content with gas prices returning to their previous levels. Nonetheless, they were a thorn in the side of the government, and were even a threat to it at some point.

Vanilla_cabs 7 Sep 2023 20:12 UTC
2 points
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in reply to: Said Achmiz’s comment on: Find Hot French Food Near Me: A Follow-up
Yes, it seems I read too fast.

Vanilla_cabs 7 Sep 2023 8:57 UTC
1 point
−1
in reply to: Said Achmiz’s comment on: Find Hot French Food Near Me: A Follow-up
It seems to be of French origin. The name is French and the French cuisine adopted first. The main hypothesis for its apparition is that Richelieu’s cook invented it out of lack of alternative ingredients while occupying the city of Mahon in Spain. Source: same as you.

Vanilla_cabs 7 Sep 2023 8:48 UTC
2 points
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in reply to: Beckeck’s comment on: Find Hot French Food Near Me: A Follow-up
Chef’ just means ‘chief’ in french (like the military rank or the man in charge) and comes from the brigade system (https://en.wikipedia.org/wiki/Brigade_de_cuisine)
In addition, in the context of cooking, chef means “cook”, and it’s common to call the cook “chef”, even if it’s your friend who’s making a barbecue. It has positive connotations, implying that the cook is skilled.

Vanilla_cabs 5 Sep 2023 21:11 UTC
2 points
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in reply to: exmateriae’s comment on: Who Has the Best Food?
That could also explain why French bakeries, with their staple and iconic baguette and croissant, seem to be faring better in my experience.

Vanilla_cabs 4 Jan 2023 13:27 UTC
1 point
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in reply to: Gordon Seidoh Worley’s comment on: Opportunity Cost Blackmail
I can’t help but notice that if for you “nothing else could have happened than what happened”, then your definition of “could have happened” is so narrow as to become trivial.

Rather, I think that by “X could have happened in situation Y”, the laymen mean something like: even with the knowledge of hindsight, in a situation that looks identical to situation Y for the parameters that matter, I could not exclude X happening”.

Vanilla_cabs 9 Oct 2022 18:05 UTC
2 points
1
in reply to: Emrik’s comment on: The Teacup Test
I was just curious and wanted to give you the occasion to expand your viewpoint. I didn’t downvote your comment btw.

Vanilla_cabs 8 Oct 2022 18:40 UTC
3 points
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in reply to: Emrik’s comment on: The Teacup Test
In what ways?

Vanilla_cabs 30 Sep 2022 9:56 UTC
3 points
1
in reply to: Alex Beyman’s comment on: Triangle Opportunity

My initial reaction to their arrival was “now this is dumb”. It just felt too different from the rest, and too unlikely to be taken seriously. But in hindsight, the suddenness and unlikelihood of their arrival work well with the final twist. It’s a nice dark comedic ending, and it puts the story in a larger perspective.

Vanilla_cabs 15 Sep 2022 14:50 UTC
2 points
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in reply to: benjamincosman’s comment on: Why Do People Think Humans Are Stupid?
I think the bigger difference between humans and chimps is the high prosocial-ness of humans. this is what allowed humans to evolve complex cultures that now bear a large part of our knowledge and intuitions. And the lack of that prosocial-ness is the biggest obstacle to teaching chimps math.

Vanilla_cabs 31 Aug 2022 18:32 UTC
4 points
3
in reply to: Viliam’s comment on: AI Box Experiment: Are people still interested?
I think I already replied to this when I wrote:
I think all the methods that aim at forcing the Gatekeeper to disconnect are against the spirit of the experiment.
I just don’t see how, in a real life situation, disconnecting would equate to freeing the AI. The rule is artificially added to prevent cheap strategies from the Gatekeeper. In return, there’s nothing wrong to adding rules to prevent cheap strategies from the AI.

Vanilla_cabs 27 Aug 2022 13:54 UTC
1 point
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in reply to: Renan Cunha’s comment on: Is population collapse due to low birth rates a problem?
But econ growth does not necessarily mean better lives on average if there are also more humans to feed and shelter. In the current context, if you want more ideas, you’d have a better ROI by investing in education.