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Ok, can someone explain the theory for this market to me now? I know how the probability part works, but for example if the equilibrium price of this market was at X%, how should I be setting my limit orders?

@jatloe My theory is I just keep betting No because I don't think you can mobilize enough people.

Guys can we agree to not trade until Danny freezes the market? Otherwise this just has to resolve N/A and like nobody would like that right

well YES holders would like that but like be a good person

Ok, nope, I'm pulling the escape cord. I can't just sit on this.

Yes holders got unlucky. There were 2 error hints.

I will not say which ones they are.

I don't think this breaks the rules as written for me to say this. Still feels icky. But I feel like this information is kinda necessary at this point so I don't get pitchforked by a bunch of math olympiads.

@DannyqnOht you should not have sent this

@DannyqnOht please freeze the market, we can deliberate how to resolve

@jatloe How do I freeze it? I don't see any buttons for it...

@DannyqnOht just close the market, you can re-open it later

@jatloe Testing.

@DannyqnOht ok now I can explain

@DannyqnOht the statement you just made would have dropped the market probability down to something like 20%

Ok, market frozen.

I think this is actually valid to say. I don't think it breaks the rules of the description to say it. Also it sucks knowing info and not being able to tell anyone.

I couldn't say anything about it before the last hint, because that would give you info on which hints were errors.

But now that all hints are out, I think it's fair game to share.

And yes, it would drop the market. But
- That would give your math olympiads more accurate entry prices
- That is actually ... correct? It's not like keeping the market high would give you better odds of solving. This actually increased the objective chance of a yes resolution, despite decreasing the market odds of it.

I don't like having the market frozen. I'll plan to unfreeze at the turn of the hour (45 min from now) plus a randomly generated number of minutes between 1 and 5, unless more people than the biggest yes holder have good arguments otherwise.

@DannyqnOht no, because if the market wasn't closed I would have noped out of my YES shares and bet NO down to 20%. i dont think the market owner should suddenly reveal information that wasn't previously said was going to be disclosed and would change the market probability so significantly.

@DannyqnOht @Eliza @bens thoughts?

Hmmm, that's a good point. It would have been much better if I had said something like "I will reveal the number of error hints at time ___"

Sorry I didn't think of that. Maybe opening the market at a fixed time can replace that?

@jatloe @DannyqnOht why would you announce this? Once you've set the rules for a market, you should really try not to change it! Announcing un-scheduled extra hints about the market is probably not ideal.

@DannyqnOht btw I am the person who would really really want the market to not be frozen. I could bail out so much of my mana right now if it was not frozen

@DannyqnOht why does this feel icky also? It's not that unlikely! My script thinks there was a 24% chance of 2 or more errors! That's a very reasonable outcome.

Likelihood of Error Counts (How many hints were lies?) Count | Probability | Bar Graph

--------------------------------------------------

0 | 34.9% | #################

1 | 41.5% | ####################

2 | 19.0% | #########

3 | 4.2% | ##

4 | 0.5% |

5 | 0.0% |

@bens yep, the probability was 23.68% ish and I knew this

I don't think I changed the rules, I just interpreted them weirdly. But yeah, it felt kinda bad to do.

I mainly did it because I didn't want people dragging in a bunch of others to the market and making their experience be "We had a good plan and a good execution and we lost." Which is a very bad motivation and makes me untrustworthy as a market manager, but I stand by my call, I didn't want to be awful to a bunch of strangers. If it was just existing betters, I wouldn't have said anything (again, making me an untrustworthy manager - I'm liable to bias things in what I see as a moral direction, and it's hard for bettors to guess what my morals are.).

@DannyqnOht isn't the point of prediction markets that there is risk? If having a good plan and a good execution always won, that would be really untrustworthy.

@DannyqnOht no one would feel bad if this resolved NO lol. It's part of the risk of betting in markets! Everyone had access to the same information already. When you make an unscheduled hint that will shift the market odds by like 50%, you're essentially just rewarding whomever reads the comment first.

@bens This is a very good point and I'm glad jatloe had me freeze the market. I apologize for handling info reveal so poorly.

@jatloe The biggest thing I was scared about was that there wouldn't be enough liquidity to onboard 20 people while having each of them get some share of the EV of the profit. In fact I probably would have toned this down quite a bit if Ben didn't set a second limit order at 60%.

@bens I agree with resolving NO

@jatloe I'm considering setting a public market open time, and then letting it continue at that time. Maybe turn of the hour is a bad call. But what about tomorrow morning at the same time I open the guesses sheet?

I think resolving NO is a valid solution, just hoping for better ones.

@DannyqnOht I don't like this because it would become a "who can buy NO faster at the reopening time" race

@jatloe That is a good point.

There's the question of "what were the odds it would have resolved no if I hadn't said anything".
And "what were the odds it would have resolved no if I had said something and not frozen".

I intentionally haven't run those numbers, but if they're sufficiently low, then maybe just resolving no is actually the closest we can get to the counterfactual worlds.

@DannyqnOht first one: like 0-2%, there's no way I would have bothered recruiting more people once we got to 32 (so the public ads would maybe get like 2-3 more people)

second one: something on the order of 3%, because everyone would have jumped to no and nobody would bother recruiting people

@DannyqnOht I'd recommend resolving to PROB (maybe the probability that 20-ish ppl would have luckily gotten the answer, per simulations, which might be like... 5%? 10%?) or N/A? I like the broad idea of the puzzle though; perhaps just N/A and take lessons learned from this one, make clearer criteria for the next puzzle, and run again?

In general, I think these kinds of things work when ppl have a very clear expectation from the start about what the information they'll be getting will be and when.

@bens although of course I would personally like resolving to something other than NO, I do think that the fairest resolution here is just NO, since this event wouldn't have happened if there were 0 or 1 errors

@jatloe Just to get this written out somewhere:

10 ways to guess 2 of the error days out of 5
3 possible correct hints for each known error day
10 guesses needed if all the mods happen to be correct
5 guesses per player
10 X 3 X 3 X 10 / (5 * numPlayers) is the fraction of the space we search, right? So if it's know there's 2 error hints, and there's 10 players, that's 1/18th the search space?

And if it wasn't known that there were 2 error hints, guesses would probably be consumed on the 0 error and 1 error cases first. How many of those are there....

10 for the 0 error
5 X 3 X 10 for the 1 error.
That's 32 people's worth of guesses.
Which makes me think that if the fact of 2 errors wasn't shared, there's a 0% probability it would have been guessed. Because I doubt anyone would get to the 2-error guesses.

@DannyqnOht read https://manifold.markets/DannyqnOht/will-manifold-solve-my-puzzle-borin#3m4cblbjos9, if you do resolve to a probability I think it would be 1% from the "leftover overflow"

Will Manifold solve my puzzle [boring math edition]

60% chance. I'm not as dedicated as Ben. I'll put 5 days into this. I asked my girlfriend questions to generate a 9 digit number X. I then took the mod of this number by 28007330 to make Y. Your goal is to guess Y. On each day, starting Monday, whenever I get to it that day, I'll check the odds in the market. I'll flip a random number between 1 and 100, and if it's more than half the current odds, I'll give a correct hint. Otherwise, I'll give an incorrect hint. I will not say if the hint is correct or incorrect. (Shout if I miss a day, this is my first time). Hints will be, in order: The number Y mod 13 (Odds 25, so number to beat: 12.5. Hint: 0) The number Y mod 17 (Odds 32, number to beat: 16. Hint: 5) The number Y mod 19 (Odds 39, number to beat: 19.5 Hint: 4) The number Y mod 23 (Odds 37, number to beat: 18.5 Hint: 5) The number Y mod 29 (Odds 58, number to beat: 29 Hint: 28) On Saturday (the day after the last hint), I'll open up the guesses sheet and each person can fill in 5 guesses. You have to have made a trade in the market to add a guess (well, to count as a win). If you mess with the format of the sheet so I can't read it, the market will resolve N/A and we'll all be mad at you. If anyone guesses correctly, this will resolve "yes". Otherwise, "no". Obviously only "yes" holders will guess. No holders, don't be evil. Update 2026-01-25 (PST) (AI summary of creator comment): Error behavior clarification: If there is an error on a hint day, the creator will add 1, subtract 1, or add 2 to the hint (instead of choosing a completely random incorrect hint) This means you will expect to need 3^(num_errors) * 10 guesses if you knew which days had errors Additional hint: The girlfriend's number before the mod by 28M looks "very human-generated" Update 2026-01-26 (PST) (AI summary of creator comment): Timing clarifications: Guesses sheet will open for editing Saturday morning and close Sunday evening by 6:00pm ET. You must have traded by sheet close for the guesses to count! Update 2026-01-30 (PST) (AI summary of creator comment): The creator has confirmed that there were exactly 2 error hints out of the 5 hints given. The creator will not reveal which hints are the errors. This information is provided to help participants understand the puzzle difficulty, but does not change the fundamental resolution criteria (market resolves YES if anyone guesses Y correctly, NO otherwise).

Are you saying that you think you would have recruited over 32 yes bettors to help guess here, counterfactually, so you disagree with the odds?

(aside: That makes me slightly more glad I screwed up. This is bad enough with just 10 yes holders. )

I'd be ok resolving between 0% and 3%, but I kinda want a second opinion on the percentage, @bens what sounds fair to you?

@DannyqnOht Well, there's kind of a Monty Hall situation here, where in worlds where you hadn't announced this... jk

Umm, ya, maybe a 2% resolution or something seems reasonable? It's plausible this market would have gone viral and like 50 ppl would have filled it out I guess?

@DannyqnOht well the thing is that if I didn't get 32 betters, this probability is still bounded below by 0% lol, so it's like easier to think of this probability as P(32 betters)E(number of betters minus 32|32 betters)/180

I'm completely ok with either 1% or 2% lol

Ok, I will plan to resolve at 2%., tomorrow at around 9:30am ET. I'll keep this open to see if anyone has any strong counterarguments - also, everyone feel free to give me 0 stars for this market resolution.

Thank you both for your help with this! Sorry I messed up!