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Did you guys have fun? What should we do next week

@Ernie I enjoyed myself, maybe you could do something with mahjong statistics: https://nodocchi.moe/tenhoulog/gradechanges.html

@Ernie When only one digit remained, I tried running a basic arbitrage against the other market by assuming it's just IID, and finding that the probability implied by one market is different from the other. Then I just spent 100 mana to bring them closer (I could spend more but I wasn't sure what the Kelly criterion says in this case).

As luck has it I got both right.

Will every digit 0-9 appear in the S&P 500 closing price for 10 days from Oct 2 - Oct 13?

Resolved NO. We only care about the integer part cutting off any fraction without rounding.. We are only referring to the closing price. This is for a timespan of 10 days. If there is a holiday or other day without a unique closing price in the interval due to the market not having been open, we will extend the deadline to get another day until there are 10 days included. If after the week, from within the ten closing prices, every decimal digit appears at least once, this resolves YES. Otherwise NO. It can resolve early. Example prices: day 1: closes at 127.45 -> 1,2,7 seen day 2: closes at 139.9907 -> 1,2,3,7,9 seen Etc If all seen by the end, YES, otherwise NO

46% of three random two-digit numbers containing a "1".

@brp

@brp Agreed that in 3 days it's about 50/50 to get a 1, provided the tens digits is actually truly random. Voting NO because EV is higher due to stacked YESs

What should we do after this market fails? I was wondering if the market can hit each number twice... or something similar. I want something where the rational price adjusts every day, but it's very hard to mathematically simulate it.

So you guys think this is going to happen, eh. Care to bet?

@Ernie I would if the prob was lower, like below 50% 😅

I've run simulations and it's amazingly hard to actually do this.

It looks like the first two digits are fixed between 42 and 46, so it is unlikely we get a 1 or 7 in the first two digits. In a totally random generation of eight two-digit numbers, there is ~66% chance of getting both a 1 and a 7. This market is way overvalued.

1 - 10/02 - 4228 => {2, 4, 8}

2 - 10/03 - 4229 => {2, 4, 8, 9}

3 - 10/04 - 4363 => {2, 3, 4, 6, 8, 9}

4 - 10/05 - 4258 => {2, 3, 4, 5, 6, 8, 9}

5 - 10/06 - 4308 => {0, 2, 3, 4, 5, 6, 8, 9}

6 - 10/09 - 4335 => {0, 2, 3, 4, 5, 6, 8, 9}

7 - 10/10 - 4358 => {0, 2, 3, 4, 5, 6, 8, 9}

Remaining: {1, 7}

No way we can miss now... right? right guys? I've bet it up for your longshot pleasure.

@Ernie put up a limit for NO at 92% until Sunday evening

@wylderai Hmm... my calculations seem to have been slightly off

okay, 5 days done. We have had:

4228 => {2, 4, 8}

4229 => {2, 4, 8, 9}

4363 => {2, 3, 4, 6, 8, 9}

4258 => {2, 3, 4, 5, 6, 8, 9}

4308 => {0, 2, 3, 4, 5, 6, 8, 9}

and so we just need {1, 7}

What's the point of this market?

@JonasVollmer to test whether people will use naive simulations to predict outcomes or whether deeper ones involving volatility or live price monitoring will be used.

If I'm doing the math right the expected number of days, assuming 42xx is fixed and the x's are independently uniformly random, is 13.5 days. If they are only partially random in such a way that the two x's are effectively one random digit, then it would be 27 days. Now that a day has passed and we only got one number we expect it to take 13 more days (or 26 more days for partially random). I haven't worked out the actual probability that it will take 14 or more days but its feeling 50/50ish to me given the two x's are not really independently uniform but probably closer to that than one random digit.

@peterpumpkin Interesting. There is a history of how volatile the market is over time, and by season, etc. Also, obviously 42** is not fixed. We're much closer to 43 than 41

@StrayClimb I went ahead and back tested it for the last two years and got success 71% of the time. Haven't looked at how much volatility has changed but this year vs last year gives 69% vs 78%. Maybe tomorrow I'll try to figure out how to back test with partial results.

day 1: 4288, the worst, but nearly so. The only worse outcomes would have been 4222, 4224, 4242, 4244 assuming that 42* is basically fixed.

We are at {2, 4, 8}

We need {0, 1, 3, 5, 6, 7, 9}

As market owner, I give permission for gentle, kind, humorous trash talk between the YES and NO sides here.