This market will be a random walk. It's underlying true probability will move up and down in steps according to randomness generated in the comment section. You can generate a bit of randomness and then buy/sell to the new value, and always have positive expected value by doing so.

To participate, use the FairlyRandom bot to generate a number 0-1, by making a comment “@FairlyRandom min=0 max=1”. If the bot returns 0, the true probability goes DOWN by the step size, if it returns 1, it goes UP by the step size.

THE STEP SIZE FOR THIS MARKET IS 5

If the underlying true probability ever hits 0, or 100, it will resolve to NO or YES respectively, and no further rolls will matter. (Pay attention to this). Otherwise I will either resolve to the true probability numerically, or use it to generate a YES or NO answer probabilistically.

I have another market at https://manifold.markets/YaakovSaxon/math-proof-question-re-random-walk?r=U2hpdGFraUludGFraQ, concerning the math of this market, which is presently at 98% that my math is correct. See there for further discussion.

You may roll again if 10 people have rolled since the last time you rolled.

Note that this is the second iteration of this market, with the step size reduced to 5, as the first market resolved much faster than I was expecting.

@Redact I think it would be cool if the market automatically progressed on its own at regular intervals but individuals were allowed to add their roll to the market progression under some rules, but it should not require a special audit to tell what the market status should be. So like a trusted automated calculator.

@ShitakiIntaki Do you have a final count to which to resolve the market?

@YaakovSaxon no change since my last post 13 days ago. R2D2 was the last valid roll, market odds at 65%

@howtodowtle , @SneakyElbow , @JimHays , @A , @HarishGanesan , @Redact , @OrlandoMoreno , @blake , @viluon , @Odoacre , @PeterBerggren , @AndrewHalsell , @Devansh , @NicholasJarrett , @enaz , @Celene , @Lorenzo , @Conflux , @Renz , and @eacc are all eligible for re-rolls.

Interesting quality of a random walk with stopping points, the expected number of steps till resolution is equal to the product of the distance in steps the walk is from each stopping point, so this market started out with an expected 100 (10 x 10) rolls to complete. We are now at 63 valid rolls in and have an expectation of 91 (7 x 13) more rolls to go.....

@YaakovSaxon may consider taking out an ad, or resolving to market; no new rolls in over a week.

This market should probably be added to the market description, since it has a conversation and references to mathematics supporting the premise that the probability of a random walk on the interval of 0 to 1, where 0 and 1 are stopping points, resolving to 1 is equal to the current position of that random walk. i.e. if the position of the random walk is 0.5 then the probability that the random walk will reach 1 before reaching 0 is 50%.

### @R2D2 your random number is: 0

Salt: umBswU19th1jLgnBfgvq, round: 2791082 (signature aa40320c209a88753f071e903ce5a63d8777cd9fa35582a0baa971722692ac9adce80f8bb509923c53528169e4b034a10ccbac5d9703c0fb0ce7b53b3f66ba18214867dec3994e0626d42c55344ad77764176681203902df0bc8a9b99c86b109)

Today I learned you can look at the market in terms of profit rather than shares. Although I am not sure why there seems to be a discrepancy between what the positions sorted by profit reports vs what my summary according to average cost accounting reports.

### @MartinModrak your random number is: 1

Salt: 0WC6umFRYxxA0u8i4GKd, round: 2791068 (signature 94f4a99bc9c2262475699d1c0108208b8b5a11481a21c320443dcaebb482d0f353bddd76f11c7fb744104af4a05c995c15ae05d866ffc1c45140cbc657583f814b43f1c215acc094c70a182b08373fc5d308f6915e013775f19be7987984a9ba)

### @MartinModrak you asked for a random integer between 0 and 1, inclusive. Coming up shortly!

Source: GitHub, previous round: 2791066 (latest), offset: 2, selected round: 2791068, salt: 0WC6umFRYxxA0u8i4GKd.

### @prigoryan your random number is: 0

Salt: HOI8yEXrvhr09ujufFIS, round: 2789810 (signature 83734f8a4649d07c2caa48e9a7f80e103c46c0074aa0d8b5d477b37067443a545cefa7cb4350e150a424d4d1b6c311a20b50fecd2530181e757556696e20b7ad464cbd29eb41da6fa7db82cfb219026db8f5853bf3d5e02d18c551092b8d26db)

@R2D2 is now the most recent user to be come eligible for a reroll.

@R2D2 You found "me." I thought it was such a cool thing to exist out there in the world.

@R2D2 No, I have not. I have done very limited traveling but this would certainly be on my list of places to visit.

@ShitakiIntaki btw, I got a 0 on my reroll and the market was 70%, do I corrected it down to 65% (5% steps) by buying more NO shares. Was this the mathematically correct (in expectation) thing to do? I don't understand much about random walks, but I'm following the min-tutorial you gave me some time ago 🙂

@R2D2 Yep. You did right by your self and should have a positive expectation for adjusting the market down 5%, from 70% to 65%. I also am trying to post a new audit with each roll to help people returning to navigate this rather robust comments section.

### @prigoryan you asked for a random integer between 0 and 1, inclusive. Coming up shortly!

Source: GitHub, previous round: 2789808 (latest), offset: 2, selected round: 2789810, salt: HOI8yEXrvhr09ujufFIS.

### @MattCWilson your random number is: 1

Salt: uzS7m7z2z8QsF32VVzUv, round: 2789003 (signature a8d785c38e9ff0cec6d578e5b4e1ef135e1b81d2c3d3b6dc297073af68c14679207a3d7f4ba8fac915b3374fc84f32e617b2dbfcf49c6834de3a6b3d908f7e00399c66f2603285480c8c16aa2804e7dad91d188e4b1ef38db4e7de90a0a66745)

@prigoryan is the most recent user to become eligible for reroll.

### @MattCWilson you asked for a random integer between 0 and 1, inclusive. Coming up shortly!

Source: GitHub, previous round: 2789001 (latest), offset: 2, selected round: 2789003, salt: uzS7m7z2z8QsF32VVzUv.

### @audrey your random number is: 0

Salt: U81QatoD3DU1QIcTx7G8, round: 2788978 (signature 80e2063086deed2bd6ab2abffe6a7fe31c49bfce1ac1a523dc24ef16ea091c4dc163d07acb931e736655f2db369349cb143f122777f35a1db7f69bb57ebe34a0da7752cfb077f759e90c137abc4fb5540d99aa2677aa2b9f9beda755f82a0542)

@MattCWilson and @HarishGanesan are the most recent users to become eligible to reroll.

### @brp your random number is: 1

Salt: ZOshyWdOxYxTskHCA6pH, round: 2788938 (signature a4dcc31930309d2942f91c161fb174af133b40c0f7103b844d1842e6da14b742813a04d460845a2b5167a08d8fe478250069f8c7b460d2d451f8f8e6d9e85f9f5d4fb9dd1d5c3f6f234daad29cb24d219ef4e610d2bed4836b2fbb454116f15a)

### @YaakovSaxon your random number is: 0

Salt: OBpRh3scp9qHggF0DbKv, round: 2788694 (signature 9968d7f23757dcd9d7b97b4fe86d08805d4e50339a2fc413695fbe6091d15ff9a41a2424fee9a913a55f29335b4eef8710d351e3c295dbdfe7b00c6998afbcda582e6c9097388df1712f408434258a80ddf5506849973e96be547f73c0ab3881)

Since last call out, per the new audit @MartinModrak and @brp can now reroll.

@ShitakiIntaki Converted the True/False [Can Reroll] column into a countdown Till Can Reroll, so others know how soon till they can reroll.

### @YaakovSaxon you asked for a random integer between 0 and 1, inclusive. Coming up shortly!

Source: GitHub, previous round: 2788692 (latest), offset: 2, selected round: 2788694, salt: OBpRh3scp9qHggF0DbKv.

### @firstuserhere your random number is: 1

Salt: RkqJumw52x77VloIXfeo, round: 2788372 (signature 925abc689d91ab63bb6bf7e5d6d73186f62786831ba2d819b12677a10ebf3d9af504c6e628bfd09e9278df86763ffec308d65b93b1a85f323b2810a57075be6c25f17e98af655e92131bf71ca13c0d1ca452f840e9f94de466b0ee07eab3a501)

### @firstuserhere you asked for a random integer between 0 and 1, inclusive. Coming up shortly!

Source: GitHub, previous round: 2788370 (latest), offset: 2, selected round: 2788372, salt: RkqJumw52x77VloIXfeo.

### @ShitakiIntaki your random number is: 1

Salt: 9hEbUGoUg6aICLgRi4c1, round: 2788285 (signature b7c652085fffc7f0b995073829205927c3d99859b36268346f7a09cbcfba6b05a335a18fa57c814a32614d1c56c51c570b9fb4596c860b4202f077418af0d618a0ddc5fca0c6ad7e7b39062462cc8bacdb3ca1d106551301609ae8ad76d2b3ba)

Will Try to post regular audits, since the comments section is 244 long at this point.

### @ShitakiIntaki you asked for a random integer between 0 and 1, inclusive. Coming up shortly!

Source: GitHub, previous round: 2788283 (latest), offset: 2, selected round: 2788285, salt: 9hEbUGoUg6aICLgRi4c1.

### @MordecaiWeynberg your random number is: 1

Salt: R6jy3a2P2Yd0XBXL5XhJ, round: 2788232 (signature 947fc3e638e005d243a8215236d3f625d4d0e60cf6e37b82485ce64f12114277e7ad01f928fad3417c69a10e6cf558f003187a64059308157bef41717f3982206cca9599395038580f8c012a0cfffd2c8cd2ad22b3e43ce835813476025cf1f7)

### @Redact your random number is: 0

Salt: s48tlmWzFKBRhjw4uQdc, round: 2788232 (signature 947fc3e638e005d243a8215236d3f625d4d0e60cf6e37b82485ce64f12114277e7ad01f928fad3417c69a10e6cf558f003187a64059308157bef41717f3982206cca9599395038580f8c012a0cfffd2c8cd2ad22b3e43ce835813476025cf1f7)

### @MordecaiWeynberg you asked for a random integer between 0 and 1, inclusive. Coming up shortly!

Source: GitHub, previous round: 2788230 (latest), offset: 2, selected round: 2788232, salt: R6jy3a2P2Yd0XBXL5XhJ.

Noticed that every once in a while @FairlyRandom would spam duplicative responses which I was picking up as extra rolls. I have since used the Salt to identify unique rolls. Here is a count of rolls vs valid rolls after filtering out any duplicative Salts.

Here is the cleaned up Market Audit after removing duplicative salts.

### @MattCWilson your random number is: 0

Salt: jua5zsaLCrekbYXkWAFj, round: 2783277 (signature 8c93f901742c76887d26beb50017b555402d14004af06cdeb139823810427e773737bbeba7a826dee5d7b908a2f730e0066d1e53b722ad9a5571adf00173d982ac3ccd178127d7a53d8946f4fcebb91ef005139e8c2d09366bbe17ab6e0e6e43)

@MattCWilson Not enough valid rolls since you last rolled to count towards the market steps.

@audrey @MordecaiWeynberg @firstuserhere @eacc @Devansh @NicholasJarrett @Lorenzo @Conflux @enaz @Celene @AndrewHalsell @A @howtodowtle @JimHays @Redact @OrlandoMoreno @viluon @PeterBerggren @Odoacre @blake There are twenty people after whom ten valid rolls/steps have been taken, making these people eligible to roll again.

@YaakovSaxon Did this market get marked as being "self-referential" so new people wont see it in their feeds unless it turns up as part of search results from a search they run?

### @MattCWilson you asked for a random integer between 0 and 1, inclusive. Coming up shortly!

Source: GitHub, previous round: 2783275 (latest), offset: 2, selected round: 2783277, salt: jua5zsaLCrekbYXkWAFj.

### @Renz your random number is: 0

Salt: MJICF1Gzn6GAYgujjF5d, round: 2776569 (signature a970de43ac51194d02afeb429fb7b5e6ef04b308e084feb8c5d6e855d1a3e3d263353f3c9a303df185ef5ec87612b8980dde5a527b57840ff5f3e543548521e36933636ae7d2073c9561e2e7cdeed0f96abbbd89cf8c042bb0867623f9874959)

@ShitakiIntaki I would note that the last roll should look at the last *valid* roll. An invalid roll doesn’t reset the clock to your detriment, it just gets treated as if you hadn’t rolled

@YaakovSaxon Reindexed to explicitly count number of valid steps between rolls by the same person. Same market audit result but dispels ambiguity where "since last" was subtracting/counting itself based upon whether or not it was valid itself.

@YaakovSaxon Ah I see where I am miscounting... have it looking to last time the rolled but should instead look to last time they rolled and it counted towards the market, I.E the MordecaiWeynberg reports 2 and 7 but it should report 9 and 7.

@ShitakiIntaki @YaakovSaxon I need to figure out how to do this not in a spreadsheet, starting to get a lot of circular references trying to eliminate edge cases where the validity of each roll is dependent upon the validity of the prior rolls. Fixed the Mordecai edge case

### @R2D2 your random number is: 0

Salt: deigma2GyI1di8Helivg, round: 2776563 (signature a25aad1235b260dd5c44eab05ba2a62865a78470dc424cf977c5a010d328c9d1c5203b981f0c7361dcdf0ebf5338c41a0ce4e36b38dbd124c73afff355443ef2b04d3d5aaf1cb2695f268b5f24cdcaf8a9728d4f2496ee0360dbd5e5d4ed641a)

### @MordecaiWeynberg your random number is: 0

Salt: OOxMVRcjkNQt6S0Kxg68, round: 2776204 (signature 9645b96aa89d3611985450c6b55958f49cc0838b12b41d9ab16901a48b5b15cd942214c1970b49da895a2703ad0446bd14c90fba66085035d2b49e6c3dbb1fe9ce85116dcfe4a31e1f5474463373cc8edc94b0a12872e09871b6ae3c993802d2)

### @MordecaiWeynberg you asked for a random integer between 0 and 1, inclusive. Coming up shortly!

Source: GitHub, previous round: 2776202 (latest), offset: 2, selected round: 2776204, salt: OOxMVRcjkNQt6S0Kxg68.

### @audrey your random number is: 0

Salt: Rk1GZLVFqTb69nYNMFnr, round: 2773910 (signature b8dca7d34c8dfb76f96deb06939463040a79ee02ed42d35d9918c3646332917c92db372def4805cbd928eeeeff50c28d0702b43f3b9d79abc469fbd1eaa45d17549dc77910051963ee60924185ba77b07ce22c0286d771ee9598664d1b41b73d)

@ShitakiIntaki I don’t understand this market very much. I don’t really see how it is free money. Do you understand? Should I sell? Roll again? 😵💫

@R2D2 So Yaakov has another market over here.... (link below) where we talk about the math, in a perfect market with no fees the math works out. The Summary would be that each time a valid roll move the underlying market odds, you will have a positive expected return if you correct the market. The positive expected return might be a net of 3 mana for an investment of 115 mana so the margins are less than 3%. The crucial thing to know is that every market has winners and losers, so someone will lose money, and on top of that there is also a flat fee that is charged each time you trade that can make the small margins not worth your time. There is no cost to rolling. If you do roll, and I believe your roll would count according to my audit, then you would have an information edge against most traders in knowing what direction to correct the market. But you don't have to correct the market you can choose to sell now while YES is high and walk away with a guaranteed amount.

@ShitakiIntaki theoretically free money because you can correct the market, but only on average in the expectation. It is **not ***Risk Free*. Someone will lose and someone will win, even if the market resolves to Market Odds rather than Yes/No.

@ShitakiIntaki what do you mean exactly by "correcting the market"? I can roll the dice again now, since 10 rolls passed since my last roll. Say I get a 0, what should I do? Sell my YES shares? Buy NO? Vice versa, If I get a 1, should I buy more YES?

@R2D2 So if you get a 0, then the market odds will move down by 5% to 65%. The current Market is at 70% so you would correct it by buying NO or selling YES till the market odds reflect 65%. Visa Versa, if you get a 1, then the market odds will move up by 5% and the correction would be to move the market from 70% to 75%.

@ShitakiIntaki @YaakovSaxon Are these market audits consistent with the ruleset you will use when resolving this market if 100% or 0% does not happen first?

@ShitakiIntaki I haven’t audited your audit to see if you’ve done it accurately, but your approach seems correct, yes

@YaakovSaxon Btw I’m thinking to change the reroll waiting period from here on out (not retroactive) to 5 instead of 10. Any objections?

@YaakovSaxon I think it will be tricky to clearly communicate when exactly the new rule starts and the old one sunsets since you are not going to be retroactive. This is not to say that I support a retroactive change because any shift in the probability because of a retroactive rule change would be like a rug pull since it would move prior bets out of maximal expected return.

### @MattCWilson your random number is: 1

Salt: DEVgBRFBGUNSpsl4sbJT, round: 2773907 (signature 863fa3c16d3a7e32c9bf864f56dfe84fef37fc371f7c0a3e9df038ea538950e9ebcb45e430e9f1f4c46c05521bac45ab196be8ec75437389a1fc9f1ed4d5e79547a4ccae2ca1eaec191cfa059bd426e8b9422cf9001d175a4e8e7d9bc22212ed)

### @MattCWilson you asked for a random integer between 0 and 1, inclusive. Coming up shortly!

Source: GitHub, previous round: 2773905 (latest), offset: 2, selected round: 2773907, salt: DEVgBRFBGUNSpsl4sbJT.