General informations
Current history : 0↓0↑1↓0↑1↓0↓0↑1↑0↑1↓1↓1↑
Next markets :
0 : https://manifold.markets/dionisos/binary-induction-game-v1-if-the-nex-38725abedcf2
1 : https://manifold.markets/dionisos/binary-induction-game-v1-if-the-nex-9a0dc1e418e4
Direct help to discover the pattern
Given I misjudged the difficulty of this game, here is some help
If the last two tokens are XY (where X is a 0/1 token), then on the counterfactual where the players has choosen another 0/1 token for X, the last two token would have been not(X)not(Y).
So if the current history is : 0↓0↑1↓0↑ another correct history could have been : 0↓0↑1↓1↓
The next token (↑ or ↓) in the pattern is determined by only 3 informations :
The lenght of the history
The last token in the history (0 or 1)
The 0/1 token before that.
So, if the history is currently "0↓0↑1↓0↑1", then the next token is determined by :
Lenght = 9
Last token = 1
Previous 0/1 token = 0
Story
Manifolds Markets was doing some market stuffs like a well-behaved prediction market, but suddenly there is a truck that appears out of nowhere at high speed.
Less than two second latter Manifold feel some deep discontinuity inside itself, and the sense that connect it to the meta-physical nature of its universe lose focus, blurs, and regain focus on a completely different set of meta rules :
Game rules
The game takes place in several steps, at each step, the "current history" of the universe grows (exemple : "0↓0↓1↑" → "0↓0↓1↑1↓"), the goal is to find the patterns that this universe follows.
At the beginning of each step, there will be two markets, one for "0", and one for "1", about whether they will be up "↑" or down "↓".
At the end of each step, the market nearer to 50% of these two, will be selected, and the other one will resolve N/A.
The selected market will resolve ↑ or ↓, following an unknown [to the players] deterministic rule (this rule/pattern can take into account the entire history, not just the last outcome).
Then the history of the universe will be updated, and the next step begin.
(Did you except heroic fantasy and magics ? Manifold is a market, not a person)
Parallel to that, if the correct rule/pattern is at more than 90% in this free response markets, for the duration of a step, then this answer is selected, and the game end.
A step end when :
There is more than 2 days since the last step.
There is more than 10 participants in both the "0" and "1" markets. (I can decide to not stricly follow this rule)
I see it, and create the markets for the next step.
Two conditions should be satisfied for the game to end :
There is one option at 90% in this free response markets.
The option describe the correct pattern.
When the game end, this market resolve to the option describing the correct pattern.
Will you help Manifold to better understand its new world ?
The md5sum of the rule is : 6a28abf346c601a5ab24bbafec70acf4
I will not bet on any of these markets.
A possible rule/pattern could be : If there is an odd number of 1 in the current history, it end with ↑, and ↓ otherwise, which could result in something like : 0↓1↑1↓1↑0↑0↑…