How many points are needed to distinguish a human-generated point set from a random one (>95% confidence)?

For context, see the following market, henceforth called the Main Market: https://manifold.markets/Loppukilpailija/which-of-these-random-data-points-i

When looking at the market after its resolution, what will I think is the amount of points Manifolders needed to get the correct answer right with >95% probability?

Details

Note that this is not quite the same when the Main Market first hits 5% or 95%, in that short spikes, market manipulations etc. do not count for the resolution.

If the Main Market visits >95% but later marketers become uncertain and the probability comes down, this will not count for "getting the correct answer right with >95% probability".

As I'm not particularly interested in precisely specifying what counts for market manipulation and don't want to encourage edge case attacks, I will leave the description in its above vague form. I might resolve probabilistically in case it's really on a boundary, but again, this market will resolve based on my sole judgement.

If we hit 100 points, I'll reserve the right to give people new information to solve the problem in case the market isn't confident by then. If this happens, this market resolves to "100 won't suffice (without hints)".

Note: the answer is already guaranteed to be over 40. (There was another market earlier on: https://manifold.markets/Loppukilpailija/how-many-points-are-needed-to-disti)

I won't trade on this market (nor the Main Market) and will not attempt to manipulate it in any way.

Which of these "random" data points is human-generated?

50% chance. Short description In the image below, there are two sets of points, green and red. One of them is "random" while another one has been produced by me via clicking points into the square. Market resolves to YES if the green one has been produced by me and NO otherwise. More points will be gradually revealed over time. Currently revealed: 1 point [image]Details One of the point sets has been produced by sampling from a uniform distribution over a square. The length of this square is strictly less than the bounding box in the square above. Call this the Hidden Square. I won't give you the exact length of the Hidden Square. Another of these point sets has been produced by sampling from me. Some details of the data generation process: The points were generated by clicking a location in a UI interface on a mousepad. I generated 100 points in roughly 90 seconds. I have practiced. If a point landed outside of the Hidden Square, I discarded that point and generated a new one. I have applied one or several entropy-increasing transformations to these points. To elaborate on the last point, here is a hypothetical example of such a transformation: "Given a point, round its x-coordinate to the nearest multiple of 10, and then add a uniformly random integer between 0-9 to it." Intuitively, this makes the set of points "more random", i.e. harder to distinguish from the "actually random set". I won't tell which transformations I've used. Schedule I aim to reveal a new point at times of form XY:00 and XY:30, assuming I am awake. Other Here is a market on how many points it will take for traders to figure out the answer: TODO The data The data in a more convenient form. The bounding box in the image has corners at (100, 100) and (500, 500). GREEN: 226 280 RED: 285 229

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