How biased is this coin?
Basic
25
1.8k
9999
49%
chance

This market resolves to the value of `p(heads)` (the probability of flipping heads) for a biased coin. The probability will be multiplied by 100 to express it as a percentage.

The first 3 flips are shown. I will flip the coin again once per day and update the results. If I forget to update the description, please remind me to do so.

Anyone who has bet at least 1000 mana on this question can DM me or publicly comment asking for the market to be resolved.

`p(heads)` was sampled uniformly randomly between 0 and 1. The salted sha256 hash of `p(heads)` is: `5c0d2da2236bcccb8c47653ec4860a113266e65d95c9d341b4eea720e5b06525`.

When the market resolves, I will publish:

- The plaintext message used to generate the hash

- The Python code used to generate the model so the results can be independently verified

``````Start: 2024-08-25
Timestamp: 2024-09-06
Elapsed: 12
Samples: 15

Flip  Date        Res  p_hat
1    2024-08-25  T    0.00
2    2024-08-25  H    0.50
3    2024-08-25  H    0.67
4    2024-08-26  T    0.50
5    2024-08-27  H    0.60
6    2024-08-28  T    0.50
7    2024-08-29  T    0.43
8    2024-08-30  H    0.50
9    2024-08-31  T    0.44
10    2024-09-01  T    0.40
11    2024-09-02  H    0.45
12    2024-09-03  T    0.42
13    2024-09-04  T    0.38
14    2024-09-05  H    0.43
15    2024-09-06  H    0.47``````

Get Ṁ1,000 play money

## Related questions

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15th flip is out

9th flip is out

7th flip is out

The rules say that a new flip will be published for every `log2(participants)`. However, I think this function grows too slowly relative to the general activity on Manifold. My bad, I'm new around here.

To encourage more participation in this market, I would like to propose modifying the rules to publish a new flip for every integer `sqrt(volume)`. For example, the volume is currently 911M, so `sqrt(911) = 30` flips, and the 31st flip would occur when the volume hits 961M. Here's a graph showing the volume required for each flip under this proposal:

What do people think? If there is pushback, that's fine, I can propose a new question at some point with this modified mechanic.

I also thought log2 is a bit low, I would rather ride this out until the end (>>12 flips). But publishing 24 flips now at once is a bit too much. You could publish the 7th flip at 961, making it flips=sqrt(volume)-24.

On second guess, sqrt might be a bit too fast, since the new volume required for the next flip is always 2*flips+1. And since we get new information from every flip, there might always be a reason to instantly increase volume by like 100, so we will get ~50 flips practically all at once.

Also basing the sampling rate on trading volume makes this open to attack via wash trading.

Yeah making bot accounts is also not that hard. We should not overthink how people can „manipulate“ the data release schedule

Perhaps it's also worth incorporating a time component (Math.floor(daysSinceCreation) or Math.floor(weeksSinceCreation)), so that the market doesn't completely grind to a halt.

In any case I'm happy for you to modify the rules for publishing new flips as you see fit.

I would also be fine with just one flip per day. Your idea to couple this to participation seems to have the only purpose of encouraging "wash trading" or sharing or botting

I like that idea. It’s resistant to attack and is likely to keep the market interesting. Also the number of flips that have been released so far isn’t too different to what would’ve been released under one flip per day.

I've updated the rules and Python script used to generate the results.

The 6th flip has been published: `p_hat = 0.50`

@biased, would you mind leaving a comment when you add another coin flip to notify us?

Good idea. Will do

How did you choose p? Uniformly random from 0 to 1?

Yep

bought Ṁ1 NO

this is a really fun idea, hope more people bet on this market