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
```

## Related questions

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.

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.