After this market closes, I will calculate the time-weighted arithmetic mean of the log odds of the market, that is, of ln(p/(1-p)), where p is the market's probability. I will use the exact probabilities, not the rounded ones displayed by Manifold.
This is like "The Market", except that it puts higher weight on extreme probabilities, with the weight being proportional to how difficult it is to hold the market at that probability (in terms of the relative price of YES and NO shares). Therefore, it makes it "worth it" to hold the market at such extreme probabilities.
🏅 Top traders
# | Name | Total profit |
---|---|---|
1 | Ṁ411 | |
2 | Ṁ285 | |
3 | Ṁ89 | |
4 | Ṁ4 | |
5 | Ṁ2 |
current average: 0.943332693752979
as a probability: 0.7197723542040516
Future average required for tie: -1.0253354498229128
as a probability: 0.2639894233452379
@levifinkelstein I think it should go into pseudo-random closing to prevent sniping, then resolve when a dogecoin block gets mined with a hashtag ending with “zz”
current average: 0.5989925388753334
as a probability: 0.6454257811891465
Future average required for tie: -0.23698380452324022
as a probability: 0.441029778027362
@deagol The market has already gone past both of those points but for such a short time that I don't think it affected the average by much (plus, it spiked in both directions, so they partially cancel each other out). If the whole average went past either of those points, I imagine it would be pretty hard for the other team to recover, though it might actually be slightly easier, given that they can in theory push the odds high/low enough to completely negate the other team's advantage in an arbitrarily small amount of time.
@JosephNoonan yea I’m responsible for both those spikes, just wanted to see the effect on the avg (but risky to hold it longer than a few seconds)
I think people here have a YES bias. Turns out the avg of this and the geometric mean (in log form) is neutral at 1/ϕ=ϕ-1 which I like, so that’s where I’ve tried to set it. Makes perfect sense! :)
@JosephNoonan c’mon it’s the golden ratio it must mean something! like, the pyramids and sunflowers!
(I’m just messin’ around)
@JosephNoonan people will be subconsciously attracted to this magical ratio, and NO bettors will have a hard time fighting the power of ancient pyramids, the Parthenon, and Fibonacci’s lustful rabbits. You’ll see!
@deagol so Levina @levifinkelstein you seem averse to that magical mirrored-digits one. Ok fine, you prefer The Answer then?
This is equivalent to "Will the geometric mean of the odds of this market be greater than 1?" That makes it a "proper" geometric mean market, as opposed to this one (https://manifold.markets/JosephNoonan/will-the-geometric-mean-of-this-mar), since the geometric mean is actually the proper mean to use for odds, whereas the arithmetic mean is the proper mean for probabilities.