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Resolves yes

Very interesting to pull up this chart and the coinbase price chart side-by-side.

If we assume random walk, this chart should be a pure function of BTC price. And it seems to mostly follow that? I have no idea what the actual function is from price to probability; but given the same price twice, you'd think we should have the same probability twice here.

Feels like there should be some way to make code that calculates that function based on the average odds(currentBTCprice) from the odds chart and the price chart; and that code could effectively arbitrage-across-time for mana here... (assuming BTC really is a random walk). Let me know if anyone feels like collaborating on that! It sounds like a lot of work, mainly the hooking-into-manifold-apis and coinbase-apis part, but the math part sounds like fun!

@DannyqnOht It's not that simple. The probability also depends on how much time is left.

@AndrewHebb Good point - assuming random walk, it should be a function of (price, remaining time).

- Does that still sound bot-solvable? (eg, a bot can look at the market & btc price, figure out a best guess for what f(p, t) must be, and bet in real time according f(p,t) to make mana on average?)

- Are there any other considerations that are missing?

@DannyqnOht https://en.wikipedia.org/wiki/Black–Scholes_model

@deagol Are you saying you should be able to use black-scholes to deduce the correct mana price for this market (or similar will-cross-threshold markets, since this is resolved now) from the price of BTC?

The black scholes math is interesting and useful, but I'm not sure.... how any of the assumptions translate here. It assumes no real arbitrage opportunity (which is honestly what I'm looking for). It assumes you can trade these two things (we can't actually trade mana made here for money, so there's no hedging allowed in this setup, just betting). And it assumes European options (but these markets are "will it ever pass this threshold" which is much closer to American options)

Can you spell it out a bit for me? How would you use any of the black scholes math in this scenario, what conclusions would you draw from it, and how would you decide where to spend mana using that math?

@deagol Ok, yeah, so I did lots of reading. Here's my understanding, please let me know where I'm wrong!

Black/Scholes: "If you have all the standard arbitrage mechanisms around, the price of an option on a stock should be based on nothing but the current price and the risk free rate. Here's the arbitrage needed to make that happen, it's kinda like selling the option and buying the stock, but requires high frequency trading because the optionality (may be used, may not be) of a European option makes things kinda complicated." source: https://gregorygundersen.com/blog/2024/09/28/black-scholes/

I think my question here is actually more about the simpler question of brownian motion directly (which black & scholes used in their derivations). In a market without any of the standard arbitrage mechanisms (eg a market with mana to money), it's reasonable to think there's an opportunity here. If you assume brownian motion with drift u on the BTC price, and assume all bettors are doing that too; then the current probability here plus current price in coinbase probably imply a given drift u for the brownian motion. I bet you could make mana if you calculated that u across a bunch of these markets (under 88K; under 80K; over 100K, ...) and arbitraged between the markets on manifold. And I bet there's opportunity there that no one's taken advantage of yet, there seems to be a lot of opportunity for arbitrage on here.

Screw it, now that I've written it out, I think that can just be done by hand in a spreadsheet. Nvm!

I'm so confused why there isn't a way to make real money on this. If we're more than 50% sure which direction the market will go, why doesn't that lead to an immediate profit opportunity? Is it just that the rare chances must include proportionally large outcomes? 70% chance for a loss of 3K and a 7% chance for a gain of 30K, or something?

@DannyqnOht this "chance" will just vary with the price at any given moment, time to expiry, volatility, etc. it's just a model. you can try arbing real money BTC with the real money option prices using a myriad of strategies, long or short or neutral (delta and gamma hedging can get quite complex and kinda idealized) leverage or not, and many do exactly that. BTC premiums tend to be high though. also a 70% chance expiring in a couple weeks is far from being sure which direction it'll go.