No firm methodology at this time. I won't bet until / unless there is one; it might be kinda vibesy.
Buckets are left inclusive, right exclusive, so a price of exactly 160 M/$ resolves to the 160-200 bucket. If there's uncertainty I will default to averaging out and taking the central estimate as best I can.
I will consider things like:
Mana purchase price available in the store, both current and recent sales
Apparent mana purchase patterns (did a sale increase sales?)
Cost of features available for either dollars or mana (for example, if you can buy a subscription with either currency)
Implied exchange rate from charity giveaways
The above list is not intended to be exhaustive.
Some recent reference points:
Black friday sale had M120000/$750 available, for a rate of M160/$. This didn't seem to generate a huge sales spike.
Charity currently lets you buy tickets at 254/M100, with a pool of 2.9e6 sold and $1000 for the giveaway. So the current implied price is M1153/$.
People are also trading
very much open to interpretation, but it's surprising/striking to me that the manifest tickets are not selling out particularly quickly.

this is people being offered a way to use mana at a 100:1 conversion rate, and people aren't rushing to take it. obviously, there are other logistical complications here—not everyone is going to manifest! but there are hundreds of people buying full-price manifest tickets, and if mana was worth vastly less than 100:1, you'd think there'd be more effort for people to transfer the mana to those who need to buy tix. presumably the main barrier is that it is against the rules to have someone pay you USD and send you the mana in return for them to buy a ticket... but the premise of a mana:USD exchange rate beyond the official one basically assumes the existence of such a black market, and it seems people aren't racing to cash out at 100:1.
(the other explanation is just that people aren't aware/aren't bothering to do it. but still, i'm surprised! in general i would say mana is not nearly worth 100:1, but this is the most direct exchange we have).
(and much weaker evidence is whatever the pace of sales is for the merch, although it's less straightforwardly clear that people would buy that without using mana—with manifest, we know lots of people are paying USD for tickets)
@Ziddletwix my guess is there are a lot of people who bought tickets before it was available through Mana purchases?
@Ziddletwix And the current prize drawing prices mana at about M$160/USDC, if I got the math right, if there aren't too many more ticket purchases. Presumably the 100 vs. 160 discrepancy isn't big enough to be a huge motivator.
@EvanDaniel obviously people don't value some aspect of the real money drawing the same, because the charity drawing is buying down past 300 at the same time....
@Eliza I hadn't even realized there was a charity drawing running in parallel. That's weird how different they are!
We are nearing the final hours of the first Mana Prize Drawing and entries are slowly trickling in still.
Some of the latest buyers have paid 100 mana for about 360 entries. I guess it's tricky to compute the exact EV on these without downloading the entire data set, since winners of higher prizes are not eligible for lower prizes, but if we just take the $500 first prize as a baseline:
360 entries out of 1778773 total entries for a chance of winning $500, seems like an expected value of about 10 USDC-cents? If we assume all the winners are just from single ticket buyers, the other prizes combined would amount to 4 cents, 2 cents, and 4x1 cent. So adding all that up maybe an EV of a hair over 20 USDC-cents for 100 mana.
That is filtering out many users who do not want USDC or do not want to cash out at this time, but if people thought this was a really good deal they would still be buying lots of shares.
Of course, earlier buyers bought in with a "better" rate but they had to have some guess of how many tickets would be sold in total.
I think I'll buy a little Yes in the 300-500 category.
@Eliza By comparison, the charity drawing was still selling 1000s of mana worth of tickets near the end, as far down as 1500 mana per EV-charity-dollar.
Setting up my own charity cashout at 250/$: https://manifold.markets/wasabipesto/how-much-will-i-donate-to-charity-a
@EvanDaniel I immediately took him up on the offer at 250 and then just now I remembered my target (posted in this thread) was 300-400. So there's another point of evidence!
For a slightly shorter timeline (3-4 months) my rough outline is:
Mana shop will be funded almost entirely through existing balances not paid mana
There will be a second charity giveaway and it will blow past 250/$ again and probably close to 500/$
Until the mana shop and charity start draining existing balances (which is not a guarantee), the mana:USD rate will remain well above 100.
@Eliza I would hope that "investing in markets" also has additional potential. More good markets, better algorithmic discovery, and better limit order UI/UX might all help there. Hopefully we're not saturated on using mana for predictions! (Though I agree that at present, without changes, it looks that way.)
@EvanDaniel Someone should study Mikhail Tal's series of markets on lithium production (and others) to form an argument for [something about how mana can convert to USD]. I think there's enough there (markets, timeframe) at this point to come up with something.