If you like this brain burner, I've got a new Inverting Resolutions market for ya: /Stralor/inverting-resolutions-what-would-be

I'd also like to do a more playful version of this market structure sometime, but haven't come up with a good concept yet. anyway, happy trading!

@Stralor “Brain burner” is exactly right. I love the setup and how simple it seems, but every time I come back here to bet I end up second-guessing my valuations for so long that I have no intuition left. I’m beginning to realize this format accomplishes something rather insidious: It takes System 1 so far out of the game that it gives up entirely, leaving system 2 demoralized, insecure and alone

edited the two that have happened to add "Resolves: TRUE", so we can bet on them accordingly

Oh god this is so counter-intuitive I love it

This is now equivalent to the hospitalized option (Biden has dropped out) and should be arbitraged as such

I bought it in the wrong direction because I'm a dumbass

I'm gonna make a call here: Trump was "hospitalized" for the purposes of this market due to being whisked to a hospital and treated after the shooting. Whether the option itself resolves YES or NO still remains to be determined by the outcome of the election.

Am I missing something? Why are people bidding down "he or his opponent is hospitalized"? That should be exactly the same as trump's chances of winning the election at this point, right?

yep, if my math is correct!

I'm sorry for feeling like I have to add this, but it seems too relevant to the current conversation. Avoid betting on it if it (reasonably) makes you squeamish

I wish I had thought of this 🙌

This market makes me want a new sort order: by decreasing distance from 50%

yeah that'd be perfect! happy to change the default but none feel right

hmm I've noticed an issue with my own recommended math. If E is solved (0 or 1), then intuitively your target price should be (1-T) or T, respectively, right? (assuming that now the correlation effect is priced in, so R = 0)

in that case, this formula breaks down. maybe it's because of the assumption that R = 0? or maybe I'm way off on what your target odds should be when E is solved.

for now, it's good enough, but I want to do right by you all so I'm in the process of scratching out a new one. hopefully I can figure it out!

okay, I've found a formula that is much more accurate. it's more complicated (*sigh* of course it is), but I think it's better. I'll post the full write up and details later tonight or tomorrow. in the meantime I havent been trading since I realized and wont resume or edit limits until after I've posted it. I was also proven wrong on an assumption or two. A couple things to know:

• events with low odds naturally have a smaller effect on his chances no matter how influential they'd be (oops)

• nothing has changed about the resolution or the basic principles of the market!

new math is up! the formula:

(TE+(1-E)(1-T))(ER+1)

This results in a few things, most of which are intuitive:

• If the chance of the event happening (E) is 1 or 0 (guaranteed resolution), then the target percent to bet to becomes T (Trump's odds) or 1-T respectively, if in that case we assume it is priced in so correlation (R) = 0

• Likewise, when T is 1 or 0, but somehow this doesn't resolve yet, the target percent is E or 1-E, if R=0

• Stronger correlation R means stronger effect

• Same for stronger anti-correlation

• Higher likelihood E means greater range of target percents based on R

• Low likelihood events (<50%) seem to anchor opposite Trump's current odds (1-T), and the lower they are the more significant this effect is

It took me awhile to get to this, and I had made some bad assumptions originally.

I thought that all the prices should be swinging around Trump's current odds, but clearly there's a natural second focal point at the inverse, 1-T. I knew that when either E or T was solved, R should equal 0 (in other words, already be priced in to Trump's chances), and the prices should converge on the focal point(s). The old formula didn't do this and instead went completely off the rails at the extremes, which is how I realized it wasn't quite right. Would it have given us confidence in bad bets? Mostly it was okay (until it wasn't) but certainly those bets wouldn't have been mathematically optimal.

As an aside, I don't recommend trying to write a formula from scratch when all you know is "when E is 1, the result must be T; when E is 0, the result must be 1-T; and somehow R needs to be crammed in there." But if those assumptions are correct then now we can trade with more confidence.

I'll probably only run the math occasionally myself. No way I want to plug everything in every time! Just gotta calibrate my instincts and then betting should be a breeze.

What I find most interesting is as this market stabilizes, you feasibly could work backwards to calculate how far Trump's odds should move as events happen!

this market is now Plus tier!

Yeehaw! 🤠

Added one about King Charles bc the autogen art is hilariously wrong

This hurts my brain, and I love it.

I've significantly rewritten the description to better explain how this market works. Big thanks to @HarrisonDorn for nerd-sniping me into formulating a mathematical model that is hopefully correct.

Is this better? Let me know if there are more questions!

Thanks for the rewrite, it certainly pushed me to brush up on my very rusty stats background!

edit: I'm probably wrong read Pat's comment

In English:
("You've woken up Nov 5, 2024, and you found out that Trump has won, what do you think is the chance X has already happened?") x (chance of Trump winning)
+
("You've woken up and found out that Trump has not won the election, what do you think the chance is that X hasn't happened?") x (1-chance of Trump winning)
= YES position chance

This is a really cool market!

hmm I don't think this math is quite right, though! look at the example Biden drops out 50% & Trump wins 80%:

if,

(0.5 x 0.8) [drops out, trump wins] + (0.5 x 0.2) [doesn't drop out, trump loses] = 100% YES

(0.5 x 0.2) [drops out, trump loses] + (0.5 x 0.8) [doesn't drop out, trump wins] = also bet to 100% for NO!

But we know that the following cases should resolve NO:

• Biden doesn't drop out, Trump wins

• Biden drops out, Trump loses

So the bottom of your range (where, at minimum to bet YES to) can't be 100%.

Here's the math I used for the examples:

• T = Trump wins

• E = Event happens

Target for NO, hurts his chances = T - (0.5 - E)

Target for YES, helps his chances = T + (0.5 - E)

Giving a target range of:

• Biden drops out 50%, Trump wins 80% = 80 to 80%

• China invades Taiwan 10%, Trump wins 80% = 40 to 120% (capped to 100)

The question then becomes one of correlation. You should be betting at least towards your range if the value is outside it (accounting for interest rate and edge), and then directionally within your range by how you think it'll affect his chances.

In reality this means to find your real target value there's another hidden value for Correlation ("R"), which is from -1 (perfectly anti-correlated, hurts his chances) to 1 (perfectly correlated, helps his chances) with 0 being completely uncorrelated:

Target = T + (0.5 - E) * R

Which for "China invades Taiwan 10%, Trump wins 80%" results in:

• if China invading means he loses the election, 0.8 + (0.5 - 0.1) * -1 = 40%

• if China invading somewhat helps him (R = 0.25, aka helps him by 25%), 0.8 + (0.5 - 0.1) * 0.25 = 90%

The silly part is when something anti-correlated has a high chance of happening. Say you disagree with the going market rates and think China will almost certainly invade (E = 0.9) and that it will severely tank his chances (R = -0.75), but for some reason think that he's still got that 80% chance of winning:

• Target = 0.8 + (0.5 - 0.9) * -0.75 = 90%

In that weird scenario, you want to bet to 90% due to the inverting resolutions! In reality, if your credence for events happening or Trump winning are way different than going market rates, any strongly anti-correlated factor with a high chance should significantly reduce your credence of T.

And if my model is correct, then the following is true:

• if one of these events has a 50% chance of happening, then its correlation has no effect and its spot in this market should be arbed to Trump's chances of winning

• if one of these events is completely uncorrelated to Trump's chances of winning, it should also be arbed to his chances

But I think most of these have at least some small correlation or anti-correlation, otherwise I wouldn't have asked the question!

Oh wow, I am really out of my depth! Whoops. I thought I understood conditional probabilities, I'm going to have a think about this haha