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Hikaru on tilt

Lol the chess.com livestream shows a prediction and everyone updates.

See the related market for side action on Magnus v. So

Seems ~arbable with my market. I don't see any reason to think the bracket outcomes aren't independent.

@BoltonBailey There's discussion about consistency between these 2 below.

@EliLifland I see, there's some weird interaction between whether they both final, whether one does, or whether neither does.

@BoltonBailey I'm actually still a bit confused. Shouldn't the probability of both finaling be more than (2 x prob magnus wins it all)(2 * prob hikaru wins it all)?

@BoltonBailey

I made this equation to check for what this and the other market imply about what P(Hikaru/Magnus beats non-Hikaru/Magnus in the final), based on @SophusCorry 's reasoning and assuming Hikaru/Magnus are equal strength:

(.43/sqrt(.63) - sqrt(.63) * .5) / (1-sqrt(.63)), where .63 is this market price and .43 is Hikaru/Magnus' price in the other market.

Right now it evaluates to .702 which seems quite low so I will bet it down some.

@BoltonBailey

> I'm actually still a bit confused. Shouldn't the probability of both finaling be more than (2 x prob magnus wins it all)(2 * prob hikaru wins it all)?

Not sure what you mean here? This would be 4P(Hikaru)P(Magnus) which would be >1

@BoltonBailey

I'm taking 2 * (probability of winning it all) as a rough proxy for probability of finaling. I guess I oriented an inequality wrongly somewhere, this should be an upper bound, not a lower bound.

@BoltonBailey @EliLifland yeah, probability for finaling if you base it on the chance of winning it all should at least assume 50% chance at winning the final. So the upper bound on finaling given a winrate of 43% is like you said 86%. Or for this market 74%

Since the opponent could be worse than hikaru/Magnus and give higher than 50%. It can become a function where you take the chance of winning it all and the chance of either player being in the final and get the chance of beating not Magnus/hikaru as Magnus/hikaru. Which is what Eli did.

I think the chance of Magnus/hikaru each being in the final is around 85%, which makes 73% in this market. I also think the chance of beating not Magnus/hikaru is quite high since whoever of the two is in the final, is likely having a good week. So maybe 80%

So then I guess I can say P(Magnus wins) = P(hikaru wins) = 0.85*(0.85*0.5 + 0.15*0.8) = 46.325%

Phew. Hope I did all the math right.

@SophusCorry also the lower bound would be 43% which this market is over so it's not a clean arb and depends on how likely you think it is that Magnus/Hikaru will win a final against non-magnus/hikaru

Edit: I'm confused about the lower bound right now but 43% seems wrong. Gotta go to sleep now it's late in Europe

@SophusCorry alright I guess I was right. If we take sqrt(0.43), we get 65.6%

Then we can do P = 0.656(0.656*0.5+0.656*1) =0.646

P(both finals) = 0.646*0.646= 41.7% which is suspiciously close to 43% but not quite 43%

I feel that this market is way too low for a few reasons:
1. So far in 4/4 speed chess championships that both Magnus and Hikaru participated in, they have been in the finals
2. the only others with a chance seem to be MVL or Alireza, and although I think MVL is underrated, he has failed to go to the final most other years and Alireza didn't look overwhelmingly strong so far.
3. If this one is 55%, why is the Magnus and Hikaru both at like 40%? I don't think these probabilities are mathematically incompatible, but I feel like it's not very congruent.
4. Say the chance of Hikaru going to the final and Magnus going to the final is about the same (and I assume the probabilities are completely independent), then the separate probabilites would be 75% each for them to be 56.25%. Which seems super low to me.

1. Not true, Magnus lost in semis to MVL in 2020 https://www.chess.com/article/view/2020-speed-chess-championship. So 4/5. And the first one only had 8 people.

2. Why not So? So has come very close before, e.g. lost by 1 to Hikaru in 2020. But yeah I agree So beating Alireza would raise these odds, which is why I sold some No while So is winning

3. Let's say Magnus and Hikaru each have 75% chance of making finals as you described in (4), that means there's ~6% chance neither make it. If they have 84% combined per other market, that means in the final they need to have a (.84-.55)/.39=74% chance of winning the final if I'm doing the math correctly, which doesn't seem unreasonable

@EliLifland

1. Yeah that's true, I got my history wrong

2. Yeah So definitely shouldn't be slept on, but he's playing firouzja right now so one of them is out. (Although the better one goes on)

3. A little bit worried about my maths on this one but since they are symmetrical you can just do: if Magnus has 75% chance of making it to the final, and 41% chance of winning the whole thing, then that's a 0.41/0.75 = 55% chance of winning, on the condition he's in the final. So if we assume that hikaru and Magnus have equal chances against each other, then we can calculate the implied probability of either of them winning against other competitors. Because that 55% could be 75% chance of 50/50 against hikaru 25% chance of 70/30 against any other player which adds up to the 220/400 = 55% chance of winning, given that he's in the final. I guess that is actually pretty reasonable, although I would think it's more like 80/20 and then with a higher chance of both being in the finals (probably like 85% each adding up to 73% for both)

@EliLifland just given your first point, you could say that our prior is 80% then, and we should only bet it lower if we think either Magnus or hikaru are weaker (definitely don't think so) or the field is a lot stronger (could be but the main contenders have been there most other years too, except Firouzja I guess)

@SophusCorry Yeah Alireza is in this year but not 2021/2022, though now he's out. Also there have been multiple close calls where they almost lost but didn't, so could adjust for that. Particularly Hikaru's 1 point wins vs. So in 2020 and vs. Ding in 2021