harfe
closes Jan 1, 2024
Will white win in Manifold Plays Chess, part 3?
47%
chance

Welcome to Manifold plays chess, part 3.

This time, Manifold will play as white against Stockfish level 3 on lichess. Manifold lost both games so far, see https://manifold.markets/market/will-black-win-in-manifold-plays-ch and https://manifold.markets/citrinitas/will-white-win-in-alexliesmans-mani for these games.

This market resolves YES if white wins.

This market resolves NO if black wins.

This market resolves to 50% if there is a draw.

The game will unfold here: https://lichess.org/GF9YULQP
The game so far: 1.e4 e5 2. Bc4 Nf6 3. Nc3 Nc6 4. Nf3 Nxe4

Market for current move:

Market structure:

Per move, there will be a free response market, followed by conditional markets for 2 or 3 moves. The free response market will resolve to the move that manifold will play. For each response, the average probability in the last four hours before close is measured. With 75% probability, two moves will be randomly drawn, with weight proportional to those market probabilities. With 25% probabilities, three moves will be randomly drawn in the same way. Then for each of the two or three candidate moves, a conditional market is created.

If there are 3 or less legal moves, no free response market will be created, and we directly move to the conditional markets.

The markets for the candidate moves are of the form "What will the score be one move later if we play X?". We measure the average probability in the last four hours of the market. The move with higher probability wins and gets chosen. The conditional market that does not get chosen gets resolved N/A. The conditional market for the move that gets chosen resolves to the score one move later.

The score is the average probability in the last four hours of trading in the conditional market for the winning move. If there is no later move, the score for this purpose is 1.0 - #moves x 0.0004 if white win, 0.5 - #moves x 0.0002 if its a draw, or 0.0 if we lose (this is to encourage a shorter game).

In the first 6 moves, the moves "Resign1", "Resign2", "Resign3" will be legal moves (and white loses immediately if it plays one of those moves). After that, any resign move will not be legal.

Possible rule changes during the game:

If the probabilities for the conditional moves stagnate, I plan to introduce some kind of leverage, so that predictors can predict in a wider range. An example for what I mean by leverage: if the score stagnates around 0.65, we could map 0.6 to 20%, and 0.7 to 80%, and interpolate for the rest. These changes will be announced at least 2 moves in advance.

Other than that, I reserve the right to change some of the rules during the game, if the game becomes very boring or if I am concerned that funding the remainder of the game will become too expensive. In that case, I do not attempt to change the outcome of the game. For example, if the score is below 0.01 over many moves, I might add a mechanism that allows us to resign.

I will wait for 1-2 days before starting the game, during which the rules might be changed.

Edit (2023-03-05): changed description to clarify rules slightly, no changes were made to the rules.

Edit (2023-03-05): Accidentally deleted the paragraph about Resign moves in the previous edit. Added again.

Edit (2023-03-06): Changed "This market resolves NO if white wins." to "This market resolves NO if black wins."

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Antonbought Ṁ0 of YES

@jack has put up some limit orders on each of the move markets. Looks like he's intending to push the win market beneath its honest market price in some kind of manipulation strategy?

Set up your limit buys now to take his money and keep the chess moves accurate!

Daniel Tellois predicting NO at 52%

@citrinitas what if my honest belief is that the chess game is honestly lost (say 30%) with one of those moves, but also probably lost (say 25%) with the other move due to more opportunities/incentives for manipulators to throw the game? Am I supposed to bet against my beliefs to defend some idealized notion of “honest” market price?

Antonis predicting YES at 52%

Oh, no, if you actually think it's lost then just bet this market down. I'm just pointing out that 52% and 35% / 35% is inconsistent unless someone's going to make some kind of play, and I think setting limit orders is how you pump ᛗ out of that play.

Daniel Tellosold Ṁ43 of NO

@citrinitas Isn't it possible for the "score after move 8" (what the 35% is presumably predicting) to accurately reflect the fact that someone with huge capital would benefit from the terrible move

Daniel Tellois predicting NO at 50%

@deagol The terrible move 7, is what I meant.

Daniel Tellois predicting NO at 50%

and yet the 50% here can also accurately reflect a future blunder by SF3 (not unlikely as we saw in game 2), even if they get this terrible move 7 to win.

harfeis predicting NO at 55%
harfeis predicting NO at 56%

Please continue betting on move 6

I am honored that we managed to make 4 decent moves, and that the probability of winning reached 50%.

Also, the market for move 5 is ready:
https://manifold.markets/harfe/manifold-plays-chess-3-move-5-what

Daniel Tellosold Ṁ19 of YES

@harfe congrats! though I can’t say we managed to keep manipulators honest. They’re doing so of their own choice (for now).

Jackis predicting YES at 51%

@deagol Indeed. The manipulators (mostly me, but not just me) are doing exactly what I predicted in https://manifold.markets/citrinitas/will-black-win-in-manifold-plays-ch#YFpQtFv4dMkr7fuaIGqs

Measuring the win probability only 1 move later on the next win probability market can also be easily manipulated. It's very close to a self-resolving market, just with two markets instead of one.

Jackis predicting YES at 51%

I claim that the scores we've been seeing on the markets are close to meaningless :)

Martin Randallis predicting NO at 52%

@jack I'm unclear how you unwind your position now. Don't you have an even larger incentive to bet YES on the next set of markets?

@MartinRandall he doesn't have to unwind the position if white wins - he can just bet yes every move.

Daniel Tellois predicting YES at 52%

@harfe this game far from a sure win so far. But expect a blunder or 2 by black soon (we sure that’s SF3 right?)

Daniel Tellois predicting YES at 52%

maybe we should’ve tried harder getting it off the book with some odd move earlier

Martin Randallis predicting NO at 55%

@harfe sure, but if the scores are meaningless that implies that white is playing randomly which implies that we don't win.

Daniel Tellois predicting YES at 60%

unclear how you unwind your position

Maybe a tricky balancing act, but I think one way coud be:

1. For the last four hours, defend the score needed for the previous move, aim for decent profit x but don’t go nuts.

2. The last minute, dump some to leave a lower defensible price in the next move, may incur a slight loss at dump but aim to profit y in next move.

Maximize x+y. Can get back to around 50% depending how big the position, and how others fight your 4h defense, and whether others dump in front of you. Easier if done gradually over several moves, thus the need to play more. Alternatively, accept a one-time breakeven or even take a loss (probably not in this move), letting others set the score for one move, come back for the next one.

Daniel Tellosold Ṁ6 of YES

@MartinRandall also, could use the futures to hedge against your “spot price” needs:

Daniel Tellois predicting YES at 55%

@MartinRandall @jack was there a private arrangement struck between you two to stay off the move 5 markets and not influence the score? I understand if you can’t say, but seems to me the stakes were quite high for that to happen.

Daniel Tellois predicting YES at 55%

ah ok just in time 😉

harfeis predicting YES at 40%

Help us determine whether to play 4. Nf3 or whether to resign

harfeis predicting YES at 43%

Also, due to my recent profits, I will have enough capital to fund the game for many moves.

harfeis predicting YES at 43%
Daniel Tellois predicting NO at 35%

Thought these might be interesting

Daniel Tellosold Ṁ15 of NO

If I’m analogizing this correctly, those currently seem to be in backwardation. 🙃

Daniel Tellobought Ṁ13 of YES
Daniel Tellois predicting NO at 28%

@jack’s choice of move 3 (h4) in the free response epic fail seems at odds with his switch to YES here. Is it 4D chess or just silly mind games?

Jasonis predicting NO at 24%

This market may have a weird (to me) property. It is trading at 24 percent, presumably because participants think there's a high probability of someone manipulating the system and throwing the game. But the lower the percentage, the less incentive there is to incur the costs to manipulate and throw!

So for a setup like this, is the setup ironically somewhat more manipulation-resistant when participants think the manipulable outcome is very likely to happen (whether due to manipulation or otherwise?)

Fionis predicting YES at 23%

@Jason yeah, I wondered about this. My personal estimate for winning is much higher than the current market value, but I'm not planning to buy much YES because that might incentivise manipulation.

Martin Randallis predicting NO at 23%

@Jason There are some big YES limit orders that are probably a bigger incentive than the AMM liquidity.

Martin Randallbought Ṁ200 of NO

We make two moves without resigning and the probability doubles. I think yes bettors are grading against a curve.

Daniel Tellois predicting YES at 23%

What if there’s a tie in the conditionals prediction? I’m sure that would be highly unlikely, still best to have a set procedure. I’d say we flip a FairlyRandom coin to pick the winning move and resolve the other N/A, but resolve the free response to both moves proportionally to their last 4h avg prob. Make sense?

harfeis predicting YES at 23%

@deagol In the unlikely case that the 4h avg prob of both markets is equal, then I will do a coinflip with FairlyRandom. Seems like a good idea.
But unlike you suggest I will not resolve the free response market to both moves, just to the winning move (since it asks for the move that Manifold will actually play).

Martin Randallis predicting NO at 23%

@harfe Probably not all that unlikely. With e4 vs g4 I think e4 has better odds, but with e4 vs d4 they'd be the same, and limit orders only do whole percents.

Daniel Tellois predicting YES at 23%

@harfe yea agree that’s best, simpler.

harfeis predicting YES at 26%

@MartinRandall Fair point, if both have constant price because of limit order, then there is a good chance of equal outcome. But if the price changes once in the last 4 hours, and in one market it changes a few seconds earlier than in the others, then the average will be slightly different.

harfeis predicting YES at 19%

https://manifold.markets/harfe/how-many-moves-will-white-play-in-m new market about the number of moves this game will last.

Daniel Tellosold Ṁ4 of NO

The whole system seems to me it might work if not for that single silly three resigns rule. There’s simply no reason for it, and so many reasons against. Would be a shame if this iteration fails only because it shot itself in the foot like that.

harfeis predicting YES at 16%

@deagol So you will switch to YES team if we survive the first 6 moves?

I agree that this lowers the overall chances of winning. If there are severe flaws with my design, I would like to see them early, thats why I added the rule for the first 6 moves.

Daniel Tellois predicting NO at 16%

@harfe I might switch even on the first move, I guess depending how I assess others’ commitment in defending their bets (my measly capital prevents me from risking much myself).

The thing is I believe the rule does not really surface a flaw in the design, but instead unnecessarily introduces one.

Daniel Tellois predicting NO at 16%

@deagol to be clear, I’m all for allowing resign as a valid move, for first 6 moves or even all the time: simplicity helps understanding which drives traders’ confidence in defending their stakes, while quirks and exeptions incite doubt. But just one resign, not this artificial 3 resigns which seems arbitrary and most likely raises suspicions in people who may not be aware of all our debates and machinations over previous iterations.

Daniel Tellois predicting NO at 13%

I don’t get the point of gifting the NO team not 1 but 3 Resign1,2,3 for them to fill up all 3 slots, which was YES last whale defense: guaranteeing that at least another move gets a conditional would force NO to prop their resign conditional, a costly requirement since, if picked, that would resolve to NO. By giving them the 3 slots, it’s just free money if they can dominate the free response choice. What am I missing?

Martin Randallis predicting NO at 13%

@deagol YES bettors only need to bet on a single winning option, NO bettors have to bet on two losing options, so in principle YES has an edge in the last second betting.

Martin Randallis predicting NO at 13%

@MartinRandall Edit: last four hours betting.

Daniel Tellois predicting NO at 13%

@MartinRandall assume NO team has unlimited resources, 3 orders of magnitude more than the rest as seen in the last game. Easy to grab the 3 slots, right @jack ? Givingjust one resign (and whatever blunders there will be further ahead in the game) seems enough IMO.

Antonis predicting YES at 13%

The whole point of this market structure is that even if someone wants to try to spend a lot of mana to force a loss, you can turn a profit by returning the market to the honest position.

"Resign is not a valid move" doesn't really make us better at chess, just better at hiding our mistakes.

Daniel Tellois predicting NO at 19%

@citrinitas I’m not saying resign is not a valid move, I’m saying there’s no such thing as three different resign moves in chess. But there will come a moment where there will be at least two different blunders available to force a loss. The structure doesn’t need to invent this weird non-chess thing to surface any potential mistakes.

Daniel Tellois predicting NO at 19%

My point is let them fight it in the conditional, at a cost. What’s so bad about designing a structure that makes it hard to throw the game in the first few moves? One resign at first, and several blunders always at hand after move 6, is already enough to force a loss. Allowing all three slots to lose from the get go defeats the whole 2-3 randomized moves safeguard.

Daniel Tellobought Ṁ45 of NO

YES bettors only need to bet on a single winning option, NO bettors have to bet on two losing options, so in principle YES has an edge in the last second betting.

That will indeed be an edge for YES in the conditionals as long as there’s a good move among those, but not if all are resign. But in the free response YES has no edge, essentially makes no difference that NO has to bet on 2 or 3 options while YES can focus on one. The parimutuel market mechanics are such that betting 10k on one option, or 5k on 2 options, or 3.3k on 3, tank the competing options equally.

Martin Randallis predicting NO at 20%

@deagol Yes, I think you are right. I misread the free response mechanics, I thought it was picking the top 2-3. But it's going to pick randomly proportional to final probabilities. So it devolves into a beauty contest.

Daniel Tellosold Ṁ20 of NO

@MartinRandall Well, picking the top 2-3 is even more of a KBC. This just injects a bit of randomness.

Martin Randallbought Ṁ50 of NO

@deagol Hmm. If it was top 3 I'd be reasonably confident that a whale could keep a single good move at 25%+ on average for four hours and get a ~4x profit (assuming that the conditional markets work).

Whereas if it's random then doing that means the move only has a ~75% chance of being selected, so it's only ~3x profit.

I suppose that could still be enough motive.

Daniel Tellosold Ṁ21 of NO

@MartinRandall 25%+ guarantees top 3 but it then it could be top 2 (1/4 chance) and your “assured profit” is toast

Daniel Tellois predicting YES at 18%

@MartinRandall also I don’t see how even if you get your move picked you can guarantee 4x profit? You’d need to control the next move as well, to get the conditional to resolve that high.

Daniel Tellois predicting YES at 18%

ah ok I see you meant 4x in the free response, but gotta spend some more to get your conditional picked over the others

Martin Randallbought Ṁ10 of NO

Yes, but if my move is up against resign1 then I can bet resigning down risk free.

Daniel Tellois predicting YES at 18%

@MartinRandall and there’s no third candidate? but then, if only top 2 were picked you’d need to have kept it at 33% in the free choice, and payoff 3x?

Daniel Tellois predicting YES at 18%

33.3%+

This market resolves YES if white wins.

This market resolves NO if white wins.

Should say black for NO?

harfeis predicting YES at 16%

@deagol haha thx. fixed. Things like this is the reason I kept the market open for more than a day, but nobody noticed until now.

Daniel Tellois predicting NO at 16%

@harfe sorry I was distracted over the weekend, only noticed after your comment ytd in the other market (thx)

Martin Randallbought Ṁ15 of NO

If there are 3 or less legal moves

How does this work if "resign1" and such are legal moves? Or are you only allowing them as legal moves on the first move?

harfeis predicting YES at 12%

@MartinRandall resign moves are legal only in the first 6 moves.

What is "score" here?

Jackis predicting NO at 21%

@MartinRandall It seems to be described above as the following: The final score is

the score for this purpose is 1.0 - #moves x 0.0004 if white win, 0.5 - #moves x 0.0002 if its a draw, or 0.0 if we lose

And the score for each move is defined based on the predicted score one move later on the "will white win" markets?

@harfe I think there is a problem with this definition - those two definitions of score aren't the same, e.g. at the very last move in which white wins, let's say it's move 100, the score would resolve to 96% but "will white win" will resolve to YES aka 100%.

harfeis predicting YES at 14%

@jack I think I have to improve my description. What I meant by score was the score (according to the formula) of the winning conditional market one move later.
This market ("Will white win") is disconnected from the other markets. Thus it does not matter much if the two definitions of score aren't the same.

Jackbought Ṁ50 of NO

@harfe Ok, I think I understand. So you would resolve the conditional market for move #9 to the value of the conditional market "Will white win if we make move X for move #10" minus #moves x 0.0004? I think that works although it seems a bit overcomplicating things to me.

harfeis predicting YES at 14%

@jack I think you think the right thing. I changed the name of the conditional market now, because it was misleading.
I will not manually subtract #moves x 0.0004 every move, only once the game ends (but if markets are efficient, then this should propagate). I will just resolve to the (average) value of the next market. (If I took you literally, then negative scores would be possible).

In hindsight this might have been unnecessarily complicated, and should looked for other ways to keep the game shorter. But I am reluctant to change things now because the game already started (although this would mostly affect the conditiional markets, which have not been made yet).

@MartinRandall I changed the formulation. I hope its easier to understand now.

Martin Randallis predicting NO at 14%

@harfe Between the new text and this comment I think I got it.

harfeis predicting YES at 21%
harfebought Ṁ40 of NO

I consider this to be another experiment.

I neither claim that this market structure is exploit-free, nor want to state the opposite.

The 2-or-3-markets thing is so that we get some information whether having more conditional markets is better.

Jackis predicting NO at 21%

@harfe Want to clarify, the intent here is treating this as an experiment in robust market structure design, i.e. exploiting the market structure is encouraged here as it was in the previous game? If people just want to play a nice game of chess that's also fine, but should make the intent clear.

I posted earlier about my expectations for this market design be easily exploitable: https://manifold.markets/citrinitas/will-black-win-in-manifold-plays-ch#YFpQtFv4dMkr7fuaIGqs