Check the game here: https://lichess.org/GF9YULQP.
The game so far: 1. e4 e5 2. Bc4 Nf6 3. Nc3 Nc6 4. Nf3 Nxe4 5. Nxe4 d5 6. Bd3 dxe4 7. Rg1 Bf5 8. Bb5 exf3 9. Bxc6+ bxc6 10. Qxf3 Qd7 11. Qc3 f6 12. g4 Bxg4 13. Rxg4 h5 14. Re4 Qd5 15. Qf3 Rd8 16. d3 a6 17. b3 Qc5 18. Kd1 a5 19. Bb2 g6 20. Qxf6 Kd7 21. Rxe5 Qd6 22. Qxh8 Be7 23. Qg7 Rf8 24. Rxe7+ Qxe7 25. Qxe7+ Kxe7 26. Ba3+ Kf7 27. Bxf8 Kxf828. Kd2 Kf7 29. Re1 Kg7 30. Re7+ Kf6
The market will resolve to the score after move 32. Note that "Market value" and "Score" do not work on the same schale.
Here is a table of the correspondence to market value and score for the current move, which will be used to calculate PROB from the score after move 32:
----- -----
value score
0.00 0.000
0.03 0.243
0.07 0.567
0.10 0.810
0.20 0.830
0.30 0.850
0.40 0.870
0.50 0.890
0.60 0.910
0.70 0.930
0.80 0.950
0.90 0.970
0.93 0.979
0.97 0.991
1.00 1.000
----- -----
This correspondence is defined by linearly interpolating between the points
(0.0, 0.0), (0.1, 0.81), (0.9, 0.97), (1.0).
The score after move 32 is the score (not market value) of the winning move in move 32.
It might have a different function to calculate scores from market values: The function assigns score z to 50% market value, z+0.08 to 90% market value and z-0.08 to 10% market value, where z is the (rounded) score after move 31, but at most 0.9 and at least 0.1.
Note that when the game ends, the score will be 1.0 - #moves x 0.0004 if white wins, 0.5 - #moves x 0.0002 if its a draw, or 0.0 if we lose.
Some more details for the overall game here:
https://manifold.markets/harfe/will-white-win-in-manifold-plays-ch
1,000
3.00I could well be being thick but I don't follow at all. I think I follow the purpose and if I expect white to win in less than 100 moves the score at the game end is over 0.96. However I am lost as to what is the score after move 32. You have stated this to be "the score (not market value) of the winning move in move 32." but I don't follow what this means.
@ChristopherRandles think of the winning market 32 probability as saying “how much will the score increase/decrease as a result of this move”. So a market of 50% means no change, and each 5% deviation from there makes the score 0.01 higher/lower. So 70% means the score will rise by 0.04, 25% the score falls by 0.05 and so on.
@deagol where I say “the score will rise/fall” it’s in relation to the (rounded and capped) score after this move, which is similarly leveraged as per the table. So there’s the exception if the score after this move is above 0.9 (or below 0.1), then the centered 50% will remain at 0.9 (what’s called z in the description here), even if the score can be higher. So in that case you could see the next conditional markets as saying something like “how much higher than 0.9 will the score be after this move” and 50% maps to 0.9.
Thanks for the replies. That begins to make more sense though I don't understand how you figure this out from the wording here. It sounds like you are saying the score is the change in market value of the "Will white win in Manifold Plays Chess, part 3?" claim despite the wording here clearly saying it is "not market value".
@ChristopherRandles No, that market is independent of the score except when the game ends. The score is only dependent on the winning conditionals probabilities. It used to be a 1:1 correspondence until now, i.e. the score after each move was the last 4h average probability or market value of the winning conditional. From this move on, the score is a piecewise linear transformation of those same average probabilities, such that the natural market center of 50% corresponds to the previous score (but rounded) and the rate of increase/decrease is leveraged 5:1.
You can check the score as reported by @harfe in comments after the close of the conditionals for each move:
This is the current score (after move 30): 0.885494
compare to the previous score (after move 29): 0.819723
and the one before that (move 28): 0.767424
Those all match the average probability over the last 4h of the respective winning conditional markets. There’s absolutely no direct relation to the main game market probability, other than traders there inducing a back-propagation evaluation. Note the current score (0.885494) has been rounded to z=0.89 and used here as the corresponding “re-centered” 50% market value for this market’s score determination as well as the resolution of move 30’s winning conditional. A similar “re-centering” will apply for the next move (32), around this new score from this market (but rounded and no higher than 0.9 giving us a new z).
For example, suppose the current market value of 65% holds constant into the close of this market. Then the score, as per the table in the description, would be 0.92, and the previous move 30 winning conditional market resolves to that as 92%. Then, for the next move 32, the table (or piecewise linear transform) will be re-centered at z=0.9 (because the score exceeded the cap) for a market value of 50%, and using the same 5x leverage you’ll note gets you to 100% for a score of 1. Now let’s say that next move 32 winning conditional market averages 35% (they must have picked some blunder candidates or perhaps some whale manipulator forced this), then that 35% market value corresponds to a score after move 32 (0.5-0.35)/5=0.03 below 0.9, =0.87, and that value would be used to resolve this market (move 31) using the table above, at PROB=40% (and I’d lose mana given my bullish bets here). And so on until the final move’s resolution which will depend on the score determined differently which you mentioned, as the game outcome penalized by the number of moves.
Phew, hope this helps! Yeah, I know it’s quite a hairy thing to explain but I feel it’s simpler to understand than communicate precisely.
@harfe I think of it as first re-centering or normalizing to 50% and then leveraging x5