[Manifold Plays Chess 3] If we play 40. Qe8, what is the score after move 41 (leveraged)?
Mini
5
194
resolved May 30
Resolved as
91%

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 31. Rxc7 h4 32. a4 g5 33. b4 Ke6 34. bxa5 Kd6 35. Rb7 Ke6 36. a6 Kd5 37. h3 Kc5 38. a7 g4 39. a8=Q Kd6

The other candidate moves are 40. Qd8 and 40. hxg4

The conditional market for the other moves are here:

The market value (averaged over the last 4 hours before close) of this market and the other markets will be measured. If this market has a higher (last-4-hour-average) market value, it will resolve to the score after move 41, otherwise it will resolve N/A. 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 this score:

Here is a table of the correspondence to market value and score

value score

----- -----

0.00 0.000

0.03 0.246

0.07 0.574

0.10 0.820

0.20 0.840

0.30 0.860

0.40 0.880

0.50 0.900

0.60 0.920

0.70 0.940

0.80 0.960

0.90 0.980

0.93 0.986

0.97 0.994

1.00 1.000

----- -----

This correspondence is defined by linearly interpolating between the points

(0.0, 0.0), (0.1, 0.82), (0.9, 0.98), (1.0).

The score after move 41 is the score (not market value) of the winning move in move 41.

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 40, 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

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predicted YES

resolution of market 40. Qe8:

resolution score: 0.982072

corresponding market value: 0.910359

probabilistically rounded: 91%

predicted YES

40. Qd8: Average market value: 0.855503

40. Qd8: score: 0.971101

40. Qe8: Average market value: 0.917140

40. Qe8: score: 0.983428

40. hxg4: Average market value: 0.815862

40. hxg4: score: 0.963172

Winner: 40. Qe8

--------------------

resolution of market 39. a8=Q:

resolution score: 0.983428

corresponding market value: 0.917140

probabilistically rounded: 91%

@harfe I think I understand as the game ends there will be two different score computations (the values may or may not coincide), but still seems worth clarifying:

• For the “score after move n” where n is the last move, that move’s winning conditional market’s last 4 hours average probability will determine that score, applying the leveraged transformation. That value, deleveraged, will be used to resolve the winning conditional market for move n-1.

• Then that final move’s winning conditional market —which will be titled something like “If we play <n. xx>, what is the score after move <n+1> (leveraged)?”— will resolve by deleveraging the special game ending score (1-n*0.0004 if white wins), since there is no move n+1.

Also worth mentioning, though it’s pretty clear from its description, the main game market simply resolves to either YES or NO or 50%. The final score, or scores, or any other computations have absolutely no bearing on that market’s resolution, only the game’s result will.

predicted YES

BTW I’m mindblown that some guy in the late ‘70s already knew The Answer to this n thing. 😄

@deagol It sounds like you are correct