What will white (Manifold) play in move 2?
Check the game here: https://lichess.org/GF9YULQP
The game so far: 1.e4 e5
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. The score of each move will be determined by the average probability in the last 4 hours. The move with higher score will be chosen (and the corresponding condditional market will resolve to the score one move later. The other market(s) will resolve N/A).
More details here: https://manifold.markets/harfe/will-white-win-in-manifold-plays-ch
The moves "Resign1", "Resign2", "Resign3" are legal moves.
Invalid moves or duplicate moves will be removed from consideration.
Previous move:
1,000
3.00Well, seems like some of you underestimated Bc4.
Please help manifold choose a next move: https://manifold.markets/harfe/manifold-plays-chess-3-move-3-what
Hey @Fion and @MartinRandall I had to defend our conditional all by myself (not huge capital here). Glad it worked, hopefully next time there’s more supportive team play.
@deagol alas, I only bet for Bc4 because I thought it would beat Ke2, so thank you for showing me what is possible. I'll pay more attention next time.
Please continue predicting on the moves Nf3 and Bc4 here:
https://manifold.markets/harfe/manifold-plays-chess-3-if-we-play-2 (Nf3)
https://manifold.markets/harfe/manifold-plays-chess-3-if-we-play-2-637a4c7e778e (Bc4)
Moves by average probability:
0.505407 Nf3
0.125788 f4
0.073342 Nc3
0.057878 Bc4
0.020348 Ke2
0.012238 Resign1
0.012149 Resign2
0.012060 Resign3
0.011444 d4
pick a number between 1 and 999999937 (inclusive)
Outcomes by integer range:
[ 1-257920041] Nf3, f4
[257920042-405014334] Nf3, Nc3
[405014335-520397133] Nf3, Bc4
[520397134-582580016] Nf3, f4, Nc3
[582580017-630265207] Nf3, f4, Bc4
[630265208-670272694] Nf3, Ke2
[670272695-694502026] Nf3, Nc3, Bc4
[694502027-718496799] Nf3, Resign1
[718496800-742316191] Nf3, Resign2
[742316192-765959326] Nf3, Resign3
[765959327-788775967] f4, Nc3
[788775968-811207805] Nf3, d4
[811207806-829040054] f4, Bc4
[829040055-844821126] Nf3, f4, Ke2
[844821127-854841809] Nc3, Bc4
[854841810-864223918] Nf3, f4, Resign1
[864223919-873536575] Nf3, f4, Resign2
[873536576-882779447] Nf3, f4, Resign3
[882779448-891543095] Nf3, f4, d4
[891543096-899498320] Nf3, Nc3, Ke2
[899498320-999999937] other
Hash of the complete table:
955f6aa8c060486bcda802339c6cf112ff98e1501b486f39076ca3d82746b439
Anyone worked out a formula for the probability of a move getting selected in terms of its last 4h avg probability p here? I feel I have a rough intuition but got lost in the weeds trying to model as a 2-3 trial multinomial, then realized must be a hypergeometric (trials are without replacement), then a non-central hypergeometric, so finally gave up on the precise derivation. I must be overcomplicating it, any thoughts?
@deagol I think the formula will be quite complicated, since it depends on probabilities of all other moves. If there is one big move (like here), the "smaller" moves have a better chance, by comparison.