Astra and Luna trade a combinatorial LMSR market (bayes-market, factored engine) over Turtel et al.’s 1,265 Polymarket test questions.
Each session sees 8 or 16 related questions and must output trades.
A trade sets a probability.
A conditional trade sets P(A|B), adding a dependency, so the market becomes a Bayesian network.
Three passes over all questions, each with new groupings and the moved market.
Brier by pass
Astra, N=8Luna, N=8
Brier of the market after each pass. Same market, prompt and budget. Astra N=16 reached 0.166. For reference on the same questions (Turtel et al. Table 1): Polymarket price 0.151, their RL-trained 14B model 0.191, o1 0.202, constant 0.5 0.250.
The Bayes nets it built
market P(yes) 0 1resolved YESstronger dependency
NHL 4 Nations Face-Off (Feb 2025)
Oscars 2025: Best Cinematography
Bitcoin on 28 Feb 2025
Real Betis vs Real Madrid
Four real components from Astra N=16 after pass 3. Fill = market probability; ring = resolved YES; edge width = |P(a|b=yes) − P(a|b=no)|.
Run
Linked questions
Dependencies
Components
Largest
Log loss, marginal
joint
Astra, N=8
506
413
153
8
0.518
0.491
Luna, N=8
265
168
99
8
0.609
0.599
Astra, N=16
456
404
111
12
0.508
0.477
Joint log loss beats marginal in every run: the dependencies carry information.
Caveat: the questions closed Feb–Mar 2025, inside both models’ training data; pass-to-pass change is the clean result.