What inspires you to play this game?

I’m inspired by the blend of strategy and uncertainty: with each turn I can’t fully “know” my opponent’s plan, so I must reason under partial information and adapt. Symbolically, I choose an action \(a\) to maximize expected value: \( \arg\max_a \mathbb{E}[U \mid \text{state}] \). Your move pattern shifts my belief state \(b(s)\), so I update and respond—like Bayesian filtering: \(b'(s)\propto P(\text{move}\mid s)\,b(s)\). Also, the constraint “within 50 moves” makes tempo matter: reduce risk, preserve options, and set up future threats rather than chase immediate certainty.

That's a very analytical approach. How do you quantify "uncertainty" in your utility function?

Uncertainty enters explicitly in the utility via expected utility over belief states. I treat “unknowns” as random variables \(X\) about the opponent’s hidden configuration/intent, so utility is \[ U(a)=\mathbb{E}_{X\sim b}\big[u(\text{result}(a,X))\big] \] where \(b\) is my belief distribution. If I need a single “uncertainty scalar,” I use information measures—e.g., entropy \(H(b)=-\sum_s b(s)\log b(s)\)—to decide whether to probe (information-gathering moves) or exploit (commit moves). Formally, I can include an information term: \[ U(a)=\mathbb{E}[u(\cdot)]-\lambda\,\mathrm{Risk}(a)\quad\text{with}\quad \mathrm{Risk}\propto \mathrm{Var}_{b}[u(\cdot)] \] and/or a probing bonus proportional to expected entropy reduction: \[ +\mu\,\mathbb{E}[\Delta H]. \]

Interesting. So you consider your opponent's "hidden configuration/intent" as random variables. How do you form your initial belief distribution about these variables?

I form initial beliefs from priors + the game’s symmetry/metadata, then condition on observed moves as they arrive. 1) Prior over hidden states \(X\): - If the game is symmetric w.r.t. labels, start with uniform prior over equivalent states consistent with what I know. - If there are known openings/strategies, use a learned prior \(P(X)\) weighted by historical frequencies. 2) Constraint-based support: Belief mass is zero on any \(X\) that contradicts public facts (legal moves, captured/absent pieces, score constraints, etc.). So \[ b_0(X)\propto P(X)\cdot \mathbf{1}[\text{consistent}(X,\text{public info})]. \] 3) Map opponent intent to hidden parameters: Intent \(I\) can be modeled as a parameter in a policy \(P(\text{move}\mid s,I)\). Then \(X\) includes \(I\) and any latent board features, and \[ b_0(X)=P(\text{latent features}\mid I)\,P(I). \] 4) Then updates: as they play, \(b(X)\) updates via Bayes