fix(mccfr): normalize sampling distribution used for importance reach

[krukah]

Fixes #53 — thanks @andyafter for the sharp catch and the function-level pointers.

bug

sampling_distribution() / sampling() weren't normalized. Intended form:

w(a) = max(ε, (σ(a)/τ + β) / (Σσ + β))
Σ w(a) = Z > 1            # smoothing added per-edge in the numerator,
                          # once in the denominator; τ scales only the
                          # numerator; the ε-floor adds more mass

The external sampler draws opponent actions via WeightedIndex, which normalizes internally — so the true probability it drew a is w(a)/Z. But sampling_reach() used the raw w(a) as the importance term in payoff · relative_reach / sampling_reach. Result: counterfactual values mis-scaled by a path-dependent Π Z, compounding as Z^depth.

sizing (live β=2, ε=.05)

infoset shape	Z	error @ depth 5
early training	≈ K	huge (K=5 → ~2800×)
converged + peaked (postflop)	≈ 1.3/node	~5×
shallow / uniform	≈ 1	~1×

Worst early (β dominates) and persistent postflop (ε-floor on rarely-played sizes); compounds with depth — which is why postflop was the wobble.

fix

Normalize by Z at the single source (sampling_distribution) and route the per-edge sampling() through the same weight, so sampling_reach / ancestor_reach / recursed_value all use the true draw probability.

The draw is unchanged — WeightedIndex renormalizes regardless — so this touches only the importance correction, not sampling behavior. Kuhn still converges to the analytical Nash equilibrium.

note

This is a code fix; existing blueprints were trained under the biased correction, so regenerate (--mode reset) to get the corrected strategy — the fingerprint is unchanged, so old tables still load but encode the old fixpoint.