The solutions, by the numbers

One subgame per (score, dealer assignment, turn-up class): 1,296 in all, each spanning 140,118 distinct deals once the lossless equivalences collapse the raw card combinatorics. Within a subgame the tree grows with how much of the raise ladder is still alive.

Except during mão de onze, the engine still permits the ordinary raise ladder. The solver removes a higher re-raise only once lower score + current stake ≥ 12: at that point the current hand already decides the match for either winner, so escalating adds no prize and no rational fold leverage. This is value-exact pruning, not a claim that those buttons are illegal. The diagonal endpoints are compact anchors: 0 × 0 → 2 × 2 also covers unequal scores such as 2 × 10 and the mirrored 10 × 2. The table shows what the solver keeps with vira 4, for one dealer orientation, across every abstract deal.

Exact vira-4 counts; other turn-up classes have not all been counted at every tier.

Those are the raw trees. The production tree also removes provably irrelevant branches — score-aware raise pruning plus proof-scoped prunes — cutting the deepest tier from 6.70B to 3.80B nodes (756.8M information sets) with no change in exactness. The shipped charts live in the two smallest tiers: an eleven root is a 49.6M-node tree, and a truco-band spot like 10×10 is a ~200M-node tree over 39.5M information sets.

Exact strategies exist for 216 of 1,296 subgames: all 23 role-ordered score states where mão or pé is on 11, across all nine turn-up classes (207), plus 10 × 10 across all nine classes (9). The other 1,080 have not been solved as a full tabular grid.

The release behind that coverage stores 225 artifacts — one per (score, turn-up, dealer seat): every 11 × N score in both dealer orientations, plus 10 × 10 in one. The two counts differ by exactly the symmetric 11 × 11, whose two orientations are the same game with the seats renamed — nine artifacts covering nine subgames counted once. The Study Lab itself bundles a 15-chart subset of the release, all with vira 4.

The current Study release carries 225 solved spots — the per-(score, turn-up, dealer) artifacts of the coverage above. Each spot ships with an exact self-certification: a genuine best response is computed against the exported strategy from both seats, and the average of the two gains is the spot's exploitability ε, on the scale where ε 0.01 ≈ 0.5 percentage points of match-win chance. By how the spot was produced:

Transfers had to clear hard gates — raw ε ≤ 0.01, purified ε ≤ 0.004, weighted mean per-node best-response gap ≤ 0.25 pp — or the worker discarded the candidate and solved the spot natively. Native solves converge much tighter globally (median ε 0.00001), but 28 of them carry broader per-node profiles — which is exactly what the lab's per-cell ≈ badges exist to surface.

Solve two neighboring subgames independently to convergence and compare them row by row. Two averages tell different stories: over all table rows, and weighted by how often play actually reaches each row. TV is total-variation distance — the share of probability mass that would have to move to turn one row's mix into the other's (0 = identical).

The asymmetry is the finding. Changing the turn-up class barely moves play anywhere: on-path distance stays near 0.02 and the root decision shifts by 0.005. Changing the score concentrates its whole effect exactly where play goes — the root accept/fold row moves by 0.196, depths 1–3 by 0.12–0.18, and only about half of play mass sits on effectively identical rows. A small, shallow, score-sensitive core carries roughly half of the played game.

Call a row pure when its biggest action takes more than 99% of the mix. Mixing dominates the tables — but not the played game:

Half-plus of actual play sits at (near-)pure decisions — the same rows that agree at 99.99%+ across neighboring solutions. The complement is just as real: roughly 45% of play mass is genuinely mixed, the part of optimal truco that resists crisp human rules. Tighten “pure” to 99.9% and on-path purity drops to 50.7% (11×10) and 39.3% (10×10) — crispness softens with the cutoff.

The solver is synchronous CFR+, adopted after measuring a ~10× cut in iteration count at the same certified ε. The 225-spot release was built by four preemptible cloud workers in 3–4.5 hours each — transferring a neighbor's solution wherever the certificate allowed (85% of spots) and re-solving natively where it didn't — for on the order of $5 of compute. A truco-band warm solve now peaks at ~16 GiB and ~18 minutes; a chain of memory work brought the same job down from a 75-GiB machine class.

Certifying is cheap next to solving: one exact whole-game best response of the deepest tier — the full raise ladder from 0×0, 14.6 billion node visits — fits in 8.1 GiB and under three hours. The frontier is the deep solve itself: merely building the 0×0 tree in memory needs over 150 GiB, which is why the lattice below the shipped bands is approached bottom-up, subgame by subgame.