Drop variant B, adopt Black-belt Exam defender, add one-sidedness metrics

- Remove variant B (Brown cap, +1 for higher beating lower) from rules,
  engine, bots and simulator; a higher belt beating a lower one gains 0.
- Final Exam: the defender fights as a Black belt (RULES.md v0.7). Ties to
  the defender and best-of-3 stay as simulator switches (`--exam`).
- Report stripe income per source as gains and losses.
- Add ten one-sidedness measures sampled at turn ends (lead gap, winner
  margin and lead share, halfway leader, last lead change, contention,
  rank swaps, leader Kumite losses, Exam challengers, winner pace).
- Plan: decisions D28-D33 and the detailed Phase 6.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

agents/plans/2026-09-25-dojo-board-and-sim.md

@@ -11,7 +11,7 @@ Deliverables:
 2. A text-based board format, with parser, full-board generator and validator.
 3. A first playable board.
 4. A rules engine + bots + Monte Carlo simulator to validate balance and pacing,
-   and in particular to choose between rule variants A and B.
+   and in particular to choose between rule variants A and B (B dropped, D28; now the Final Exam options, D29).
 
 ## Decisions log
 
@@ -36,7 +36,7 @@ Deliverables:
 | D17 | Meditazione: pass-through; ending on it forces one extra step | Developer rule. |
 | D18 | Central Dojo is one logical space, several entrances, Brown only, no exact count to enter | Avoids end-game "need exactly a 3" frustration. |
 | D19 | Final Exam: highest opponent defends; challenger wins → game; challenger loses → −3 and Start; defender gains nothing | Avoids the top-two flip-flop. Brown's extra stripes protect against the board, not the exam. |
-| D20 | Two rule variants to be decided by simulation: **A** (no Brown cap, higher-beats-lower 0) vs **B** (squares/cards cannot move 14→15, higher-beats-lower +1) | Neither is clearly better a priori. |
+| D20 | Two rule variants to be decided by simulation: **A** (no Brown cap, higher-beats-lower 0) vs **B** (squares/cards cannot move 14→15, higher-beats-lower +1) | Neither is clearly better a priori. *Superseded by D28.* |
 | D21 | Board 16×16, 4×4 Dojo in the centre, authored as one 8×8 quadrant rotated 3× (C4 symmetry) | Fairness by construction. Small asymmetries may be wanted later (see Q2). |
 | D22 | Tooling in Python, environment managed with **uv** | Developer choice. |
 | D23 | Rules drafted in English; Italian final edition generated separately | Developer choice. |
@@ -44,6 +44,12 @@ Deliverables:
 | D25 | Only the Tunnel square is optional. Sfida (square and card), Irimi and Tunnel Segreto are mandatory; every Nebbia card must be resolved | Sfida prevents stalling; Nebbia cards are chances that can also turn out badly. |
 | D26 | Tecnica cards are secret: drawn face down, others only know *whether* you hold one, a replaced Tecnica is discarded face down, revealed only when played | Hidden information and bluffing. Bots must not see opponents' Tecnica identity (Phase 4). |
 | D27 | Edge rules (RULES.md v0.5, inline + FAQ): boxed-in → move as far as possible (safeguard; boards have no dead ends); Uke-saved attacker stops on its previous square, turn ends, no square effect; extra-step rule for ending on any unfightable pawn; tunnel exits with a meditating pawn unusable; meditating players cannot defend the Exam; Tecnica window after both dice, attacker first; relocations never fight or trigger squares; Tsugi-ashi has its own origin; becoming Brown mid-move opens the Dojo | Developer confirmed all ten. |
+| D28 | Variant B dropped (developer, after the Phase 5 baseline): no Brown cap; a higher belt beating a lower one gains nothing. Removed from engine, bots, simulator, RULES.md (v0.6) | B made games shorter (13 vs 18 rounds) instead of adding an endgame challenge; the cap barely bit and the +1 applied to every such win. Too complex for what it gave. |
+| D29 | Final Exam options under test: **a** ties go to the defender; **c** the defender fights as a Black belt (defender +1 vs a Brown challenger); **d** best of 3. Combinable (`--exam ac`). Option b (no belt bonus in the Exam) not pursued. Developer favours c | Baseline pass rate ~80%: the defender is usually 1–2 belts below the Brown challenger, who also gets Senshu. |
+| D30 | Simulator reporting: income per source as gains and losses separately (Kumite is zero-sum, so its net hid the flow); standings sampled at the end of every turn; ten one-sidedness measures (see 5.4) | Developer request after the Phase 5 baseline. |
+| D31 | Final Exam rule: **the defender fights as a Black belt** (option c; RULES.md v0.7). Options a (ties to the defender) and d (best of 3) stay as simulator switches only; `--exam` lists the options in force and defaults to `c` | c gave a 44% pass rate, more distinct challengers (1.58/game) and closer endings; d alone raised the pass rate to 91%. |
+| D32 | Phase 6 targets confirmed by the developer as a starting point (table in Phase 6) | Q5. |
+| D33 | Fatica fix: test **option 2 first** — a chance square (stop on it, roll 1d6: 1–2 lose a stripe, 3–6 gain one) replacing Fatica and some Allenamento; then **option 1 must also be tested** — Fatica costs a stripe when walked through as well as when stopped on (breaks D10 for that square only). Options 3 (fewer paths: board rework) and 4 (fewer / once-per-room Allenamento) kept in reserve. The casual bot (6.0.1) is built regardless | Q6. Any on-stop penalty is avoidable when a move reaches ~24 end squares; the chance outcome cannot be dodged. Developer likes 1 and 2. |
 
 ## Phases
 
@@ -125,13 +131,68 @@ Deliverables:
   | Lead changes, final spread | 5.6, 9.3 | 3.5, 11.5 |
   | Wins by seat | 23–27% | 23–27% |
 
+- [x] 5.4 Follow-up to the baseline review (D28–D30):
+  - [x] remove variant B; `--variant` replaced by `--exam` (Exam options, `RulesConfig.exam_ties_to_defender / exam_defender_black / exam_rounds`); "turns on 14" metric removed with it;
+  - [x] income per source as gains / losses;
+  - [x] one-sidedness measures, sampled at turn ends: (1) gap 1st–2nd (mean per game) and winner margin over the best rival at the end; (2) share of turns the winner led; (3) halfway leader wins; (4) point of the game of the last lead change; (5) rivals within one belt of the winner at the end; (6) share of player-turns more than two belts behind the leader, and the worst player's share; (7) rank swaps between any two players; (8) Kumite lost by the leader; (9) distinct Exam challengers; (10) winner's own turns to reach Brown.
+- After 5.4 (300 games per option, 4 players, lineup balanced/farmer/aggressive, seed 0):
+
+  | Metric | none | a | c | d |
+  |---|---|---|---|---|
+  | Rounds mean (p10–p90) | 18.5 (14–23) | 19.3 (14–25) | 21.9 (16–29) | 18.0 (14–22) |
+  | Minutes mean | 67 | 70 | 80 | 66 |
+  | Exam pass rate, attempts per game | 81%, 1.24 | 67%, 1.50 | 44%, 2.28 | 91%, 1.10 |
+  | Distinct challengers per game | 1.13 | 1.24 | 1.58 | 1.06 |
+  | Winner margin at the end | 4.7 | 4.6 | 3.9 | 4.8 |
+  | Halfway leader wins | 40% | 41% | 40% | 41% |
+  | Rivals within one belt at the end | 0.32 | 0.37 | 0.62 | 0.30 |
+  | Player-turns out of contention | 22% | 22% | 21% | 22% |
+
+  Also measured: Kumite moves +0.44 / −0.40 stripes per turn; heuristic bots almost never stop on Fatica (square losses 0.0002 per turn vs 0.08 for random bots): with 2d6 and many paths an Allenamento is nearly always reachable. Seat 3 (last in turn order) won 28–31% in every option.
+
 ### Phase 6 — Balance experiments
 
-- [ ] 6.1 Variant A vs B.
-- [ ] 6.2 Kiai +2 vs +1.
-- [ ] 6.3 Player counts 3/4/6/8; start on 3 for 6+.
-- [ ] 6.4 Square mix tuning; board income per turn (target ≈ 0.8 stripes/turn net, to be confirmed).
-- [ ] 6.5 Update `RULES.md` with the decisions.
+**Method** (applies to every step):
+
+- Runs use `uv run dojo sim`. Default 1,000 games per scenario (a 25% win rate is then known to about ±1.4 pp); 4,000 games where seat effects are measured (about ±0.7 pp).
+- Compared scenarios share seeds (`--seed 0`), so differences come from the rules, not the dice.
+- Every conclusion is checked on at least two lineups (mixed `balanced,farmer,aggressive`, and one same-style lineup), because results depend on bot quality.
+- One change at a time. When a change is adopted, re-run the 6.1 baseline so later steps start from the current rules, and log the decision (D-number) here and in `RULES.md`.
+- Results go in this file as a table per step (command line, scenario, key measures).
+
+**Next action:** 6.0 (tooling), then 6.1. Everything up to D33 and RULES.md v0.7 is committed; commit only when the developer asks.
+
+**Targets** (confirmed by the developer as a starting point, D32):
+
+| Measure | Target |
+|---|---|
+| Minutes, 4 players | mean 60–90, p90 ≤ 110 |
+| Exam pass rate | 35–55% |
+| Halfway leader wins (4 players) | 35–55% |
+| Player-turns out of contention | ≤ 20%; worst player mean ≤ 35% |
+| Rivals within one belt of the winner at the end | ≥ 0.5 |
+| Win rate by seat, 4 players | each 25% ± 3 pp |
+| Win rate by bot style (mixed lineup) | spread ≤ 6 pp |
+| Games finished within 200 rounds | 100%, every lineup |
+
+**Steps:**
+
+- [ ] 6.0 Tooling needed by the experiments
+  - [ ] 6.0.1 "Casual" bot: the heuristic bot scoring only a small random sample of the offered moves (sample size is a parameter, default 6), as a stand-in for a human who cannot compare ~24 end squares every move. Added to `BOTS` as `casual`.
+  - [ ] 6.0.2 `--summary-csv PATH`: one row per scenario with the summary measures, to compare scenarios side by side.
+  - [ ] 6.0.3 Seat breakdown in the summary: per seat, mean final track, Exam attempts, and share of games where that seat defended the Exam (for 6.2).
+  - [ ] 6.0.4 Square reachability measure: share of moves where an Allenamento / Fatica end square is reachable, and mean distinct end squares per move (the Phase 6 probe, made a metric; for 6.4).
+- [ ] 6.1 Baseline on rules v0.7 (Exam c): 4 players, 1,000 games, lineups mixed / `balanced` / `casual` / `random`. Record the table; check it against the targets.
+- [ ] 6.2 Seat order (monitor; developer concerned): 4,000 games, 4 players, lineups mixed and `random`; 2,000 games at 3 and 6 players. If a seat is outside 25% ± 3 pp, diagnose with the 6.0.3 breakdown (hypotheses: moving last means seeing everyone else move first; Exam defender selection; Sensei / Peso cards) and bring candidate fixes to the developer. No fix without agreement.
+- [ ] 6.3 Style dynamics: same-style lineups (`farmer`, `aggressive`, `balanced`, `casual`) and one-against-three (`aggressive,farmer,farmer,farmer`, `farmer,aggressive,aggressive,aggressive`, `balanced,farmer,farmer,farmer`). Watch: all-farmer stalling (length, games finished, Kumite per round), a dominant style, time out of contention.
+- [ ] 6.4 Fatica and the square economy (D33). Each candidate is a board draft in `board/drafts/` (new square codes need `Square`, `board/FORMAT.md`, validator stats and `RULES.md` entries) and/or a `RulesConfig` switch, compared with the 6.1 baseline on square gains / losses per turn, reachability (6.0.4), game length, style win rates, casual vs heuristic gap:
+  - [ ] 6.4.1 Option 2, chance square: new code (proposal `C`, name to choose with the developer, e.g. "Sorte" / "Randori") — on stop roll 1d6, 1–2 → −1 stripe, 3–6 → +1. Draft: replace every Fatica and some Allenamento with it (start: all F plus about a third of A, keep the square mix inside the validator's Tatami range). Bot: value = expected change (+1/3 stripe, risk-weighted: gain 2/3, loss 1/3). Try variations of the split (e.g. 1–3 / 4–6) if income is off.
+  - [ ] 6.4.2 Option 1, Fatica on crossing: `RulesConfig.fatica_on_crossing` — each Fatica square entered during a move costs 1 stripe, **1 in total per square whether or not the move stops there** (developer, D33); stopping on it adds nothing more. Engine: apply in `_walk` per square entered (not on teleports / relocations, which never walk). Bot: count Fatica crossed in `_path_score`. Likely needs fewer Fatica squares; test on the current board and on a draft with fewer F.
+  - [ ] 6.4.3 Compare 6.4.1, 6.4.2 and both together; bring the table to the developer for a decision (then `RULES.md` and D-number).
+- [ ] 6.5 Home farming: after 6.4, if the own-quadrant share of square income is still above 60% (baseline: 71%), move Allenamento squares away from the Safe Rooms in a board draft (`dojo sim --quadrant board/drafts/...`) and compare. The board must still pass `dojo board validate`.
+- [ ] 6.6 Kiai +2 vs +1: 1,000 games each on two lineups. Watch the Exam pass rate, upset rate and how often a Tecnica turns a fight.
+- [ ] 6.7 Player counts: 3 / 4 / 6 / 8 players, start 0; plus start 3 at 6 and 8 players. Minutes per count; decide whether 6+ players start on Yellow.
+- [ ] 6.8 Consolidation: the final configuration at 3 / 4 / 6 / 8 players with all lineups, 2,000 games each; every target checked; `RULES.md` v0.8 with the decisions; open items moved to Phase 7.
 
 ### Phase 7 — Finalisation (later)
 
@@ -155,19 +216,24 @@ Deliverables:
 - Player count → focus 4, support 3–8.
 - Tests → the agent runs the suite (`uv run pytest`), plus `ruff check`, `ruff format --check`, `pyright`.
 - Minutes estimate → 45 s per turn, +30 s per Kumite.
+- Q4 Target net income per turn → current pace is fine: A already runs ~66 min (p90 ~85); the winner's pace is measured instead of a table average.
+- Variant A vs B → B dropped (D28).
+- Final Exam → the defender fights as a Black belt (D31).
+- Q5 Phase 6 targets → confirmed as a starting point (D32).
+- Q6 Fatica avoidable (bots stop on it once in ~4,000 turns; ~24 distinct end squares per move; Allenamento reachable on 79% of moves, Fatica never forced) → test the chance square first, then Fatica on crossing (D33).
 - Safe Room placement → the owner places the pawn on any square of their room (setup and when sent to Start).
 
 ### Open
 
+- Q7 Casual bot sample size: 6 offered moves is a guess at human play; revisit if 6.1 shows it is far weaker or stronger than the heuristic bot.
 - Q2 Board asymmetry: keep the quadrant as source of truth, or later switch to the full board as source of truth with a symmetry *report* (warnings) instead of generation? *(Deferred by the developer.)*
-- Q4 Target net income per turn — derived from 1–2 h and ~15–20 turns per player; confirm with first simulations. Baseline measured net income ≈ 0.56 (A) / 0.75 (B) stripes per turn.
 
 ### Risks
 
 - Movement enumeration: self-avoiding walks of length up to 12 can explode in open rooms. Keep rooms small; prune by outcome (destination + ordered opponents crossed + Dojo entry).
 - Engine speed ~1,400 turns/s (random and heuristic bots, real board). If Phase 5 needs more: precompute neighbour lists in `Board`.
 - Simulation conclusions depend on bot quality; compare several profiles before trusting a result.
-- Board draft 1 puts 4 Allenamento in each 3x3 room next to the Safe Room: possible "home farming" (see the Phase 2 review). Measured (Phase 5 baseline): square income is +0.38/turn in the own quadrant vs +0.14/turn elsewhere; 6.4 decides whether that is a problem.
+- Board draft 1 puts 4 Allenamento in each 3x3 room next to the Safe Room: possible "home farming" (see the Phase 2 review). Measured (Phase 5 baseline): square income is +0.38/turn in the own quadrant vs +0.14/turn elsewhere; 6.5 decides whether that is a problem.
 
 ## External documentation