This is the integrated, tactical playbook. It merges the Merchant and Sheriff strategies, the bribe math, bag-loading rules, psychological play, and explicit corrections for game length by player count so you can schedule trust-building, deception windows, and inspection cadence precisely.
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$P$ = penalty total on declared legal cards (coins). -
$M$ = penalty total on misdeclared/illegal cards (coins). -
$p_T$ = sheriff’s subjective probability the merchant is truthful (0–1). -
$B$ = bribe offered (coins).
Sheriff:
Accept bribe if
Merchant indifference bribe:
Merchant cap (never overpay):
All decisions are EV-driven; psychology shifts perceived
Use these exact round budgets to plan reputation and deception windows.
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3 players → 9 rounds (each player Sheriff 3 times).
- Trust-building window: Rounds 1–2.
- Mid-game deception: Rounds 3–6 (one clear push).
- Endgame control: Rounds 7–9 (bonus denial critical).
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4 players → 8 rounds (each player Sheriff 2 times).
- Trust-building: Round 1.
- Mid-game deception window: Rounds 2–5 (one concentrated push).
- Endgame: Rounds 6–8 (two rounds to force bonus decisions).
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5 players → 10 rounds (standard) — if your table uses the standard 2× Sheriff rotation.
- Trust-building: Rounds 1–2.
- Two deception windows: Rounds 3–5 and 6–8.
- Endgame: Rounds 9–10 (bonus denial & final pushes).
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5 players → 5 rounds (compressed variant) — some groups compress to one Sheriff rotation.
- No long trust-building. Play accelerated: early deception, mid-game scramble, immediate endgame. Increase inspection frequency.
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6 players (Deputies module) — mechanics change (two inspectors). Treat every merchant bag as having higher inspection probability; bribe must sway two minds or be structured to make one deputy act alone. Round count and end condition depend on table rules—treat as high inspection risk environment.
Tactical implication: plan reputation investments proportional to number of rounds. More rounds → invest in reputation early; fewer rounds → front-load aggressive plays.
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Early phase (build
$p_T$ ): be honest.- 3-player: Rounds 1–2 honest.
- 4-player: Round 1 honest.
- 5-player standard: Rounds 1–2 honest.
- Compressed: 0–1 honest rounds (if any).
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Mid phase (harvest trust with calibrated lies): insert small contraband mixes (one illegal + 3–4 legal). Use one or two deception windows depending on total rounds.
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Late phase (positioning for bonuses or comeback): shift according to score — if leading, revert to honesty; if trailing, increase contraband density and accept higher bribes subject to
$B_{\max}$ .
- Prefer 1 illegal + 3–4 matching legal. Reason:
$M$ small,$P$ large → low$B^*$ . - Never load a bag where
$B^* > B_{\max}$ . If computed$B^* > B_{\max}$ , repack. - Avoid concentrating contraband in a single bag unless you have strong information that
$p_T$ is high (≥0.7) or Sheriff is broke/out of motivation.
Given computed
- If
$p_T \ge \dfrac{M}{M+P}$ → offer 0 (sheriff loses EV opening). - Else compute
$B^* = p_T(-P) + (1-p_T)M$ and offer$B = \lceil B^* \rceil$ , but cap at$B_{\max}$ .
Practical quick table (rounded):
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$p_T \ge 0.5$ → 0–1 coin. -
$0.35 \le p_T < 0.5$ → 1–2 coins. -
$0.20 \le p_T < 0.35$ → 2–3 coins. -
$p_T < 0.20$ → 3+ coins or repack.
Bag: declare 5 Apples (Apple penalty 2 each →
- Break-even trust:
$p_T^c = M/(M+P) = 6/16 = 0.375$ . - If
$p_T \ge 0.40$ → offer 0. - If
$p_T = 0.30$ →$B^* = 1.2$ → offer 2 (round up). -
$B_{\max}$ computed with values: pass goods value 13, caught value 6 →$\Delta_{\text{goods}}=7$ ,$B_{\max}=7+6=13$ . So offering 2 is well under cap.
- 3 players: be stingy with lies; sheriffs inspect often. Use one reliable deception window only.
- 4 players: follow main guide. One or two deception pushes.
- 5 players standard: you can execute two deception windows; reputation decay slower.
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5 compressed / 6 players: push earlier, expect more inspections; favor smaller
$M$ and higher reliance on honest passes for penalty income.
For each bag compute:
Open if
Round-count impact:
- In short games (compressed 5-player), prioritize immediate EV and bonus denial; less tolerance for reputation manipulation.
- In long games (3-player, 9 rounds), use signaling early, conserve coins mid-game, then ramp inspections late.
Order by:
- Player who threatens your lead (highest current score / nearest bonus swing).
- Player uninspected for multiple rounds.
- Player with low
$P$ and suspected high$M$ . - Pattern-breakers (card type/count sudden changes).
- Low bribe offers when your EV indicates inspection profitable.
- Early: accept small bribes to seed coins and set baseline.
- Mid: raise minimum bribe acceptance threshold publicly (e.g., “Under 3 isn’t worth my time”) to increase expected merchant payments.
- Randomly inspect a truthful bag occasionally to signal unpredictability — lowers overall lying at modest coin cost.
- If leading: accept bribes more often; deny large swings only if inspection secures a direct denial of an opponent’s bonus that would overtake you.
- If trailing: inspect aggressively; accept short-term coin losses for higher variance to flip standings.
- Always treat potential King/Queen flip as additional
$M$ when computing EV: add the expected point swing converted to coin-equivalent to$M$ .
- Bribe must satisfy two inspectors or be structured so one deputy accepts and acts alone. Anchor bribe higher. Overall inspection probability increases; tighten acceptance thresholds.
For each opponent keep three quick counters:
- TruthfulCount
$T$ (times inspected and truthful) - LieCount
$L$ (times inspected and lying) - LastInspectedRound (round index)
Compute
- Merchant: keep ~10–15 coins mid-game to sustain bribes and penalties.
- Sheriff: keep ~10 coins to credibly threaten inspection. If broke, anchoring and signaling lose power.
- Public math: state your estimate of
$p_T$ and the computed EV to shift perceptions. - Praise someone you’ve just caught (signals impartiality).
- Token bribes: merchants offering 1 coin often expect leniency; accept occasionally to build funds and maintain unpredictability.
Context: Round 4 of 8. You are Merchant, behind by one bonus. Sheriff is conservative (has paid once earlier). You estimate
Bag: declare 5 Apples →
- Break-even
$p_T^c = 6/16 = 0.375$ . Your$p_T = 0.45 > p_T^c$ → Sheriff loses EV opening. Offer 0 (or token 1 to be safe). If you need the Apple set for a King bonus next round and$\Delta_{\text{bonus}}$ is large, you can offer 1 coin to secure pass certainty.
Alternate (if Sheriff looks suspicious;
- Compute
$B^* = 0.30(-10) + 0.70(6) = -3 + 4.2 = 1.2$ . Round up → offer 2. Compare to$B_{\max} = 13$ → safe. Offer 2, keep a chip reserve.
Sheriff reaction (if you are Sheriff instead):
- With
$p_T=0.30$ ,$EV_{\text{open}} = 1.2$ . Accept no bribe <2; inspect if merchant offers 1. If merchant offers 2, accept it.
Merchant:
- Compute
$P, M$ . Compute$p_T^c = M/(M+P)$ . If estimated$p_T > p_T^c$ , offer 0. Else offer$\lceil p_T(-P)+(1-p_T)M\rceil$ capped at$B_{\max}$ . Repack if$B^* > B_{\max}$ .
Sheriff:
- Compute
$EV_{\text{open}} = p_T(-P) + (1-p_T)M$ . Inspect if$EV_{\text{open}} > B$ . Prioritize high-score threats, uninspected streaks, and pattern-changers. Adjust inspection frequency by round-budget position.
Round budgeting:
- 3-player (9 rounds): build trust early, one midgame push, aggressive endgame.
- 4-player (8 rounds): single deception window midgame, two endgame rounds.
- 5-player (10 rounds): build trust, two deception windows, last two rounds decisive.
- 5 compressed/6 players: accelerate deception; expect heavy inspections.
- Update ledger
$T, L$ . Compute$p_T$ . - For your candidate bag compute
$P, M, V_{\text{pass}}, V_{\text{caught}}$ . - If Merchant: compute $B^{}$, $B_{\max}$. If $B^{} > B_{\max}$ → repack. Else offer
$\min(\lceil B^{*} \rceil, B_{\max})$ . - If Sheriff: compute
$EV_{\text{open}}$ . If there’s a bribe$B$ , accept when$B \ge \lceil EV_{\text{open}}\rceil$ ; otherwise open. Use priority tiebreakers. - Adjust based on round number and standings (apply endgame bias to deny bonuses when necessary).
This guide is the full operational manual: the formulas, the heuristics, the round-aware timing, and the examples to execute at the table. Use the ledger and the round budgets to convert the abstract EV rules into exact, repeatable actions.