Leader containment

Who should pay to slow the leader, and when should you decline to help?

The decision at the table

Moving the robber onto a leader can benefit every rival while costing you a better theft or production target. Refusing to trade with a leader may be sensible, but a blanket embargo can deny you the only route back into the game.

The mechanism to test

Estimate immediate winning routes, likely hidden potential, and whose turn arrives next. Compare the cost of blocking with your own continuation. Temporary cooperation creates a shared benefit, but the burden can fall unevenly. A threat to punish is credible only if carrying it out remains worthwhile when the time comes.

Proposed experiment

Compare own-resource robber placement, visible-point targeting, and threat-aware targeting that includes a cost of retaliation. Separately test public coordination language with the same actions. Hypothesis: threat-aware containment improves wins without systematically donating the game to the second-place rival.

Use a public timeline of robber moves, lost production, award transfers, and winning opportunities. Analyze the focal player’s win rate and the distribution of other winners. Predefine a diagnostic for avoidable rival wins; motive cannot be recovered from outcome alone.

First ablation

Switching every opponent term off changed the contrast by +0.000 wins per game (95% interval -0.105 to +0.105), and raising them by half through the aggression slider by +0.020 wins per game (95% interval -0.084 to +0.123): against builders that do not retaliate, containment terms neither help nor hurt at depth 2. Details and every run ID are in the ablation report; this is a development-tier result on one lineup.

Endgame racing

Three switches that treat the late game differently from the middle looked strong in one seating and carried no effect once the seating was averaged out. With the candidate always in slot 0, a race leaf against a near-winning leader won by +0.129 wins per game on 64 seeds (+0.029 to +0.228), counting the victory cards inferred from public purchases by +0.172 (+0.080 to +0.264), and biasing the robber and blocking roads toward the leader after two thirds of the game by +0.168 (+0.073 to +0.263). Those are the size of the arena's seating term. Swapped pairs on fresh boards 64 to 127, both halves on one engine, put the seating-corrected effects at +0.018 (−0.018 to +0.053), +0.006 (−0.030 to +0.041), and +0.012 (−0.018 to +0.041), each crossing zero: the switches stay off by default and the strength claim is withdrawn. The endgame report has the mechanisms, all twelve run IDs, and the seating terms; this is development-tier evidence on one lineup of fixed builders.

Robber placement and victim choice

The robber shortlist can target instead of just blocking the most pips. Three switches each beat the default shortlist on 256 paired development boards (blocking the leader's best hex +0.125, stealing the card this seat needs +0.160, sparing trade partners +0.117 wins per game, each interval excluding zero), but none held that strength on fresh seeds, where all three read between +0.035 and +0.039 with intervals crossing zero. The direction is consistent, nothing is confirmed, and the switches stay off by default. The default search lands on the leader's best hex on a quarter of its robber moves; the leader arm raises that to a third. The robber-targeting report has the arms, the plot, and where the robber went.

Third round: under the learned leaf

The four switches came back under the learned n-tuple leaf, each again one switch on top of the tables baseline, now as swapped pairs from the start and through three stages: development on the hand-leaf seeds 0-63, confirmation and population on fresh seeds 800-863, and a preregistered extension to seeds 864-927 for the two arms whose pooled builders effect stayed positive near zero (need and leader-biased endgame). All 36 cohorts completed. Pooled over stages, the seating-corrected effects are leader +0.007 and +0.031, need +0.016 and +0.009, threat −0.005 and +0.043, block leader +0.011 and +0.015 wins per game in the builders and population lineups, every interval crossing zero; the block leader population extension is the only single cohort to exclude zero (+0.033), and combining the two positive arms disagreed across lineups (+0.035 builders, −0.039 population). The mechanisms visibly move the robber, none moves wins, and no switch is worth the browser. The robber-tables report has every run UUID, the hand-leaf comparison, and where the robber actually went.

What could disprove it

Targeting the visually strongest player can miss hidden points. Successful containment is not necessarily a personal success. Keep kingmaking, spite, and rational self-interested blocking as hypotheses rather than labels inferred from one move.

All approaches · Player’s guide · Experiment program

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