Risk and timing

When should a player prefer reliable progress or a volatile route to victory?

The decision at the table

Two plans can have similar expected progress and very different chances of finishing before an opponent. A player behind may need a successful long shot. A leader may prefer a line that avoids handing anyone else an immediate win.

The mechanism to test

Compare distributions of terminal outcomes or time to victory, conditional on the public race and plausible hidden points. Include exposure to seven, robber targeting, and holding bottleneck cards. Risk sensitivity should emerge from the chance to win when that objective is represented well; a separate risk bonus is a hypothesis about an imperfect evaluator.

Proposed experiment

Compare mean heuristic value, a downside penalty, and a race-conditioned risk policy. Freeze beliefs and budgets. Hypothesis: race-conditioned risk improves wins across leading and trailing states, rather than merely increasing final points in losing games.

Show outcome distributions and a heatmap of decisions by estimated race position and hand exposure. In diagnostic continuations, keep original-state clusters intact; many rollouts from one position are not independent games.

First ablation

Switching the discard-exposure term off changed the contrast by -0.023 wins per game (95% interval -0.134 to +0.087); halving its weight through the risk slider changed it by -0.062 wins per game (95% interval -0.175 to +0.050). Neither is distinguishable from zero; the slider arm is registered again on fresh seeds. On 192 fresh seeds the slider arm was -0.055 (95% interval -0.118 to +0.008): leaning harmful, unresolved. Details and every run ID are in the ablation report; this is a development-tier result on one lineup.

A follow-up on discard decisions tested spending down when over the limit, ranking discards by the target preserved after expected production, and the risk weight at 0, 2, and 4: every contrast sat inside the turn-order seating term, and the swapped pair for the projected-discard arm corrects to -0.029 wins per game (95% interval -0.073 to +0.015). The mechanisms move the discard counts they target without changing results. See the hand-management report.

Third round

The same three mechanisms were retested under the learned n-tuple tables leaf, the protocol-arena baseline, with swapped pairs from the start: spend_down and discard_projection under the tables alone, and the hand_risk weight at 0 on the quarter blend (the blend the program adopted after the full blend screened at -0.207 wins per game). Across development, confirmation, and population lineups, every seating-corrected interval crosses zero: pooled, spend_down reads -0.020 wins per game over 192 seeds at 19% more decision time, discard_projection +0.006 over 320 seeds at no cost, and the removed risk term -0.001 over 192 seeds. Under the tables the search holds 4.8 cards at the roll and discards half as often as under the hand-written leaf, so the priced situation is rarer. No switch meets the browser threshold and no default changes. See the hand-tables report.

What could disprove it

Trailing positions are selected by earlier policy choices. A naive comparison of only trailing turns can confound risk choice with how the player got behind. Whole-game randomized arms remain the strength test.

All approaches · Player’s guide · Experiment program

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