Risk sensitive

Judge a column by how bad its worst futures are, not only by how good its average future is — because one collapse ends the game and there is no next game to average it against.

The intuition

An ordinary expectimax search values a column by the average over everything that could happen next. Averages are the right thing to maximise when you get many independent tries. In Drop7 you get one: a move whose average is excellent but which loses the game one time in eight is not an excellent move, because the losses are permanent and the score stops.

The fix borrowed from finance is conditional value at risk: rank a column by the average of its worst quarter of outcomes instead of the average of all of them, or by a blend of the two. Set the risk weight to 0 and you have the ordinary search back; set it to 1 and the policy only cares about disasters; anything in between trades mean for safety.

How it works, step by step

1. Read the public position — board, next disc, rise clock.
2. For each legal column, build a fixed set of scenarios — sampled immediate chance outcomes, the same set for every column so that the comparison is paired.
3. Continue each scenario with an ordinary risk-neutral search of a couple of plies, using stratified samples at its chance nodes.
4. Collapse each column's scenario outcomes into a mean, a lower quantile, and a conditional-value-at-risk over the worst tail fraction; select on a blend controlled by one number.
5. Play the winning column.

The planner takes a solver-local seed only. It refuses the game seed, and no future disc or reveal tape can reach action selection.

What happened, in plain English

Every setting of the risk dial was retired. The best mild-risk configuration — the one that only leans slightly toward caution — still finished behind the plain phase-conditioned baseline it was tested against, and the strongly risk-averse settings were worse.

The same idea was tested separately, and much more thoroughly, inside the reference search, where it is recorded properly. There it did not merely fail to help: it made the policy worse on every measure at once, including the lower tail it was designed to protect.

The technical record

This lab. The experiment index records it as rejected, task-record only: "the best mild-risk pilot trailed the phase baseline." Task-record only means the pilot is reported in a research conversation and was never promoted into the experiment history; no score, move count, or per-game outcome for it is retained in this repository.

Repository-verified from the source. main.ts sweeps risk weights 0, 0.5, 1 with a 0.25 tail fraction, seven root scenarios, a two-ply risk-neutral continuation and three chance samples per continuation node, over 4 pilot and 16 confirmation games at a 500-move cap, with 500,000 work units for the risk planner against 1,000,000 for the baseline and a REQUIRED_MEAN constant of 300,000. Pilot games come from 0x3d70… and the probe range is 0x4d70…; 0x5d70… is explicitly forbidden. The comparator is the phase-horizon evaluator inside a sparse search. src/core/typescript/risk-sensitive-planner.ts documents the boundary directly: "Solver-local seed; no game seed or future chance tape is accepted."

The properly recorded sibling experiment. fair-root-risk.cpp in the fair expectimax family applied the same mechanism to the reference search with a preregistered root utility of 0.75 × mean + 0.25 × CVaR25 over seven scenarios per action. It is rejected, ledger-recorded. On its eight-game screen the unchanged depth-3 fair search averaged 176,819.75 points and 114.125 moves; the risk version averaged 87,112 points and 61.5 moves — a paired difference of −89,707.75 points and −52.625 moves, losing seven of eight games on both measures. Clear and reveal throughput fell from 2.043/1.141 to 1.730/0.945 per move and mean maximum chain fell from 7.875 to 5.125. It switched away from the fair recommendation on 28.25% of decisions. Confirmation seeds were not read and nothing was retuned.

That screen is a historical 7,000-point Sequence-scored run: the level award was 7,000 rather than the 17,000 of the Hardcore mode studied here, so its absolute scores are not evidence about the million-point target. The comparison between the two policies on the same eight games, and the throughput and chain measurements, remain valid (mode-specific scoring correction). Eight games is a small screen.

What this taught us, and what is still open

• Changing the objective does not repair the action model. The strategy catalog states the conclusion for the whole conservative-override family: confidence gates and tail objectives are a safety mechanism, not a source of new strategic information, and they become useful only after the underlying challenger can rank legal siblings on disjoint data.
• Mean-protecting and tail-protecting came apart in the wrong direction. The recorded root-CVaR screen lost mean score, survival and flow. A risk-averse policy that dies sooner is not being cautious about the right thing — with a short horizon, "avoid the worst sampled outcome" is a statement about sampling noise as much as about danger.
• What is still open. Distributional gates are still in the recommended decision standard for a future candidate — but as a check applied after a challenger already ranks moves well, not as the thing that makes it rank moves well.