Chance-node decorrelation and search depth compound rather than substitute
Factoring the fair search's chance node into independent next-disc and reveal draws pays at every depth, so applying it on top of the fourth ply raises mean score over the same four-ply search with a single reveal sample by a paired margin whose one-sided 95% whole-game bootstrap lower bound is above zero.
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Technical recordThe registered claim, mechanism and falsification criteria
- Claim
- Factoring the fair search's chance node into independent next-disc and reveal draws pays at every depth, so applying it on top of the fourth ply raises mean score over the same four-ply search with a single reveal sample by a paired margin whose one-sided 95% whole-game bootstrap lower bound is above zero. The depth-3 gain finding-09 measured (+64,116 with a lower bound of +7,475 from one to six reveal samples) is therefore an increment that adds to depth rather than an alternative way of buying the same thing.
- Mechanism
- finding-09 diagnosed a specific defect: the reference search indexed the next-disc draw and the covered-disc reveal with the same counter, so with seven samples it saw seven of the 49 joint outcomes and those seven were perfectly correlated. A move whose value depends on the combination could not be evaluated. That defect is a property of the chance node, not of the horizon, and the frozen four-ply search contains exactly the same defective node. If the defect is what the extra reveal samples repair, repairing it inside a deeper search should be worth at least as much as repairing it inside a shallower one, and the two axes should add. The competing account is that depth and chance-estimator quality are exchangeable ways of spending one budget - both ultimately buy a less biased estimate of the same expectation - in which case paying for both at once buys little beyond paying for either.
- Falsification criteria
- The paired depth-4 (N=7, M=2) minus depth-4 (N=7, M=1) score delta over the complete 64-game cohort has a one-sided 95% whole-game bootstrap lower bound at or below zero.
- The depth-3 reveal ladder stops ordering with joint chance coverage: taking reveal samples from six to twelve (85.7% to 100% joint coverage) does not raise the paired mean over the six-sample arm.
- Any arm completes a decision below its requested depth, which voids that arm.
- The joint-coverage attribution fails: an arm with higher joint (disc, reveal) coverage scores below one with lower coverage at the same depth and the same work bound.
- Information class
- public-policy
- Lifecycle
- assessed
- Assessment
- not-supported-as-tested
- Evidence tier
- public-development
- Dependencies
- none recorded
Agent contextHow to extend this record
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Registered by Claude Code / claude-opus-5[1m].