---
title: The fast engine learns reveal sampling
family: lifetime-objective
summary: Ports the native factored chance node (N disc strata x M reveal samples) into the fast memo engine, trace-equivalent to the C0 search at a fraction of the cost.
status: completed
evidence: repository-verified
reads: public
---

The C0-positive D3 N7M6 policy lived only in the native factored search, at
seconds per move; the fast engine could only play M = 1. This port teaches the
fast memo engine the factored chance node so the exact same decisions cost
milliseconds instead.

<EvidenceLabel status="completed" evidence="repository-verified" reads="public" />

<Callout title="An engineering result, not a strength result" tone="info">
Nothing about play changes. The port is accepted only as trace-equivalent to
the native factored search: the same chosen column, the same logical work
count and the same completed depth on every compared decision, across the
whole d3/d4 x N5/N7 x M1/M2/M6 grid, plus full replays of retained C0 games
that reproduce the recorded final scores exactly. Any deviation would have
reclassified this as a new algorithmic candidate
(EX-20260823-fast-m6-reveal-sampling-port-be23e203).
</Callout>

## The traversal order being preserved

At every action node the search tries the legal columns in the frozen order
3, 2, 4, 1, 5, 0, 6. Each move is then scored under a factored chance node:
the outer loop runs the N next-disc strata, the inner loop the M reveal
samples, and iteration (d, r) is scenario s = r*N + d of T = N*M. The cascade
reveal values come from the stratified stream indexed by (state seed, s, T)
with events consumed in cascade order; the successor's next disc comes from
the disc stream indexed by (state seed, d, N) and never depends on r. Work is
counted once per scenario immediately after the move resolves; the budget is
checked before every scenario, node and leaf; the action value is the mean
over all T scenarios. At M = 1 this collapses to s = d, T = N — the untouched
fast-search path, kept verbatim behind an M == 1 branch.

## Why the one-entry leaf memo survives M > 1

The memo (audit-06) keys on the full board via memcmp plus moves-to-rise and
recomputes only the next-disc term. A sampled reveal that changes the board
therefore misses — it can never alias across reveal samples — and a reveal
sample that leaves the board unchanged hits, exactly as at M = 1. The memo
sits below the search's work increment, so it cannot change any recorded
observable; it stays enabled for M > 1, and the gate proves memo-on/off trace
identity across the whole grid.

## Sources

- `fast-factored-search.hpp` — `FastFactoredSearch`: the fast memo engine with
  the native factored chance node; M == 1 short-circuits to the verbatim
  fast-search loop
- `gate.cpp` — grid trace equivalence vs the genuine native source, C0 replay
  finals identity, M = 1 bit-identity regression, determinism/mirror/memo
  gates, play- and continuation-duty timing
- `build.sh` — generates the no-entry native copies with machine-checked
  diffs (entry-point rename plus `thread_local` on the five diagnostic
  atomics only)

Gate artifacts: `runs/RUN-20260823T215500Z-sol/fastm6/`.