Drop7 strategy catalog

This guide explains the strategy ideas represented in this repository, the evidence for each one, and the most useful directions that remain open. It starts with a plain-language overview and then uses more precise research language.

The problem in plain language

In Drop7, you choose one of seven columns for the next numbered disc. A 3, for example, breaks when it sits in an unbroken horizontal or vertical group of exactly three occupied cells. One break can make other discs fall and break, creating a chain. Breaks beside covered discs also crack or reveal them.

In the fast five-drop mode studied here, a new covered row rises after every five drops. This creates three competing jobs:

1. Stay alive. Keep stacks away from the top before the next row rises.
2. Open the board. Break and reveal covered discs, especially dangerous ones that are already high.
3. Prepare useful chains. Leave numbered discs in arrangements that can clear several waves later instead of making only the easiest break now.

A move can help one job and hurt another. Clearing one disc immediately may destroy a future chain. Building a chain may leave the board too tall to survive the next rise. Random future discs and random covered-disc reveals make the tradeoff harder.

The easiest way to understand the computer strategies is to imagine three kinds of player:

• A rule-following player gives points to board features such as low height, open edges, revealed covers, and chain readiness.
• A look-ahead player tries each legal column in a simulator, imagines several possible random outcomes, and chooses the move with the best future.
• A learning player plays or observes many games and learns which board patterns tend to lead to long survival or high scores.

The strongest established baseline in this repository combines the first two. It looks four decision steps ahead and uses a carefully designed board evaluation at the end of each simulated branch. It is called fair D4. “Fair” means that it uses only information a real player could know; it does not peek at the hidden random seed or future disc sequence.

Fair D4 is a baseline, not a solution to Drop7. On the corrected Hardcore scoring replay, its eight-game confirmation mean was about 401,000 points. It did not establish a million-point policy, and no search performed here proves that its moves are optimal.

What counts as evidence

Rules and mode

The research target is the numbered-disc-only, five-drops-per-rise mode called Hardcore in the original app and Blitz in some later descriptions. It awards 17,000 points at a level rise. Normal and Sequence modes begin with much longer levels and use a 7,000-point level award. Their score distributions and strategic constraints are different.

Some early experiments accidentally used the 7,000-point Sequence-style level award. Those runs can still show that one policy beat another on the same games, or that an idea was too slow, but their absolute scores are not evidence for the Hardcore target. See the mode correction and full experiment record.

Information boundary

A deployable policy may use the visible board, the next visible numbered disc, and the number of drops until the next row rise. It may not use the game seed, hidden covered numbers, future discs, future reveals, score history, or an offline scenario identity. Oracle experiments that use hidden futures are diagnostics, not playable strategies.

Status words used here

• Baseline means the implementation is verified and has survived the repository's comparison gates well enough to serve as a reference.
• Rejected means the tested version failed its frozen gate. It does not prove that every possible version of the broad idea is bad.
• Signal only means a diagnostic or small pilot was interesting but did not provide enough independent evidence or meet the runtime requirement.
• Proposed means there is not yet an implementation and result.

Small samples are especially dangerous in Drop7. A policy can win because one random game becomes unusually long. The strongest claims therefore require paired games, disjoint fitting and evaluation seeds, frozen thresholds, whole- game uncertainty estimates, censoring counts, and no tuning after a protected cohort is opened. The experiment record describes the repository's seed discipline.

Current reference: fair D4

The reference implementation is fair-only-depth4.cpp. It considers every legal root move, completes four decision plies, and uses five deterministic, stratified samples at chance nodes. Its leaf evaluation rewards build readiness and latent chain potential while penalizing height, covered-disc altitude, low-number clogs, danger near a rise, and other public risks. The search has fixed work and cache bounds and completes the promised depth instead of silently returning a partial iteration.

The most useful result is the corrected-score replay on an already-consumed eight-game confirmation cohort:

D4 changed about 34% of the decisions that D3 would have made. It used about 1.35 million logical work units per move and ran at roughly 0.74 moves per aggregate game-second in that replay. These data establish a strong local baseline and show that the fourth ply matters with this leaf. They do not establish optimality, a stable population mean, or a million-point result. The protected validation and final seed banks were not opened. Full context is in the D4 experiment and corrected Hardcore replay.

Strategy families already studied

Hand-built heuristics and shallow search

Idea. Describe a good board with understandable features, then choose the move that produces the best immediate or short-horizon evaluation.

The repository includes phase-aware scoring, tunneling, gray-disc throughput, virtual ignition, risk-sensitive planning, recursive potential, edge priority, cycle abstraction, rollouts, sparse expectimax, and evolved feature weights. The TypeScript implementations are organized under approaches/heuristic-search, with reusable evaluators in src/core/typescript.

Evidence. These policies were fast and helped identify useful concepts: height danger, reveal flow, build readiness, and the timing of a row rise all matter. Several became ingredients in later fair evaluators. As complete policies, however, they were brittle. Feature evolution often improved the fitting games but regressed on disjoint games, and nonlinear imitation of a search teacher showed state-distribution overfit. No tested hand-built policy displaced fair D4.

Conclusion. Keep interpretable features as diagnostics and leaf inputs. Do not treat a higher fitting score from another weight sweep as a new result without a fresh, paired gate.

Fair expectimax and deeper tactical search

Idea. Explicitly branch over legal moves and representative chance outcomes. This is the most direct way to value a move without knowing the real future.

Code for the reference searches and their extensions is under approaches/fair-expectimax. The major variants tested different leaf terms, transition rewards, seven rather than five chance strata, root downside/CVaR, CEM-tuned weights, selective extra depth, vertical-ladder energy, and full-width D5.

Evidence. Completed fair D4 was the clear positive result. Most additions made the policy worse on held-out or gameplay gates. In particular, more chance samples, explicit clear/reveal rewards, risk-sensitive root aggregation, and learned/tuned leaf changes did not reliably improve the whole game. Selective D5 variants failed gameplay screens, while full-width D5 variants were stopped by their runtime gates. “Deeper” was therefore not assumed to mean “better.”

Conclusion. Fair D4 remains the strongest known baseline. Exact or completed D5 is still scientifically interesting only if its cost can be reduced enough for a properly powered comparison.

N-tuple value learning and Q-learning

Idea. Learn values for overlapping board patterns. N-tuples can represent local shapes with far fewer parameters than a table containing every complete board.

Implementations under approaches/ntuple-rl include episodic and chance-state values, hierarchical position residuals, temporal-coherence updates, phase-conditioned values, Rainbow-style Q-learning, native PPO experiments, and a bounded two-rise rollout driven by an optimistic phase-conditioned n-tuple.

Evidence. The early hierarchical n-tuple plus depth-2 sparse search beat its own greedy value policy on a historical development probe, making it a useful research baseline. It was not selected after cleaner comparisons. A later temporal-coherence audit found and corrected a real shared-parameter update error, but the corrected policy still performed poorly. The phase-conditioned extension closed only a small fraction of the gap to D4. Rainbow-style Q-learning improved at an early training stage and then failed its larger gate. The optimistic phase-conditioned system completed 50 million training transitions, but its direct policy averaged 181,733 points and 56.4 moves on the mandatory 64-game gate; its two-boundary rollout fell to 113,644 points and 37.4 moves.

Conclusion. Pattern learning is computationally attractive, but the tested TD and Q-learning targets did not learn a reliable long-horizon action ranking. Future work needs better coverage of legal siblings and less extrapolation from the single action chosen by the data-collection policy.

Learned values, policies, and neural evaluators

Idea. Train a compact model to predict survival, score, or the advantage of one legal move, then use it directly or as a search leaf.

The experiments in approaches/value-policy-learning and approaches/d4-long-outcome cover Monte Carlo state values, structured and denoised NNUE-style models, DQN, policy cloning, sibling-advantage learning, D4 distillation, and long-outcome classifiers.

Evidence. Direct Monte Carlo value policies and structured multi-head models failed prediction or gameplay gates. A denoised public-state value once improved a weaker behavior policy on small training-range cohorts, but its veto of a stronger guided ensemble reversed on confirmation. Counterfactual- successor leaves, D4-Q clones, and learned 25- or 200-move sibling rankers usually improved fitting metrics and then regressed on whole-game-held-out roots. Behavioral cloning also struggled to match D2/D4 decisions on states generated by another policy.

The repeated failure pattern is important: learning the played action or a sparse sample of siblings does not provide trustworthy values for every action the learned policy will later consider. This is a coverage and distribution- shift problem, not merely a need for a larger network.

Conclusion. A learned leaf remains plausible, but a new attempt should begin with a data-coverage proof, whole-origin splits, calibrated uncertainty, and exact fallback parity—not with additional model capacity.

Policy-gradient and actor-critic methods

Idea. Learn the column choice directly from complete interaction rather than fitting a separate value for every candidate move.

Native and PyTorch experiments include PPO, direct PPO, curriculum options, oracle-manifold features, and a primal-dual actor-critic. See approaches/ntuple-rl/torch-ppo, approaches/ntuple-rl/native-ppo, and approaches/ntuple-rl/primal-dual-actor-critic.

Evidence. The public behavior clone missed its agreement gate and remained below fair D2. A direct PPO configuration first exceeded its memory ceiling; the admitted smaller run then failed its performance gates. The primal-dual actor-critic reached training but averaged about 176,000 points and 54 moves at its final calibration, so it never opened a gameplay screen. Oracle-manifold variants failed coverage or improvement gates.

Conclusion. The tested policy-gradient pipelines were neither competitive nor sample-efficient enough. Reconsider them only with a demonstrably better state representation, training curriculum, and resource plan.

MCTS, PUCT, and open-loop planning

Idea. Grow a search tree around the current board, sampling chance events instead of enumerating the entire stochastic future.

Implementations live in approaches/tree-search and the open-loop experiments in approaches/heuristic-search/open-loop.

Evidence. Observable-state UCT failed its held-out action-ranking gate. A confidence-gated MCTS override of fair D3 reduced the number of switches but still worsened held-out pairwise accuracy and regret. Scaling MCTS to more simulations, a longer horizon, a larger chance reservoir, and a fair cutoff made it imitate short-horizon D4 much better, yet made it worse at ranking 25-move outcomes. The audit traced the problem to the weak public D1 rollout and repeated empirical chance reservoir rather than simply too few simulations.

Conclusion. Increasing the tree budget alone is not a promising next experiment. MCTS needs a stronger continuing policy or long-value model and a less biased treatment of fresh chance events.

Long rollouts and terminal policy improvement

Idea. Keep fair D4 as the default, but compare close alternatives by playing them forward for several complete five-drop rise cycles.

The most direct implementation is d4-d2-rollout-veto.cpp. Related compression, learned-ranker, and policy-iteration experiments live under approaches/d4-long-outcome and approaches/terminal-policy-iteration.

Evidence. A public 25-move, seven-scenario continuation driven by completed D2 produced a striking single pilot: 404,047 points and 250 moves versus 159,616 and 105 for D4. That is signal only, not statistical evidence. The candidate was far beyond its runtime limit. Exact compression preserved its decisions but remained too slow. Completing four fitting pairs left the mean higher largely because of the original long game, failed the robustness gate, and included one loss and one tie among the three added games. Compact outcome rankers, teacher compression, survival rollouts, and regenerative policy- iteration panels did not reproduce the signal on disjoint data.

Conclusion. Multi-cycle comparison is one of the more informative open directions, but the existing implementation is neither fast nor robust enough. A successor must be cheaper by design and must not turn the one positive pilot into a tuning target.

Oracle and hindsight curricula

Idea. Let an offline teacher see the future random tape, learn what makes its actions successful, and distill that knowledge into a public policy that cannot see the future.

These diagnostics are under approaches/oracle-curriculum, including a perfect-information oracle, topology and accessible-energy residuals, DAgger, state curricula, and hindsight planning.

Evidence. The perfect-future oracle reached the move cap in a small cohort and averaged more than one million points even under the historical 7,000-point score. This proves that valuable long-horizon structure exists in the simulator; it is not a legal public strategy. Attempts to transfer that advantage through action distillation, topology summaries, accessible energy, synthetic tapes, or oracle-manifold features failed held-out label, ranking, or gameplay gates. Several apparent fitting or screen wins reversed on confirmation.

Conclusion. The oracle is useful for measuring information and representation gaps. Future distillation should first show that its public features predict oracle preferences across whole held-out games before it is allowed to control moves.

Constructive reservoirs and complete-cycle planning

Idea. Deliberately store high numbered discs in useful ladders or reservoirs, then release them in a long chain while continuing to expose covered discs.

The experiments are collected in approaches/constructive-reservoir. They include vertical reservoirs, discrete charge/dig/release/repair options, seven- to 27-move constructive spectra, terminal vetoes, and tail-focused CEM.

Evidence. Literal reservoir and viability controllers were weaker than fair D1. A constructive complete-cycle planner was a real improvement over D1: its first 32-game stage averaged about 267,000 points and 79.5 moves versus 157,000 and 49.9. But inserting the signal into D4 made frequent unstable switches and reduced the fitting mean from about 373,000 to 283,000. A 12-move horizon was better than seven on fitting data, while 17 and 27 were not monotonically better. The 12-move variants still failed their robustness gates. Explicit vertical-ladder features and relaxed build-then-release features also failed D4 transfer or held-out ranking tests.

Conclusion. Planning across a whole rise cycle contains information that one-ply heuristics miss. A visible reservoir shape by itself is not a reliable policy, and longer sampled rollouts are not automatically more accurate.

Conservative overrides and tail-risk objectives

Idea. Preserve a trusted search action unless a learned or simulated alternative clears a strict confidence, survival, and flow threshold.

This pattern appears in conservative fitted policy iteration, denoised-value vetoes, D4 long-outcome vetoes, structural terminal vetoes, regenerative panels, root CVaR, and tail-focused evolution.

Evidence. Conservative gates successfully prevented many weak policies from reaching protected tests, but the admitted switches were usually too rare, poorly calibrated, or unstable across whole games. Mean-only gains often hid damage to the lower tail. Root CVaR and tail-focused CEM did not rescue their underlying evaluators. The public regenerative B0 panel changed only 11 of 477 roots and was statistically indistinguishable from retaining D4, with weak split stability.

Conclusion. Confidence gates are a safety mechanism, not a source of new strategic information. They become useful only after the underlying challenger can rank legal siblings on disjoint data.

Compact evidence map

Strategies still worth considering

The following are research directions, not claims that an untested policy will work. Each should be preregistered and compared against unchanged fair D4.

1. Resolve AFBR-40's data closure before implementing it

AFBR-40 is a working-name proposal for a state-only, action-free public afterstate model. The intended target spans roughly 40 moves, or eight row-rise cycles. Training data would be successor-closed: every training decision would need the afterstates for all legal actions rather than only the action that the behavior policy selected. Fair D4 would remain the fallback.

This is only a proposal. Work stopped before implementation, and there is no source file, frozen protocol, checkpoint, or result. There is also a known feasibility problem: the available logged panels may not contain every transition and successor needed to construct truly successor-closed training and held-out examples without opening new seeds. That must be audited first. Calling a sparse sibling panel “successor-closed” would repeat the coverage problem seen in earlier value models.

A valid next step is therefore a read-only closure inventory: define the exact afterstate key, enumerate the required legal successors for each candidate root, and report the percentage whose outcomes can be reconstructed from existing artifacts. Only a complete or explicitly bounded construction should advance to a source and protocol.

2. Make multi-cycle sibling comparison affordable

The 25-move D4/D2 rollout and the constructive H12 experiments both suggest that decisions across complete rise cycles contain useful information. A new method could use a cheaper verified continuation, batched transitions, incremental D2 evaluation, admissible early elimination, or a model trained on complete sibling panels. It should preserve common random numbers across siblings and keep the current one-game pilot out of parameter selection.

3. Accelerate completed D5 without changing its semantics

D5 has not received a sufficiently powered, runtime-admissible comparison. Incremental board evaluation, compact transposition keys, reuse across chance strata, and measured cache locality are possible engineering directions. The first milestone should be bit-equivalence with the existing D5 decision on fixtures, followed by a prospective runtime projection. A faster D5 still has to beat D4; deeper search is not assumed superior.

4. Learn a leaf from complete legal-sibling data

Many failures came from training on the behavior action and evaluating unseen alternatives later. A better corpus would record every legal action at a root, use aligned public chance samples, attach multi-cycle outcome distributions, and split by whole origin game. Before gameplay, the model should beat D4 or exact D2 in top-action accuracy, pairwise accuracy, normalized regret, and calibration on every preregistered held-out half. AFBR-40 is one possible formulation, but not the only one.

5. Replace MCTS's weak continuation, not just its budget

A continuing public policy near D4 strength, an independently validated long-value cutoff, and progressive widening or fresh event-keyed chance samples could address the diagnosed MCTS bias. The key offline test is long-outcome ranking, not agreement with D4's short-horizon Q values.

6. Treat human strategy as testable feature hypotheses

High covered discs, weak edge connectivity, and simple 3–4-wave chains are plausible human ideas. They can be converted into reflection-safe public features and tested first on preserved sibling panels. This is more informative than copying a human rule directly into the policy. A feature should advance only if it adds stable held-out action-ranking information beyond D4/D2.

7. Study objectives after establishing action quality

Survival probability, lower-tail return, reveal throughput, and catastrophic rise risk remain valuable evaluation measures. Past CVaR and tail-CEM failures show that changing the objective cannot repair a weak action model. Once a challenger ranks siblings reliably, distributional gates and conservative D4 fallback can test whether it improves both the mean and the bad-game tail.

External prior work

These sources are useful context, but none supplies a benchmark directly comparable with this repository's public-information Hardcore protocol.

Approximate Q-learning report

Erez Klein and Ben Friedmann's Drop7 Q-learning report formulates the game as an MDP and uses linear feature approximation because exact state tables are infeasible. Its reward and reported units emphasize surviving moves, and its environment and evaluation protocol are not interchangeable with this repository's corrected Hardcore score benchmark. It is useful prior work for feature-based Q-learning and for explaining the state-space problem, not a numeric baseline here.

David Walton's Sequence-mode solver

David Walton's solver source and project write-up search fixed blocks of a known Sequence-mode disc stream. The reported play reached more than five million points, including long chains and repeated board clears. It demonstrates the value of macro-scale chain planning when the future sequence is known. Sequence mode exposes a fixed future and has different rise/scoring rules, so the method and score are not evidence for a public stochastic Hardcore policy. Its block-search idea is still relevant to bounded cycle planning if future knowledge is replaced by fair chance models.

Experienced-player strategy — anecdotal

The Drop7 strategy notes by an experienced player recommend prioritizing high covered discs and watching the less-connected edge columns in Hardcore mode. The author explicitly warns that the ideas may be wrong or luck-dependent. Treat them as anecdotal hypotheses, not experimental evidence. They are valuable because they suggest small, interpretable features that can be tested without giving the policy private information.

Recommended decision standard for the next candidate

A serious successor should satisfy all of the following before any million-point claim:

1. Use the verified rules in engine.hpp and pass native/TypeScript parity tests.
2. Make decisions from public state only and prove deterministic reflection behavior, legal fallback, and resource bounds.
3. Freeze the source, data manifest, model, search budget, thresholds, and seed ranges before evaluation.
4. Compare against unchanged fair D4 on paired, disjoint whole games; report score, moves, clear/reveal flow, lower-tail outcomes, uncertainty, and censoring.
5. Require stable improvement across preregistered halves or folds, not only a higher aggregate mean.
6. Keep protected validation and final cohorts sealed until the candidate and its qualification rule are fixed.

The complete chronological record, including exact commands, gates, artifacts, and negative results, remains in docs/research/history.md. This catalog is the map; the history is the audit trail. The ordered, hardware-aware next program is in the research roadmap.