Solitaire Cube: How This Guide Was Derived

Why this page exists

This page documents where the guide’s rules came from, how they were tested, and which details remain uncertain. You can use it to check the research before or after buying the guide.

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The simulator

I built a full Draw-3 Klondike simulator with Solitaire Cube’s scoring. The core scoring model, fit against 14 real game-over score panels, is:

base score =
  about 20 × cards brought into play (first tableau placements,
             face-down reveals, and first stock exposures)
+ about 85 × cards moved to foundation
− modeled stock-cycle penalties after the free passes

finish score =
  current score
+ floor(0.2 × seconds remaining × foundation count)

Model fit: This linear model explains the 14 real panels at an R-squared of approximately 0.997. An independent regression over the same panels produces slightly higher coefficients: roughly 90 per banked card and 23 per in-play card. The guide therefore quotes foundation value as a range of about +85–100 rather than a single number. Both fits agree on the direction and approximate size of the effect.

Key mechanics confirmed in the simulator and against observed play:

• The timer starts on the first move, not at deal time
• Legal “board-hop” routes (move a foundation-ready card onto the tableau first, then to foundation) collect both the into-play credit and the foundation credit. The observed gain was roughly +20 over a direct foundation move.
• Kings are the only cards that can move to empty columns
• Stock-cycle penalties apply after the free passes; the exact real-game penalty is not confirmed from panels, but the clock cost of pointless cycling is real regardless
• The time-bonus coefficient 0.2 is confirmed on finish-early games; a noisier regression over all games, including near-zero-time ones, fits 0.16. The guide’s advice to estimate and protect the bank holds under either value.

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Strategies compared

Three levels of play were benchmarked on the same deals:

1. Rule-based heuristic: essentially the system in the paid guide (reveal priority, redundancy-aware foundation safety, stock-cycle progress checks, guarded finish timing)
2. Determinized Monte Carlo search (PIMC): a strong computer player that samples possible hidden-card worlds and searches each one
3. Perfect-information oracle: a benchmark that sees every hidden card and searches for a full solve

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Key benchmark results

Solvability (100 deals, perfect information)

The oracle solved 72 of 100 test deals with access to all hidden cards. The other 28 resisted deep search with full information, which makes score extraction especially important on hard deals. Search depth limits this result: some of the 28 “unsolved” deals might yield to more computation, so 28% is an upper estimate of truly unsolvable deals.

Rule-based play versus deep search (200 paired deals)

Metric	Rule-based play	Deep search (PIMC)
Deals fully solved	7.0%	15.5%
Mean final score	1,611	2,097
Mean foundation cards	9.7	15.2
Head-to-head wins	68	120 (12 ties)

The human-playable rules captured a meaningful share of the game’s value. The search player’s advantage came mainly from estimating hidden-card odds more accurately than a person can. Its +486 mean score gap also shows that decisions on the same deal can be worth hundreds of points.

Redundancy-aware foundation rule

The guide’s foundation safety check (Rule 3) was benchmarked directly, added to the search player on 420 paired deals:

Metric	Improvement
Mean final score	+241 points
Mean foundation cards	+2.5
Additional deals solved	+15
Paired t-test	p = 0.002

A separate 300-deal paired run against the classic “move when safe” rule showed approximately +148 mean final score. Banking safely redundant cards produced a measurable advantage.

Finish timing

On a 300-deal sweep, a strategy that played until the clock ran out banked zero time bonus on the large majority of unsolved deals. The guarded finish policy from the paid guide gained roughly +235 to +240 points per deal over that baseline while almost never hurting a deal that still had play left.

Archival note: the finish-timing and foundation-rule sweep summaries are recorded in the research code and notes (the +235 figure appears in a strategy module docstring, with parameters: n=300 deals, seeds 0–299). The raw per-deal output files for those two sweeps were not archived the way the 200-deal paired benchmark was. I have kept the numbers here with that caveat because the methodology is clear and the finding is corroborated by the 200-deal benchmark.

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Limitations

• The stock-recycle penalty is a modeled prior, not a measured value. Real panels do not expose it cleanly. The guide’s advice does not depend on the exact number: cycling a dead stock costs clock regardless.
• The time-bonus coefficient (0.2 vs. 0.16): both fits are reported. The guide says “about 0.2” for the finish estimate because that is confirmed on finish-early games, where finish timing matters.
• The finish-timing (+235) and foundation-rule (+241) numbers are documented in code with clear parameters; the raw sweep files were not separately archived. See the archival note above.
• The board-hop +20 is a real-game observation. The simulator books the into-play credit at draw time rather than placement time, so it does not directly model routing order. The +20 board-hop delta comes from observed play, not simulation.
• The 72% oracle solve rate is bounded by search effort. Treat 28% as an upper estimate of truly unsolvable deals.

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The paid guide contains the exact finish guards, human foundation safety check, board-hop routing decisions, and practice drills.