1
Choose the phrase
The app chooses three word-list entries independently with Apple’s secure random API. Duplicate spellings are possible.
Full Deck Solitaire · Backgammon
Don’t take the dice on faith.
Paste the exact three-word seed shown by Full Deck Solitaire. This standalone page reproduces the published deterministic dice stream. It depends only on the seed and stream position—not the player, board, score, or AI difficulty.
Exact seeded dice stream
Seeded roll 1
apple-river-sunset
Game roll 1
32-bit seed
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Hex
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Reference checks
Running reference vectors…
Checking standard MT19937 plus native-derived phrase and dice fixtures.
Die mapping
No modulo bias
The top four 32-bit values are rejected before mapping the rest evenly to faces 1–6.
Source snapshot
Two published files
The complete dice roller and seed generator are pinned below with source-file fingerprints.
Roll ledger
Follow every value.
Roll N is the Nth rollDice call in chronological order. The stream
does not assign rolls to players. A double uses two dice and grants four moves.
| Game roll | Seeded roll | Die 1 | Accepted raw #1 | Die 2 | Accepted raw #2 | Usable moves |
|---|
The raw values are unsigned 32-bit outputs after any rejection. Rejections are expected only about once per 1.07 billion die rolls.
Long-run balance
Random does not mean alternating.
A fair die has no memory. Repeats, runs, and lopsided short samples are expected; a streak is not evidence of bias by itself.
Dice sampled
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Two per roll
Doubles
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Expected 16.67%
Largest deviation
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From exactly one sixth
Rejected values
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Removed to keep faces even
This chart is a useful sanity check, not a proof by itself. Short samples can be uneven and still be fair.
Published implementation
Read the published RNG source.
These are the only two Full Deck Solitaire game-source files published here: the complete Objective-C dice roller and seed-phrase generator. No board, rules, AI, UI, or other commercial game source is included.
2
Hash to 32 bits
The lowercased ASCII phrase is converted to one reproducible 32-bit number with DJB2.
3
Advance MT19937
The standard Mersenne Twister produces a deterministic stream shared by both players in chronological order.
4
Map without bias
Four excess values are rejected, then the remaining range divides evenly into the six die faces.
What this verifies
- The published algorithm produces the exact sequence shown for a seed.
- Each accepted 32-bit value maps evenly to one of six faces.
- In seeded games, the roller has no player, board, score, or AI-difficulty input.
Important limits
- MT19937 is deterministic pseudorandomness, not cryptographic randomness.
- A known seed reveals future rolls; treat it as a replay key during active play.
- In retail Black-first games, the system-random opening pair is mapped without modulo bias but cannot be derived from the phrase.
- This page alone cannot prove a released app binary uses these exact two source-file snapshots.