One tile, two games: every deal in the campaign, played twice
8,000,000 games in 4,000,000 matched pairs — identical shuffles, identical goals, identical seats. The only difference: whether the Prism sits at the centre.
The campaign's two blocks were built for this page. Study 5 replays study 1's million deals without the Prism; 6 replays 2; 7 replays 3; 8 replays 4. Determinism does the rest: every difference between a game and its twin is caused by that one tile, because nothing else differs.
The blocks' own reports (prism, open) compare table sizes within a rule. This one asks the sharper question: take the exact same table — how much of the game was the deal, and how much was the rule? The answer is not subtle.
The headline: the rule beats the deal
If you know who won a deal with the Prism, how well can you predict the same deal without it? Barely better than chance. The dashed ticks mark pure independence — the same-winner rate you'd get pairing two unrelated games.
Same deal, same winner — observed vs. what independence would predict
FindingRemoving the Prism reshuffles the outcome almost as thoroughly as re-dealing the cards. The same shuffle keeps its winner only 22.6% / 28.5% / 37.3% / 53.8% of the time across 5 / 4 / 3 / 2 players — an edge of just 2.6% / 3.5% / 4.0% / 3.8% over pure chance. The winning colour survives in barely a third of pairs. One tile is not a modifier here; it is most of the difference between one game and another.
TempoThe same deal takes 8.7 more moves without the anchor — and runs longer in 69.3% of pairs, a share that holds almost exactly constant from the full table to the duel even as the average gap narrows (+10.0 / +9.3 / +8.3 / +7.1).
Four games from the corpus
The aggregate says the rule dominates; these pairs show what that looks like at the table. Every pair below is one shuffle, playable and replayable from its seed.
5 seats: The Liar, The Hunter, The Hoarder, The Opportunist, The Spender — identical hands, identical goals, identical order.
11 moves — The Hoarder wins by chain of 7 in Green
108 moves — The Liar + The Opportunist + The Spender wins by deck exhaustion
The most stretched pair in four million: with the anchor gone, the same hands that produced a quick Green chain grind to deck exhaustion — and the Liar, who lost the fast game, shares the crown in the long one.
5 seats: The Honest One, The Spender, The Hoarder, The Opportunist, The Hunter — identical hands, identical goals, identical order.
99 moves — The Honest One + The Spender wins by deck exhaustion
9 moves — The Hoarder wins by chain of 7 in Green
The largest swing the other way, proof the effect is not mechanical: WITH the Prism this deal stalls into a 99-move exhaustion tie; without it, the Hoarder closes a chain in nine moves.
2 seats: The Hoarder, The Liar — identical hands, identical goals, identical order.
9 moves — The Hoarder wins by chain of 7 in Green
83 moves — The Liar wins by deck exhaustion
The archetypal persona swing in miniature: the Hoarder wins the anchored game in nine moves; strip the anchor and the Liar outlasts everyone to an 83-move exhaustion win.
3 seats: The Hoarder, The Liar, The Spender — identical hands, identical goals, identical order.
12 moves — The Hoarder wins by chain of 7 in Blue
95 moves — The Liar wins by deck exhaustion
At three players: the Hoarder’s 12-move Blue chain with the Prism becomes the Liar’s 95-move Blue exhaustion win without it — the goal colour held, everything else changed hands.
Who the Prism was working for
Net wins gained or lost per million deals when the Prism is removed — same deals, both directions counted. Positive: the persona wins deals open that it lost anchored.
Net win swing from removing the Prism, per persona and table size
FindingThe anchor is honesty's amplifier. The Liar gains the most from its removal at every single size (+15.9k / +17.0k / +18.1k / +16.7k net wins per million); The Honest One loses the most everywhere (-6.7k / -7.8k / -9.4k / -9.7k). In ratio terms: with the Prism the Liar runs 0.84–0.82–0.81–0.84× fair share and the Honest One 1.14–1.16×; open, the gap compresses to 0.92–0.94× vs 1.09–1.11×. A guaranteed connection rewards the player who simply builds; ambiguity about where chains can even begin is the closest thing to cover a bot bluffer gets. Nobody escapes the ladder — the order never changes in either block — but the rungs move.
The two games, side by side
Block-level contrasts at every size — blue with the Prism, amber open. The blocks' internal trends (both shrink with the table) are in their own reports; here, the gap between the dots is the story.
Mean moves per game
Stealth wins
Exhaustion endings
Goal changes per game
First mover vs fair share
Wins ended by an action
Wins with an acquired goal
Forced passes per game
What the campaign established
1The persona ladder is a property of the rules, not the table. Honest first, Liar last, at every size, in both blocks — eight million games, zero exceptions to the ordering's endpoints. Table size never reordered the open ladder at all; the Prism moves the rungs, not the ranks.
2Bot deception costs, everywhere — as pre-registered. With no minds to deceive, sustained bluffing is pure tempo loss: the Liar pays 19% of fair share anchored, and even at its open-start best still pays 6%. The interesting flip is who the Prism protects: it more than doubles the bluffer's penalty while paying honesty a premium.
3The first-mover premium was the anchor's, not the opener's. 1.05× at an anchored full table, 0.99× open. Guaranteed first connection, not first action, was the edge.
4The rule outweighs the deal. The flip-rate chart above is the campaign's sharpest sentence: knowing a deal's anchored winner tells you almost nothing about its open winner. Structure dominates shuffle.
5Structural fairness survives everything. No seat, no colour drifts meaningfully from fair share in any of the eight studies. Whatever else the Prism changes, the game underneath stays balanced in both forms.
The full table
Paired-deal metrics at every size. Block-internal metrics live in the two block reports; per-study detail in the eight study reports.
Appendix
| Metric | 5 players | 4 players | 3 players | 2 players |
|---|---|---|---|---|
| Winner unchanged (same deal) | 22.6% | 28.5% | 37.3% | 53.8% |
| … expected if independent | 20% | 25% | 33% | 50% |
| Winning colour unchanged | 27.4% | 29.6% | 32.8% | 37.2% |
| Open ran longer | 69.5% | 69.4% | 69.2% | 69.1% |
| Mean extra moves without Prism | +10.0 | +9.3 | +8.3 | +7.1 |
| Chain became exhaustion | 2.5% | 3.4% | 4.5% | 6.0% |
| Exhaustion became chain | 0.7% | 0.9% | 1.3% | 1.7% |
| Liar net swing (wins/million) | +15,914 | +16,980 | +18,051 | +16,705 |
| Honest net swing (wins/million) | -6,719 | -7,779 | -9,362 | -9,707 |