How this article was made

We use AI as a supervised research tool: to help locate and compare original sources, work through ancient and modern Greek material, prepare working translations, and test our reconstruction models. This article draws on 27 reviewed principal sources and source records: 14 direct records of ancient texts, excavations, objects or images, and 13 peer-reviewed or institutional secondary and reference sources.

AI accelerated the search; it did not decide what was true or what we would publish. The article still required hours of human source checking, argument, rewriting, game design, testing and editorial review.

We are against AI slop—fast, unaccountable material that hides its sources and substitutes fluency for thought. We believe the same tools can support careful, original work when the evidence, uncertainty and human judgement remain visible.

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Achilles and Ajax should be fighting a war.

Instead, Greek artists repeatedly imagined the two heroes bent over a board, absorbed in a game while the heroic world waited around them. On the famous amphora painted by Exekias, their names are written beside them and their announced throws—four and three—hang in the space between the warriors. They have armour and weapons. What holds their attention is play.

The scene is irresistible. It is also a trap.

The pictures cannot tell us that Achilles and Ajax are playing Pente Grammai. They cannot tell us that warriors at Troy played this game. But the scene appears again and again, and that tells us something important: ancient Greek artists thought gaming belonged beside their mightiest heroes. They placed play alongside armour, danger and fame.

Nor did Greek artists and makers leave us one neat, standard board. Across the evidence are depictions and models with different shapes, marks and numbers of lines. Some heroic scenes belong in that wider visual world. They do not all show the same game.

Within that varied world, one five-line case reaches us through a stranger, more tightly convergent collection of clues: five pieces for each player; five lines; a middle line called sacred; an association with dice; and an ancient expression about the moment someone moves away from that line. A five-line clay funerary model survived, with a hollow at each end of every line. An image can be read as a five-line arrangement. The metaphor survived. The rules did not.

This is the story of how those fragments travelled—through earth, fire, painted clay, quotation, miscopying, Byzantine manuscripts, modern excavation and scholarly disagreement—until we tried to place them on one table again.

This is the reconstruction problem at the heart of the story. The evidence can show us the pieces, the lines, the dice, the marked line ends and the sacred-line clue; it cannot recover what the game felt like to an ancient player. Nor are the surviving clues enough to play. So we make the missing choices explicit, build three versions that complete the clues differently, and compare the kinds of play they create.

Play and simulation can expose broken encodings and hidden modern assumptions. They cannot turn a modern experience into evidence about antiquity.

Achilles and Ajax at a gaming table, with Athena between them. Attic black-figure hydria attributed to the Leagros Group, c. 510 BCE. The Metropolitan Museum of Art, 56.171.29. Public Domain/Open Access (CC0). The Metropolitan Museum of Art

The evidence will not stay still

The arrangement Exekias painted—Achilles and Ajax facing one another, leaning over a small gaming table in the middle of a war—did not remain isolated. Other artists returned to the two heroes at play, but they did not copy one standard set of equipment. The board changes from image to image.

One small painted cup in Brussels offers the first apparent breakthrough. Ulrich Schädler reads the surface between Achilles and Ajax as five parallel lines, with five counters at each end. Five lines. Five counters. Perhaps the picture has given the lost game a face.

Then the same arrangement appears in clay.

A terracotta table found at Vari, south of Athens, has five lines cut across its top and a hollow at both ends of each one. Four mourning women stand at its corners. It belongs to the early seventh century BCE—centuries before Pollux would describe five counters on five lines. The image and the object now seem to converge.

But this is where the investigation becomes more interesting, because the Vari table is not alone.

Five objects change the question

n 2022, Maria Chidiroglou, Ulrich Schädler and Stine Schierup published “Archaic Greek Terracotta Gaming Tables Revisited”. Their study brought five surviving terracotta table models into one comparison: Vari; a fragment from the Kerameikos cemetery in Athens; Myrrhinous in Attica; Copenhagen’s National Museum model; and a table now at the Swiss Museum of Games in La Tour-de-Peilz.

Putting those objects beside one another did not fill in the rules. It changed the questions.

First, the line ends matter. Every surface that survives clearly marks both ends of every line. At Vari they are hollows. At Myrrhinous and La Tour-de-Peilz they are painted or drawn circles. At Copenhagen the counters themselves are moulded in place at the ends.

The marks are Known. The authors infer that they represent positions for single counters. That reading is persuasive enough to overturn our earlier twenty-position circuit, which barely used the lines at all. But it still does not tell us how a counter travelled from one end to another.

Second, five lines were not the only form. Vari has five. Copenhagen has nine. Myrrhinous and La Tour-de-Peilz have eleven. The broken Kerameikos table preserves three, although we cannot know whether three was its original total.

That variation closes one tempting story and opens another. We cannot arrange the objects into a simple march from an original five-line game towards larger descendants. Instead we have a family of related table forms, scaled to different numbers of lines. Why did the number change? Did the same game expand, or did the form hold several games? The objects do not decide.

The Copenhagen model makes the uncertainty tangible. Its table is miniature, but its dice are full size. Its counters are not loose pieces ready for play; they are part of the model. This was an image of gaming, not equipment for a match. The other tables also come from funerary settings and are best understood as models or votives. No ordinary playing board has survived.

That creates a new problem. Do the hollows reproduce practical sockets that held counters on a real board, or do they depict the places where counters belonged? Either way, the ends are central to the image of the game. But a model can preserve what looked recognisable without preserving how the object worked.

Third, one model may mark the sacred line. On the eleven-line La Tour-de-Peilz table, a larger circle sits at the centre of the middle line. The circle is Known. The 2022 authors infer that it identifies the sacred line. If they are right, this is the only surviving table feature that singles out the middle—but it still cannot tell us what made that line special.

The five objects therefore do something more important than illustrate a game. They change its possible structure. Across three, five, nine and eleven lines, the number of marked end positions is always twice the number of lines. If Pollux’s relationship—one counter per line for each player—extended beyond his five-line description, every model would begin completely full.

That generalisation is ours, not the authors’ conclusion and not an ancient rule. Yet it creates a powerful design constraint. With every end occupied, an opening move cannot simply advance into empty space. Something must give: movement along or between the lines, capture, stacking, a privileged middle, or a rule we have not imagined.

Other objects widen the field again. A Praenestine mirror in the British Museum has been identified by the Museum as a Five Lines scene, but the board is seen obliquely and does not expose a playable layout. An Etruscan mirror published by Gustav Körte shows Achilles and a companion with seven lines between them. That seven-line image is separate from the three-, five-, nine- and eleven-line terracotta models, but it reinforces the warning that ancient gaming imagery was not geometrically uniform.

Etruscan mirror scene with a seven-line board, from Gerhard, Klügmann and Körte, Etruskische Spiegel, vol. 5, plate 109. Digitized by Heidelberg University Library. Public Domain Mark 1.0. Heidelberg University Library

The Praenestine object record is British Museum 1898,0716.4. The Brussels cup record is Classical Art Research Centre / Beazley Archive 306097. The Vari excavation is described in Kallipolitis’s Anagyrous report.

None of these objects securely shows entry, direction, capture, stacking, dice procedure or victory. Nor can we borrow those rules from a similar-looking game. Polis, diagrammismos, naumachia, XII scripta, tabula, enlarged line games and cup-mark circles all belong in the comparison—but each comes with a warning not to import its mechanics. Reports of two rows of eleven across Roman Asia Minor remain without a scholarly anchor and stay out of the public story.

So the material trail leaves us somewhere more useful than certainty. We now know what makers repeatedly chose to show: parallel lines, marked ends, counters and sometimes a distinguished middle. We also know what they did not preserve: the route between those positions, the interaction between counters, and the reason anyone would leave the centre.

For that, the investigation has to move from objects to words.

Five pieces. Five lines. Then silence.

Centuries after the earliest objects in our story, Julius Pollux set down a compact description. Ioulios Polydeukes—Pollux in Latin—was a Greek teacher, rhetorician and scholar of words from Naucratis in Roman Egypt. He taught in Athens in the closing decades of the second century CE and dedicated all ten books of his Onomasticon to the emperor Commodus.

Pollux was not a player reporting from Archaic or Classical Greece, and the Onomasticon was not a game manual. It gathered useful words and expressions by subject, including terms from literature, public life and everyday activity. That made it exactly the kind of later work that could preserve the vocabulary of a game after its working rules had faded.

A later writer, Philostratus, says Pollux’s sweet delivery charmed Commodus into awarding him an Athenian chair of rhetoric. The anecdote belongs to the competitive world of imperial intellectuals; the dedications in Pollux’s own work provide the firmer connection to the emperor.

In Erich Bethe’s critical edition of Onomasticon 9.97–98, checked directly against the Greek and then compared with Stephen Kidd’s discussion, each of the two players had five counters on five lines. One line in the middle of the five was called the hiera grammē—the sacred line. Pollux also quotes a fragment attributed to Sophocles that places five-lined pieces beside throws of dice.

That is a remarkable amount to survive in a few lines:

• two players;

• five pieces each;

• five lines;

• a named middle line; and

• dice somewhere in the game.

Then the description stops.

It does not give us the starting position. It does not say how the lines connect, where a piece enters, which way it travels, whether pieces block or capture one another, what protection the sacred line provides—if any—or what a player must do to win. Even the dice remain elusive: the surviving phrase does not settle whether players used one die, two dice, or another arrangement.

Even Pollux reaches us through fragments. The original Onomasticon did not survive intact. The medieval manuscripts descend from an abridged text that shows interpolation as well as loss; by the ninth century, the original was already inaccessible. The Byzantine scholar Arethas of Caesarea owned an epitome close to the form from which the surviving tradition descends.

Modern scholarship still considers the bulk of the surviving work recognisably Pollux’s. But we cannot assume that every cluster of words retains exactly the shape it had when he arranged it. And the Sophoclean phrase is not an independent second witness: it is an older fragment carried inside Pollux, whose own work was then carried inside a later epitome.

And “Pente Grammai” itself needs a small warning label. It is a useful modern conventional name assembled from the ancient language of five lines. Pollux does not present it to us as a securely preserved proper title.

The passage gives us the outline of equipment, not an algorithm. Yet an object made many centuries earlier seems to give those lines physical form.

Modern diagram by Forgotten Games, based on Pollux, Onomasticon 9.97–98, checked in Bethe’s critical edition and compared with Stephen Kidd.

The little table from the fire

The object itself is difficult to forget. Five lines cross a painted clay table. Ten hollows sit at their ends. At each corner, a woman pulls her hair in mourning.

This is not how we normally imagine a game surviving.

The table was made around 675–650 BCE. Restored, it is about 24.8 centimetres long, 18.3 centimetres wide and 18 centimetres high—large enough that someone could physically place counters on it. Lotus flowers, triangles and zigzags run across its surface. It looks like play and grief have been made into one object.

It did not emerge from a neat, sealed grave. The modern trail begins with a false lead: illicit digging exposed antiquities at one Anagyrous cemetery in 1935, but the table came from a different, smaller cemetery discovered by accident in 1961, about 800 metres away. Vasileios Kallipolitis excavated the site systematically the following year.

Even then, the context was messy. The cemetery contained twenty-seven recorded burials—cremations and inhumations, some within funerary enclosures—and the ground had already been disturbed by digging and deep ploughing. The table came from the combined area of the cemetery’s two oldest cremation pits. We cannot assign every object securely to one pit, still less to one known person.

That matters because the surrounding finds are elaborate. Decorated vessels, the miniature table and a painted clay die all came from the disturbed two-pit area. It is tempting to turn them into the possessions of a wealthy individual. The evidence allows only a probably elite-value funerary setting. This is an assemblage, not “the grave of a rich man.”

The die deepens the mystery. Its faces carry a horse, female figures and what may be Athena holding an owl. Kallipolitis judged it probably associated with the table. “Probably” has to remain: the context had been disturbed. But table and die together make the language of gaming difficult to dismiss.

The more important question is no longer simply whether this was a game. It is why an image of gaming was placed among burnt funerary offerings.

Chidiroglou, Schädler and Schierup argue that the table was a purpose-made model or votive, deliberately broken and burned during ceremony rather than used for an ordinary match and then placed intact in a grave. The mourners are part of that argument. So are the decoration, damage and offering context.

If that interpretation is right, the object preserves something different from a rulebook. It tells us that someone considered gaming recognisable—and meaningful enough—to represent in a ritual concerned with death, memory and perhaps status. It does not tell us that the deceased owned this game, that the table belonged to one person, or what any move meant.

The line-end hollows remain Known features. Reading them as positions for single counters is Inferred from the comparison with the other models. The die is probably associated. Everything beyond those boundaries—the route, the opening arrangement, capture and victory—is still absent.

Two histories now separate. The table belonged to a seventh-century BCE funerary world in which, on the 2022 interpretation, it was made, broken and burned as an offering. Then it disappeared. More than two and a half millennia later, it returned through a chance discovery in earth churned by graves, ploughs and illicit digging.

Its evidence did not reach us through players teaching players. It waited in the ground.

Why would anyone leave the sacred line?

The table waited underground. The question survived in language.

By Plato’s time, moving “from the sacred” was a useful image for doing something out of the ordinary. In the Laws, he compares an unusual legislative move to counters moving “from the sacred [position].” His audience was apparently expected to feel the force of the comparison without having the game explained to them.

That is Known from the text. What Plato does not write is just as important: he does not say “line,” and he does not describe a rule. The connection to the sacred line comes from the wider proverb and commentary tradition. The passage tells us that leaving mattered, not why anyone left.

An older poetic fragment makes the mystery sharper. Alcaeus, writing in a world of political conflict and exile around 600 BCE, is quoted in D. A. Campbell’s translation as saying: “and now he is master, having moved the stone from the holy line.” A move in a game has become an image for a reversal of power.

But this is not a pristine sentence lifted from an Alcaeus manuscript. It survives through the twelfth-century scholar Eustathius, in damaged wording. Editors have reconstructed the word translated as “holy”; another word remains too uncertain to translate. The quotation gives us the drama of departure, but not its original scene, speaker or rule.

Centuries later, Theocritus turns a similar move into an erotic reversal. Galatea flees the man who loves her and chases the one who does not: “and she moves the counter from the line.” Here the Greek says only line, not sacred line. It does not give us capture, safety or victory. It shows that the image of a counter leaving its line could still carry an emotional turn.

These are separate trails, not one unbroken memory handed down by players. Alcaeus reaches us through Eustathius. Theocritus travelled through a different manuscript tradition. Pollux preserved the compact description of five lines and five counters centuries later. Each fragment passed through its own chain of poets, commentators, scribes and editors.

Eustathius adds one more complication. In Antonios Makrinos’s critical text, a player who is being beaten “hastens” or “resorts” towards the sacred line. Kidd infers that the difficult final phrase describes the loser reaching it last. That makes the line sound like a goal—or perhaps a last refuge—but the Greek does not preserve a clear victory condition. Makrinos also identifies the surrounding discussion as substantially reworked from an earlier text by Suetonius. This is late, source-mediated testimony, written more than a millennium after the earliest tables; it cannot make those alternatives disappear.

Then the objects answer back.

Every surviving table marks both ends of every line. On a five-line table, that gives ten ordinary end positions. Pollux gives two players with five counters each: ten counters. The marks are Known; Chidiroglou, Schädler and Schierup infer that each one represents a position for a single counter. On that reading, the five-line board began exactly full.

We infer that the same counters-equal-lines relationship extended to the tables with three, nine and eleven lines. Pollux attests only the five-line case, so this generalisation is ours. If it is right, every attested table began with exactly as many counters as ordinary end positions.

That is a structural inference, not an ancient rule statement. But it changes the question. On a full board, how can the first counter move at all?

The three authors infer one counter per ordinary point, compulsory movement where a move is legal, and an exemption for the sacred line. In their reconstruction, the centre is the board’s pressure valve: a counter can enter the sacred line without displacing another, creating the empty end that lets the rest move. Later, a counter may have to leave that apparently privileged place because it is the only legal move.

For the first time, the baffling proverb has a possible mechanical answer: perhaps a player left because the structure forced them to. But “possible” is doing essential work. Compulsory movement and the exemption are scholarly inferences. The sources never state them, and the full-board pattern does not prove them.

So the old question returns in a more useful form. Was leaving the sacred line forced? Was it a chosen attack? Was the line a goal, a refuge, a temporary release from a crowded board—or something none of the surviving fragments lets us see?

The word sacred does not itself prove a cultic meaning. The metaphors preserve consequence, not mechanism.

Modern diagram separating the historical settings of the Vari table, Alcaeus, heroic gaming images, Plato, Theocritus, Pollux and Eustathius from the different material and manuscript routes through which their evidence survived.

Two scholars, two different games

The full board does not solve the old question. It divides it in two.

Ulrich Schädler’s answer is: you leave because you must. His race reconstruction makes the sacred line a privileged destination, but not a place where a counter can always remain. If no other move is available, zugzwang forces a player to move a counter that has already reached safety.

This is an Inferred rule, not a surviving instruction. It makes mechanical sense of the full board and the proverb, but no ancient text says that movement was compulsory. Eustathius’s much later account makes the sacred line sound goal-like or like a last resource; it does not say that a player was forced to leave it.

Stephen Kidd’s answer is almost the opposite: you leave because you see an attack. He reconstructs a game in which a single counter is exposed, two counters together are “yoked” and safe, and a counter on the sacred line may abandon protection to strike an opponent. Kidd explicitly rejects zugzwang as the explanation of the proverb.

Here his argument finds its strongest foothold—and reveals its largest gap.

In a poem about the emperor Zeno’s disastrous throw in another game, the sixth-century writer Agathias distinguishes counters that are yoked from those that have become unyoked. That opposition is Known in the later game. It shows that paired and unpaired counters belonged to real Greek gaming language. It does not show that Pente Grammai used the same rule centuries earlier.

Kidd then turns to Aristotle. In the Politics, an isolated person is compared to an azyx board-game counter, “desirous of war.” The word is Known, but the game is not: Aristotle writes only en pettois—among board games—and never names Pente Grammai. Kidd infers capture by elimination. He argues that the other known Greek games do not fit the aggressive image, leaving Pente Grammai as the best candidate.

That is an ingenious chain, but it remains a chain of reasoning. Aristotle does not cite a capture rule. Agathias describes a different game. No surviving Pente Grammai image clearly shows two counters sharing a position, a point Kidd concedes and Schädler presses against him. Paired safety, capture and return after capture therefore remain Inferred or, where a playable procedure has to complete them, Invented.

The same proverb has now produced two opposing games. In one, leaving safety is an unwanted obligation. In the other, it is a chosen act of aggression. Both are scholarly reconstructions; neither is recovered ancient play. A scholar’s name tells us whose argument we are testing, not what category of evidence it belongs to.

Even the race interpretation does not end in a single settled ruleset. The 2022 study co-authored by Schädler says the five counters assemble on the sacred line. His Locus Ludi rules instead finish in the half opposite the player’s starting side. These are two different reconstructed victory conditions in Schädler-authored accounts.

Neither is Known: the 2022 study offers the sacred-line finish as an Inference, while the playable Locus Ludi finish is an Invented completion. We do not choose between them.

Any playable reconstruction must still add Invented decisions about setup, route, dice and what happens when the evidence falls silent. That is why a reconstruction is best understood as an argument you can play.

The point is not to make the blanks disappear. It is to make them visible.

Modern side-by-side diagram comparing Schädler’s compulsory-departure race argument with Kidd’s capture-and-yoking argument, showing the known evidence, contrary evidence and invented playable procedures required by each.

From fragments to a test

At this point the investigation changes. A text can leave a gap on the page. A game cannot. Someone has to decide where the counters begin, how a throw becomes a move, what blocks what, and how play ends.

That does not make game design a machine for recovering ancient rules. It makes it a way to expose every decision the evidence did not make for us.

How three versions complete the fragments

The evidentiary floor

All three versions begin on the same small floor:

• Known: Pollux gives two players, five counters each, five lines and a sacred middle line. A fragment he quotes associates the pieces with dice throws, but does not tell us the number of dice or how a throw became a move.

• Known: the surviving models carry three, five, nine or eleven lines, with marked ends wherever the surface is sufficiently preserved. They are funerary models and votives, not surviving playing boards.

• Inferred: Chidiroglou, Schädler and Schierup read each end mark as a position for one counter. Copenhagen’s moulded counters strengthen that reading and may show an opening array.

• Inferred by us: if Pollux’s counters-equal-lines relationship extended to the other table sizes, every board began completely full.

• Known: ancient texts preserve counter-movement metaphors involving “the sacred” or “the line.” Inferred: read together, they make departure from the sacred line consequential. The much later Eustathius passage may instead make the line a goal or last refuge. Neither trail supplies a victory procedure.

No source supplies a complete route, secure opening rule, direction of travel, die allocation, capture system, return rule or unambiguous victory procedure. Every playable version must cross those gaps.

The interesting question is not which author can avoid invention. No one can. It is what each reconstruction chooses to make the sacred line mean.

Schädler’s version makes compulsory departure the central Inference, then adds Invented route, die and blocking procedures to produce a non-capture race. Kidd makes capture the central Inference, then completes the exact circuit, entry, yoking, knock-off, return and finish as playable Inventions. Our v0.8 makes a design Inference from the visible form—that the end positions and the lines between them should control play—then adds Invented stacking, refuge and exchange-of-ends rules.

These are three different arguments, not a ranking. “Evidence-compatible” means only that a version respects the small floor and shows where its additions begin. It does not mean equally likely, historically verified or recovered.

And compatibility does not guarantee that a game works. We learned that by building one that could not begin.

The models we had to throw away

Our first capture model, v0.1, made an Invented choice that looked harmless: every counter began off the board and entered at the same shared position. Landing there knocked off an opponent.

The game immediately became a trap.

1. Player one enters a counter at zero.

2. Player two must enter at zero and knocks it off.

3. Player one must re-enter at zero and knocks the other counter off.

4. Player two does the same.

The die changed. Nothing else did.

Across 2,000 seeded runs—1,000 under each of two simple policies—not one game finished within the 400-turn limit. The entry rule had removed the decision before play had really started.

That failure says nothing about ancient capture. No ancient source told us to enter at shared zero. We had Invented the rule, encoded it, and then stopped seeing it. Simulation did one legitimate job: it exposed a broken modern encoding.

An Invented safe-entry rule removed the lock in v0.2. An Invented dice-led entry removed it again in v0.3 and survived into the now-retired v0.4. Those tests established only that the new encodings escaped this particular loop. They did not verify an ancient entry rule or prove capture.

The next failure was not a lock. It was an absence.

Versions v0.3, v0.4 and v0.5 each Invented a different reason to leave the sacred line. Under the recorded simple policy, players used those mechanics exactly zero times. A secured counter was worth more than the promised reward. The dramatic “sacred departure” existed in our description, not in the game.

Then the new object evidence exposed a deeper problem. Versions v0.4 through v0.7 asked players to remember which counter had travelled how far, completed a lap or acquired a special state. Nothing in the surviving equipment displays those distinctions: the Copenhagen counters are plain, and no individually marked counter is securely associated with the game. Invisible state is not therefore impossible, but in our reconstruction it was unsupported.

By v0.7, another patch was no longer the answer. We needed to ask four more basic questions. Could every counter begin on the visible ends? Could the five drawn lines themselves carry the movement? Could the sacred line matter without being the goal? Could the entire state of play remain visible on the table?

Those questions produced v0.8. The failures explain why we designed it; they do not make any of its answers ancient.

Modern design-history diagram showing the v0.1 reset loop, later departure mechanics that were never used, unsupported invisible counter states, and the inferred and invented choices that led to Exchange of Ends v0.8.

Our proposal rebuilt: Exchange of Ends v0.8

Version 0.8, Exchange of Ends, begins by doing what our earlier versions avoided: putting every counter on the table.

Five counters stand on the five ends nearest one player. Five face them from the opposite side. Before the first throw, every ordinary position is occupied. Copenhagen’s moulded counters make an endpoint opening Inferred; dividing the ends between the two players in this exact way is Invented.

The objective is visible in the same arrangement. All five of your counters must reach the endpoints on your opponent’s side; their five must cross towards yours. Counters may share an endpoint, so victory requires every counter to cross rather than one counter on each distinct end.

That victory condition is Invented, but it needs no lap count, marked counter or secret history.

How Exchange of Ends plays

• Known: five counters each, five lines, a sacred middle line, marked ends and an association with dice.

• Invented movement: the throw that begins the game decides who starts. One six-sided die then moves one interchangeable counter. The route crosses a drawn line, steps to the next and crosses back, so the five lines become the road rather than scenery.

• Invented stacking and capture: a solitary enemy counter can be knocked off and returned to an eligible endpoint on its own side; on re-entry it may knock off a solitary opponent there. Two or more counters of one colour gather into a stack that bars the opponent.

• Invented sacred-line effect: the middle line is a refuge open to both colours. Nothing can be captured there, but standing there wins nothing. Every counter that enters must eventually leave to complete the exchange.

• Invented victory: move all five counters onto endpoints on the opponent’s side. They may share endpoints.

Everything required to continue the game is visible in the counters’ current positions. That is our modern design principle, not evidence that ancient players rejected memory or kept no information away from the board.

Why let counters stack?

This argument is ours. If counters only ever sit in the end cavities, the lines between those cavities appear to do no work. A maker who wanted ten isolated positions could have made ten cups. Our reading that the drawn lines should matter is Inferred by us from the object’s form.

Stacking is the Invented rule we use to make them matter. It also gives the sacred line a visible exception: every line can hold one colour, while the sacred line alone can hold both.

The evidence against our argument sits beside it. Chidiroglou, Schädler and Schierup’s one-counter-per-point reading is Inferred. Copenhagen models counters at the ends, not between them. Schädler rejects stacking. Kidd defends his different Inferred yoking rule through playability rather than through a depicted stack.

Our proposal is an argument from form, not a material finding.

Simulation cannot decide that disagreement. We kept stacking because it made the lines active, kept the state visible and produced a functioning modern design—not because a simulation score can establish an ancient rule.

Why make the sacred line a refuge?

Because our earlier designs had made leaving irrational. If the sacred line is the final destination, a secured counter normally has no reason to abandon it.

Exchange of Ends instead makes the line shelter on the journey: valuable when a counter is threatened, useless as progress towards victory. Departure follows from the objective rather than from a special reward.

This is our Invented answer to the proverb, and the evidence against it is substantial. Eustathius’s late and difficult account makes the sacred line sound goal-like or like a last resort; that reading is Inferred. Schädler’s and Kidd’s reconstructions both build around an Inferred destination.

We deliberately diverge from them and build around the older departure tradition instead. That is a design argument, not an upgraded fact about ancient play.

Three games, one public test

The investigation can now put its three answers on one table.

• Schädler — Inferred explanation, Invented playable rules: leave because compulsory movement forces you from safety.

• Kidd — Inferred explanation, Invented playable rules: leave because an exposed opponent gives you a reason to attack.

• Sacred Departure v0.8: Exchange of Ends — Inferred design principle, Invented playable rules: leave because refuge offers shelter but no progress towards the exchange of ends.

Modern three-column comparison of Schädler’s compulsory-departure race, Kidd’s capture-and-yoking game, and Forgotten Games’ Exchange of Ends proposal, separating each inferred argument from its invented playable procedures.

hese are not stages in a recovery, candidates in a vote or a ranking of historical likelihood. The first two are implementations of attributed scholarly arguments. The third is our modern proposal. Every version shows its Known, Inferred and Invented rules inside the companion experience.

The board and controls stay visually consistent so the differences come from the rules. Changing version begins a new game; no position crosses from one ruleset into another.

Before putting a chair out for a human player, we ran each encoding through the same deliberately simple test: 10,000 seeded matches, one shared policy and a 400-turn limit. Every run finished without reaching the cap or triggering the loop detector.

The Schädler encoding averaged 33.1 turns, with a median of 29. Kidd averaged 73.9 turns, with a median of 71; importantly, the policy now exercised Kidd’s defining yoke mechanic in every match, averaging 18.6 yoking moves. Sacred Departure v0.8: Exchange of Ends averaged 24.9 turns, with a median of 21.

Those figures answer one narrow question: can each modern encoding produce a game that ends?

They are not a league table. Speed, balance or activity cannot make a version older, truer or historically preferable.

The empty chair at the table

imulation cannot tell us what it feels like to make these choices. That is why one chair remains empty.

This is the narrow, honest role that experimental play can have. The surviving evidence defines a possible space. Scholarship and design connect its fragments in explicit ways. Simulation removes a broken encoding. A human player can then test the modern game those choices create.

Were the rules clear? Did the sacred line feel valuable? Was leaving forced, chosen or simply necessary? Did capture create tension or merely irritation? What kind of decision did each version put in front of you? Which would you play again—and why?

What a modern player cannot do is stand in for someone who lived 2,500 years ago. Cultures, expectations and individual players are not interchangeable across time. Enjoyment cannot authenticate a rule, and preference cannot move an Invented choice into antiquity.

But games survive through human attention. People teach them, alter them, argue over them, remember them and choose to set them up again. Play cannot prove the lost rules. It can test whether a reconstruction creates meaningful choices and the desire for another game.

That is evidence about our design, not evidence recovered from ancient Greece—and it is still worth knowing.

The playable itself does not collect or transmit feedback. Our optional Substack Reader Survey is the disclosed collection point: it asks what readers played, which modern version they would return to, where leaving the sacred line created a meaningful decision, and what felt clear or frustrating.

That is feedback about the games we built, not a vote on the ancient rules. Substack requires respondents to be subscribers and may associate a response with the subscriber’s email address or profile.

If later, explicitly shared testing reveals a compelling modern game, we hope eventually to develop a physical Field Edition: a playable object that carries the evidence, uncertainties and reconstruction choices with it. It is a concept, not currently for sale, and that testing would improve the modern design—not authenticate ancient rules.

A Field Edition would use a new board design. It would not reproduce the Vari table’s mourners or funerary decoration as product ornament; that object belongs to a burial context and would remain part of the evidence story.

We cannot ask the ancient players why this game mattered to them. What we can do is put the fragments on the table, keep the joins visible, and leave an empty chair.

That chair is yours.

Play all three. Notice where each becomes clear, tense, frustrating or worth another game.

You will not be voting on the ancient rules.

You will be testing three different modern completions—and asking what makes a game live.

Continue the investigation

Play and compare all three

Share your playtest experience

Examine the complete evidence dossier

Sources and evidence notes

These notes point to the principal sources behind the article and preserve the boundary between direct evidence, scholarly reconstruction and our modern playable choices.

1. Heroes at play: Vatican Museums, Exekias amphora MV.16757; Metropolitan Museum of Art hydria 56.171.29and lekythos 62.11.2; Stephen E. Kidd, “Pente Grammai and the ‘Holy Line’”. The images establish broad gaming iconography, not Pente rules or identity.

2. Pollux and the sacred line: Erich Bethe’s critical edition of Pollux, Onomasticon, vol. 2, printed p. 174, 9.97–98, checked directly against the Greek; and Kidd, pp. 89–90, for transcription, translation and modern discussion. The syntax does not establish exact board geometry.

3. Terracotta table models: Vasileios Kallipolitis’s excavation report, pp. 115–124; Chidiroglou, Schädler and Schierup, “Archaic Greek Terracotta Gaming Tables Revisited”, especially paragraphs 6, 18, 24, 28 and 33–36. These support the marked line ends, the three-, five-, nine- and eleven-line spread, and the funerary-model reading. The one-counter occupancy, compulsory movement and starting-array suggestions are attributed reconstructions, not Known rules. The Vari die is probably associated; pit assignment and individual ownership remain unresolved.

4. Sacred-line language and transmission: Plato, Laws 5.739a; Kidd, pp. 86–94; Alcaeus context; Antonios Makrinos’s critical edition of Eustathius, section 1397, printed pp. 53–54 and source note 1188 on p. 103; Eustathius textual history; and Ambrosian manuscript Ambr. C 222 inf..

   The Alcaeus and Theocritus routes are parallel late-Byzantine survival paths, not one transmission chain. Eustathius’s game discussion is late testimony and substantially reworks an earlier Suetonius source; it is not a clear ancient victory rule.