Perpetual Motion has no player choices — only a question to answer.

History and character

Perpetual Motion belongs to a small family of patience games that are fully deterministic: every action is forced by the rules, leaving the player no meaningful choices about which card to move or where to place it. The closest relative on this site is Clock Solitaire, which also produces a fixed outcome from any shuffle. Unlike Clock, Perpetual Motion can theoretically run indefinitely without resolving — hence the name. A “bad” deal does not merely fail to win; it loops.

The game first appeared under various names in nineteenth-century patience literature. Its appeal is mathematical rather than tactical: players are drawn to the hypnotic rhythm of dealing and collapsing, and to the puzzle the deal sets — will this particular arrangement of 52 cards converge, or cycle?

Because no decisions are made during play, Perpetual Motion has no strategy in the usual sense. What it does have is a reading skill: the ability to monitor round-to-round change and detect loop behavior before it becomes obvious. That is what this guide covers.

How the game works: the full mechanics

The 52-card deck is placed in a face-down stock. Four empty tableau piles are the playing surface. The game proceeds in automatic rounds:

1. Deal four cards. One card is dealt face-up to each of the four tableau piles. After each card is placed, check whether the top of any earlier pile matches the rank of the newly placed card. If a match exists, move the newer card onto the matching pile (collapsing equal tops to the leftmost matching pile).
2. Discard four-of-a-kind.Whenever a pile’s top four cards are all the same rank, those four cards are permanently removed from the game.
3. Gather and redeal. When the stock empties, collect the four tableau piles from right to left into a new stock and deal again. This gather step is the moment that can create a repeat: if the right-to-left merge produces the same card order as a previous gather, the game will cycle identically forever.

The game ends in one of two ways: all 52 cards are discarded in thirteen four-of-a-kind groups (a win), or the gather step recreates a previously seen stock order (a loop, meaning no further progress is possible).

Measuring progress round by round

Because no choices are made, the only meaningful thing to track is whether the game is making real progress. Progress has a precise definition: the total number of cards in the system decreases only when a four-of-a-kind is discarded. Everything else — dealing, collapsing, gathering — moves cards around without removing them.

At the start of each round, note the total card count. A round that removes at least one four-of-a-kind is a productive round: the count drops by four. A round that completes without any discards is a static round: the count is unchanged and the gather step will attempt a redeal of a slightly different order, but if that new order also produces no discards, suspicion of a loop is warranted.

• Healthy sign: Discards happen in the first two or three rounds. Early discard speed is the best predictor of a winning game. If the first round already produces three or four four-of-a-kind removals, the deal has a strong structure.
• Warning sign: A full round passes with no discards. This can happen in a winning game, but if it happens in consecutive rounds, the game is likely approaching a loop.
• Loop confirmation: The four pile tops at the end of a round exactly match the pile tops seen at the end of a previous round. From that point, no new discard can form.

Loop detection: when to stop early

The implementation here tracks game states automatically and halts when a loop is detected. In physical play without automation, recognizing a loop requires attention to the pile structure after each gather.

The gather step always collects piles right-to-left. The order of cards entering the new stock is therefore determined by the current distribution across the four piles. If you notice the same ranks appearing in the same positions across two consecutive end-of-round states, the gather has entered a repeat cycle.

In practice, most experienced players stop and restart after two consecutive non-discard rounds rather than rigorously verifying the loop condition. The probability that a game produces two consecutive non-discard rounds and then recovers to clear is low enough that early restarts are a reasonable time-saving heuristic.

Why the shuffle determines everything

The mathematical structure of Perpetual Motion means the initial card order determines the outcome completely. A “good” shuffle is one where the rotation-and-discard process naturally groups same-rank cards together across rounds. A “bad” shuffle is one where the gather always intermixes ranks in a way that prevents four-of-a-kind formation.

This is different from most solitaire games, where skill affects the win probability. In Perpetual Motion, the question is not “how should I play this?” but “what did this shuffle produce?” A player who understands the mechanics and can read progress quickly will waste less time on losing deals and restart sooner, which is the only form of skill the game rewards.

Published win-rate estimates for Perpetual Motion vary, but many sources place the fraction of winning shuffles somewhere around 50–65 percent, depending on exact rule variants (especially whether the collapse rule always targets the leftmost pile or allows choice). With forced leftmost-collapse rules and no player agency, the rate is set entirely by the deck composition.

Perpetual Motion vs. Clock Solitaire

Both games are mechanical patience games with no player choices. The difference is in how and when they end. Clock always terminates: the deck runs out and the result is visible (all kings face up = win, any king face up before the last card = loss, but the game always reaches a definite end). Perpetual Motion can, in principle, continue indefinitely without terminating — hence the name. The loop detection feature of this implementation ends the game when a cycle is detected, converting an infinite process into a finite result.

Clock is fully transparent: all cards are dealt to fixed positions, and the win condition is readable from the initial layout. Perpetual Motion unfolds dynamically and its outcome is only revealed through observation of how same-rank cards accumulate across rounds.

Frequently asked questions

Can any play choice affect the outcome?

No. In the leftmost-collapse variant implemented here, every action is forced. There is no moment where a player must decide between two valid moves. The process is entirely automatic once the deck is shuffled.

What is the earliest I can know a game is a winner?

In some deals, all thirteen four-of-a-kind groups form within the first two or three rounds, giving a very early win. In others, the structure requires many rounds before enough groups consolidate. There is no reliable early indicator of a specific winning deal; the only signal is that discards continue to happen across rounds.

Why does the game sometimes feel like it’s making no progress for many rounds and then suddenly clears?

The gather step can intermix ranks for several rounds without forming the groups needed for discard. Each gather changes the stack order slightly. Sometimes a deal requires many redeals before the right-to-left gather happens to place all four cards of a rank together at the top. This delayed-clearance pattern is rare but occurs in genuinely winning deals. It is distinct from a loop in that discards eventually resume.

Is there any value in watching a looping game rather than restarting?

Only the mathematical interest of observing the cycle. Once the loop is confirmed, no new information is produced. The practical advice is to restart when two or more consecutive rounds produce no discards.