EST

EST is a free, open-source iPhone and iPad game about finding patterns in cards. It is inspired by SET, but it has its own name, artwork, and code.

The deck has 81 cards. Each card combines four traits:

• count: 1, 2, or 3
• color: red, blue, or yellow
• shape: circle, square, or triangle
• fill: solid, shaded, or outline

Find three cards where every trait is either the same on all three cards or different on all three cards. Game Center is optional. You can play alone, pass one phone around the table, or play a live duel across two devices.

Play

• Solo 81 clears the full deck against the clock. A personal best stays on the device, and an eligible run can also go to Game Center.
• Quick 27 uses the 27 solid cards for a shorter round. The fill trait stays fixed, so you check three traits instead of four.
• Duel lets you race another player on one phone or across two devices. On iPad, four players can share one table with a buzzer on each edge. Buzz first, then tap the three cards before the claim window closes.
• The tutorial teaches the rule with worked examples, and the math explorer lets you see the deck as a four-dimensional space.
• You can choose a color theme, pick a fill style, and turn sound effects or haptics on and off.

Solo leaderboard timing uses a monotonic clock and rejects physically impossible completion times before submitting to Game Center. Hinted runs remain local-only.

Hints keep the run off the Game Center leaderboard, but you can still set a local personal best. EST has no ads or subscriptions. An optional one-time support purchase adds a permanent supporter mark, optional Dusk card colors, and an optional warm background, while leaving every mode and gameplay feature free for everyone.

Why EST

I love SET. I have given away more copies of it than of any other game. Its rules are also a neat piece of mathematics: the 81 cards are the points of AG(4,3), a four-dimensional affine space over a field with three elements. EST is my attempt to make that structure visible without turning the game into a textbook.

The name shuffles its own letters while you play. The cards use square shapes and simple marks. That is about as far as the homage goes.

If you have never played the original, buy a copy of SET. It is a near-perfect game.

The mathematics

Represent a card as four base-3 digits: count, color, shape, and fill. A valid set is a line in AG(4,3), which means the three cards add up to zero in every coordinate modulo 3. Once you choose two cards, that rule gives you one and only one completing card. The 81-card deck contains 1080 such sets.

The same rule explains a few endgame details. The whole deck sums to zero, and every set you remove also sums to zero. The cards left at the end must therefore sum to zero too. Three leftover cards would make a set, so a game ends with either a perfect clear or at least six cards that contain no set.

A set-free group of cards is called a cap. Giuseppe Pellegrino proved that the largest cap in AG(4,3) has 20 cards, so any 21 cards contain a set. Later work by Croot, Lev, Pach, Ellenberg, and Gijswijt established how the maximum cap size grows in higher dimensions. EST's endgame screen shows the cap you finished against.

Further reading:

• Davis and Maclagan, "The Card Game SET," The Mathematical Intelligencer, 2003.
• McMahon, Gordon, Gordon, and Gordon, "The Joy of SET," Princeton University Press, 2016.
• Ellenberg and Gijswijt, "On large subsets of F_q^n with no three-term arithmetic progression," Annals of Mathematics, 2017.

Build

EST is an XcodeGen project for iPhone and iPad. You need Xcode, an iOS 17 SDK, and XcodeGen 2.30 or newer.

The Xcode project is generated from project.yml. Edit that file, then run:

xcodegen generate
xcodebuild -project EST.xcodeproj -scheme EST \
  -destination 'generic/platform=iOS Simulator' \
  build CODE_SIGNING_ALLOWED=NO

Game Center features need an App Store Connect app record and the Game Center capability. The leaderboard identifiers are est.solo.completion.time and est.quick.completion.time. Two signed-in devices, or a device and a simulator, are needed to test a network duel.

Do not hand-edit EST.xcodeproj. Regenerate it after adding or removing a source file.

Forks and telemetry

The first-party build reports to the dedicated EST Worker, with anonymous diagnostics enabled by default on new installs and adjustable in Settings. If you distribute a fork, set your own ESTTelemetryEndpoint and ESTFeedbackEndpoint Info.plist build settings—or leave either unset—only after reviewing the collection contract and privacy policy. Also replace the Centaur Labs team, bundle identifier, Game Center configuration, and optional StoreKit product identifiers with values you control. App Store publishing also requires an explicit EST_TEAM_ID for your Apple Developer account.

Repository layout

• EST/Models contains the card model, set math, game engine, and multiplayer sessions.
• EST/Views contains the SwiftUI screens and reusable card and button views.
• ESTUITests contains the stable screenshot tests used for App Store metadata.
• appstore contains the listing copy, metadata generator, and release assets.
• telemetry contains the optional aggregate diagnostics intake Worker and schema.
• project.yml is the source of truth for the Xcode project.

Contributing

Bug reports, copy edits, and small code changes are welcome. See CONTRIBUTING.md for the local build and test workflow. Open an issue before a larger change so the direction is clear, then include the clean build command above in your pull request or issue notes.

For security reports, see SECURITY.md.

Keep the set-validation logic in Card, and keep table behavior in GameEngine. That separation lets the tutorial, solo game, and multiplayer views use the same rules.

Privacy

EST stores preferences and personal bests on the device. Optional anonymous diagnostics send one coarse aggregate record per week when enabled and configured, including activity totals such as games started, games completed, and sets found; they never include personal data or per-game events. Game Center handles its own account, leaderboard, and matchmaking data. See the privacy policy and telemetry details.

License

The code and artwork are available under the MIT License. The license does not grant rights to the SET trademark.

SET is a registered trademark of Cannei, LLC, and the game is published by PlayMonster LLC. EST is not affiliated with, sponsored by, or endorsed by either company.