# SameGame
**SameGame** (チェインショット!, originally "Chain Shot!") is a single-player tile-clearing puzzle in which the player removes groups of two or more orthogonally adjacent blocks of the same color from a rectangular board, with the remaining blocks falling down and empty columns closing up. It was invented by Kuniaki Moribe in 1985 under the name Chain Shot and has since appeared under many names, including SameGame, Clickomania!, Same Gnome, and Jawbreaker, with the core rule of clearing adjacent same-colored clusters largely unchanged.[2](https://puzzlebyrinth.com/en/articles/samegame-1985)
| Key fact | Detail |
|---|---|
| Origin | Invented by Kuniaki Moribe in 1985 as Chain Shot!, submitted to the magazine Monthly ASCII and distributed for the Fujitsu FM-8/FM-7[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) |
| Name "SameGame" | Re-created by Eiji Fukumoto under the name SameGame in 1992[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) |
| Standard board | 15×15 grid filled with blocks of 5 colors at random; a move removes a group of at least two orthogonally adjacent same-color blocks[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) |
| Scoring | Points per removed group follow \( (n-2)^2 \), where \( n \) is the group size; clearing the board earns a 1,000-point bonus, while leftover blocks cost points[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) |
| Complexity | SameGame is NP-complete; the related game Clickomania was proven NP-complete with 5 colors and 2 columns[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) |
| Search-space size | Game-tree complexity about \( 10^{85} \) for a random initial position; state-space complexity about \( 10^{159} \)[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) |
| Notable ports | Super Famicom, Texas Instruments calculators, TiVo, and Hudson's Pop 'Em Drop 'Em Samegame for Wii (2009)[4](https://games.jayisgames.com/review/samegame.php) • [5](https://www.nintendolife.com/reviews/2009/01/pop_them_drop_them_samegame) |
## Rules and gameplay
The player is presented with a grid of colored blocks and removes groups of at least two orthogonally adjacent blocks of the same color. Blocks above a removed group fall down, and when a column empties, the columns to its right shift left. The game ends when the board is empty or no more groups can be removed.[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) In the standard 15×15, 5-color version, each removed group of \( n \) blocks scores \( (n-2)^2 \) points, so groups of two score nothing and a group of five scores 9. Clearing the entire board earns 1,000 bonus points; if blocks remain, points are deducted using a similar formula applied iteratively for each color left, treating all blocks of the same color as connected.[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf)
**Scoring families.** Different implementations use different reward functions, such as \( n(n-1) \) in Bubble Breaker or \( (n-2)^2 \) in the research standard. These functions share one property: removing one large group of size \( r \) always yields a higher score than removing two groups of \( p \) and \( q \) blocks where \( p + q = r \) and \( 1 \le p, q \le r-1 \). This is what pushes skilled play toward building and then clearing very large groups rather than popping small ones early.[6](https://citeseerx.ist.psu.edu/document?doi=fe05d9836e683683e7f763dd67322e64240e7e8e&repid=rep1&type=pdf) Variants that differ in scoring function are often given distinct names, such as Jawbreaker and Clickomania.[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf)
## History
Chain Shot! was submitted by Kuniaki Moribe to Monthly ASCII in 1985 and released for the Fujitsu FM-8/FM-7 home computers. Little is known about the author beyond the name.[2](https://puzzlebyrinth.com/en/articles/samegame-1985) • [3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) The puzzle was re-created by Eiji Fukumoto under the name SameGame in 1992, and the game has since been ported to many platforms.[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) It has appeared on devices as varied as the Super Famicom, several [Texas Instruments](https://www.edgepedia.org/texas-instruments) calculators, and the TiVo home television recording unit.[4](https://games.jayisgames.com/review/samegame.php)
**Later implementations.** In 2004, Simon Tatham included the rule in his portable puzzle collection as "Samegame".[2](https://puzzlebyrinth.com/en/articles/samegame-1985) The KDE project maintains KSame, a GPL-2.0+ game described as similar to SameGame, whose goal is to clear a board filled with multicolored items;[7](https://apps.kde.org/ka/ksame/) the KDE game Klickety can also be launched in KSame mode with the command `klickety --KSameMode`.[8](https://docs.kde.org/stable_kf6/en/klickety/klickety/faq.html) Hudson released Pop 'Em Drop 'Em Samegame for WiiWare in 2009, a version in which clearing the screen refills it entirely rather than ending the game.[5](https://www.nintendolife.com/reviews/2009/01/pop_them_drop_them_samegame)
## Computational complexity
SameGame is a one-person, perfect-information puzzle, and the decision problem of whether an initially filled board can be emptied is NP-complete. The proof reduces SameGame to Clickomania, which had been proven NP-complete with 5 colors and 2 columns; because Clickomania's only goal is to remove as many blocks as possible while SameGame also rewards points for large groups, SameGame is at least as hard.[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) Finding the maximum-score path is just as hard.[6](https://citeseerx.ist.psu.edu/document?doi=fe05d9836e683683e7f763dd67322e64240e7e8e&repid=rep1&type=pdf)
The search space is large and dynamic. For a random initial position the game-tree complexity is about \( 10^{85} \) on average, and the state-space complexity is about \( 10^{159} \), computed from the number of possible column combinations. A typical starting position has a branching factor of around 40, and an average solution takes about 45 moves.[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) • [6](https://citeseerx.ist.psu.edu/document?doi=fe05d9836e683683e7f763dd67322e64240e7e8e&repid=rep1&type=pdf)
**Classical search methods fail here.** A* and IDA*, the standard tools for puzzles such as the 15-puzzle and Sokoban, depend on an admissible evaluation function, and no accurate admissible under-estimator has been found for SameGame. An over-estimator that assumes all blocks of a color are connected and removable at once is far from the real score and makes A* and IDA* behave like a simple breadth-first search.[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf)
**Monte-Carlo methods.** Maarten P.D. Schadd and Mark H.M. Winands, researchers at Maastricht University, proposed Single-Player Monte-Carlo Tree Search (SP-MCTS), an MCTS variant adapted to puzzles, which does not require an admissible heuristic (an estimate that never overstates the true remaining score). Their SP-MCTS program gained the highest scores so far on the standardized SameGame test set at the time of publication.[3](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf) Later work from [Leiden University](https://www.edgepedia.org/leiden-university) studied the chessboard variant, a subclass of SameGame for which exactly which puzzles are solvable can be defined, and described improved solving algorithms.[9](https://liacs.leidenuniv.nl/~kosterswa/samegame.pdf)
## Variants and research uses
Beyond the standard game, SameGame has been adapted into research benchmarks. MO-SameGame, part of the MOMAland multi-objective reinforcement-learning environment collection, is a multi-objective, multi-agent variant in which 1 to 5 agents play on rectangular boards from 3 to 30 squares per side (default 15) filled with 2 to 10 colors (default 5).[10](https://momaland.farama.org/environments/mosame_game/) The standard settings used for SameGame within research are a 15×15 board, which is the configuration solvers and score comparisons typically target.[11](https://www.diva-portal.org/smash/get/diva2%3A813153/FULLTEXT01.pdf)
Compared with match-3 games such as Bejeweled, where players swap adjacent tiles to form matches, SameGame requires selecting blocks that are already grouped together, shifting the emphasis from rapid reflexes to methodical planning.[12](https://www.cannacompanionusa.com/daily/Y52/962/readTLTPtb-samegame)
## References
1. [Same Game manual, Simon Tatham's Portable Puzzle Collection (TwistyMaze mirror)](https://puzzles.twistymaze.com/help/manual/samegame)
2. [SameGame (1985) — The Grammar of Clearing Same-Colored Clusters, Puzzlebyrinth](https://puzzlebyrinth.com/en/articles/samegame-1985)
3. [Schadd, M.P.D., Winands, M.H.M., van den Herik, H.J., Aldewereld, H. — Addressing NP-Complete Puzzles with Monte-Carlo Methods, Maastricht University](https://dke.maastrichtuniversity.nl/m.winands/documents/SameGame.pdf)
4. [SameGame — Walkthrough, Tips, Review, JayIsGames](https://games.jayisgames.com/review/samegame.php)
5. [Pop Them, Drop Them SameGame Review (WiiWare), Nintendo Life](https://www.nintendolife.com/reviews/2009/01/pop_them_drop_them_samegame)
6. [Solving SameGame and its Chessboard Variant (CiteSeerX)](https://citeseerx.ist.psu.edu/document?doi=fe05d9836e683683e7f763dd67322e64240e7e8e&repid=rep1&type=pdf)
7. [KSame — KDE Applications](https://apps.kde.org/ka/ksame/)
8. [Klickety FAQ, KDE documentation](https://docs.kde.org/stable_kf6/en/klickety/klickety/faq.html)
9. [Solving SameGame and its Chessboard Variant, Leiden University](https://liacs.leidenuniv.nl/~kosterswa/samegame.pdf)
10. [MO-SameGame, MOMAland Documentation](https://momaland.farama.org/environments/mosame_game/)
11. [Degree project on SameGame solving, DiVA portal](https://www.diva-portal.org/smash/get/diva2%3A813153/FULLTEXT01.pdf)
12. [SameGame overview and comparisons, Cannacompanion USA](https://www.cannacompanionusa.com/daily/Y52/962/readTLTPtb-samegame)
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*Topic: Encyclopedia › Sports, games, and recreation › Video games and digital play › Games and gameplay › Individual game titles › Individual PC and computer-platform game titles › Platformer and puzzle titles*
*Initially written Sep 17, 2026 · Reviewed: Oct 21, 2026 · Edited: Oct 15, 2026; Oct 21, 2026; Oct 25, 2026 · Last review: Oct 21, 2026*
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License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license