Sudoku Written by Brian Hamilton and Karan Hamilton.
Brian and Karan are the puzzle lovers and game makers behind Sudoku Online Puzzles. You can learn more on the About page.
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Both games have a reputation as exercise for the mind, and both look like logic on a grid, but they are different kinds of thing. A sudoku is a puzzle with exactly one answer, which you find on your own. A chess game has no answer at all, only an opponent trying to stop you. The question in the title has a shorter honest answer than most comparisons give, so we start there, and then compare the two on what can actually be checked.
We make sudoku, so we have a side. That is one more reason to keep to what the studies say rather than what we would like them to say.
Is sudoku or chess better for your brain?
Neither has been shown to make you smarter in general. Three sources cover most of what is known:
- Brain games in general. In October 2014 the Stanford Center on Longevity and the Max Planck Institute for Human Development gathered cognitive psychologists and neuroscientists to review the evidence. Training improves the skill you practise, they wrote, but “there is little evidence that playing brain games improves underlying broad cognitive abilities”, and there is “no compelling scientific evidence” that brain games reduce or reverse cognitive decline (Stanford Center on Longevity).
- Chess. Giovanni Sala and Fernand Gobet pooled studies of chess and music lessons for children, and of working-memory training. The better a study was designed, especially with an active control group, the smaller the effect it found, and they concluded that “far transfer of learning rarely occurs” (Current Directions in Psychological Science, 2017).
- Sudoku. In the PROTECT study of more than 19,000 people aged 50 and over, those who did number puzzles such as sudoku more often scored better on tests of attention, reasoning and memory. That is a link, not a cause, and the lead researcher, Anne Corbett, said so: “We can’t say that playing these puzzles necessarily reduces the risk of dementia in later life” (University of Exeter, via ScienceDaily).
So the better game for your brain is the one you will keep playing. The Stanford group’s own advice was to lead “physically active, intellectually challenging, and socially engaged lives, in ways that work for them”, and either game can be part of that. What each one trains is mostly itself: practise sudoku and you get better at sudoku.
Psychologists call it near transfer when practice helps with closely related tasks, such as practice on one kind of sudoku helping with another, and far transfer when it helps with something unrelated, such as school maths or memory in daily life. Claims that a game “trains your brain” are claims of far transfer, which is the kind the studies above rarely find.
What is the difference between sudoku and chess?
The second row of the table matters most: a sudoku has an answer, and a chess game has an opponent. A sudoku move is right or wrong, and you can prove which. A chess move is only good or bad against what the other player does next.
| Sudoku | Chess | |
|---|---|---|
| Players | One | Two |
| Is there a right answer? | Exactly one, in a properly made puzzle | No; perfect play is unknown |
| Rules to learn | Each digit once per row, column and box | Six kinds of piece, plus check, castling, en passant, promotion and draws |
| Solved by computer? | Yes, in a fraction of a second per puzzle | No; perfect play is known only with seven pieces or fewer on the board |
| How big is it? | 6.67 × 1021 completed grids | About 4.8 × 1044 legal positions |
| On bigger boards | Solving is NP-complete | Perfect play takes time exponential in the board size |
| How long it takes | As long as you like | Blitz: 10 minutes or less per player; rapid: more than 10, less than 60 |
Sudoku: our own counts and the sources on our mathematics of sudoku page. Chess: Wikipedia’s Solving chess and Shannon number articles, and the FIDE Laws of Chess in force from 1 January 2023.
The size row looks like a contest chess wins, but the numbers measure different things: completed sudoku grids against chess positions. The bigger difference is what a computer makes of each. Our own checker confirmed that each of the 49,158 puzzles on our 17-clue sudoku page has exactly one answer in less than a minute for the lot, while chess is still unsolved, and Claude Shannon put a conservative lower bound of 10120 on the number of possible games in 1950.
Is sudoku harder than chess?
Sudoku is easier to start, and it has a finish line; chess has neither. How much a sudoku asks of you can even be written down. Our sudoku page keeps a generated board only when a short, fixed list of moves can solve it:
- Easy and Medium: naked and hidden singles only;
- Hard: locked candidates as well;
- Expert: naked pairs as well.
We dealt 200 puzzles at each of those four levels and checked them with the same steps: all 800 were finished. Not one of the 5,000 puzzles behind our Evil sudoku page can be finished that way. The 18 named techniques our Sudoku Helper knows finish almost three in four of them, and the rest need longer chains of reasoning. Even so, the list of sudoku techniques has an end. Chess has nothing like it: computers have worked out perfect play only for positions with seven or fewer pieces.
So a hard sudoku is hard the way a long proof is hard: every step can be checked, and the difficulty is in finding the next one. A hard chess game is hard because the other player gets a say. Neither kind is simply the bigger one.
Does sudoku make you better at chess?
Nobody has shown it, and the far-transfer studies above suggest not expecting much. The evidence we could find is one anecdote. In 2020 the ChessBase writer Arne Kaehler solved some sudoku built on chess moves and felt he played “much better than usual” online afterwards; he asked whether the sudoku was the reason, and a reader suggested it might simply have warmed his mind up.
What does cross over is the chessboard itself. Sudoku setters borrow chess moves as rules. In anti-knight sudoku a digit may not repeat a knight’s move away, and Mitchell Lee’s Miracle Sudoku of 2020, the puzzle that ChessBase article was about, added a king’s-move rule and a ban on consecutive neighbours and started from just two digits. If you play chess, those rules will feel familiar from the first move.
Which uses more memory, sudoku or chess?
Chess, as players get stronger. In Chase and Simon’s 1973 experiments, skilled players shown a position briefly recalled much larger groups of pieces than novices did; with the pieces placed at random, the gap shrank (Wikipedia: Chunking, citing that work and later studies by Fernand Gobet and colleagues). Chess strength rests partly on a store of familiar positions.
A sudoku keeps its own state. With pencil marks you write down what each square can still be, so the page holds the facts and you hold the method. The method is the short list above, so there is little to memorise and a lot to notice.
Should you play sudoku or chess?
Choose by what you enjoy, not by a promised effect on your brain:
- Sudoku if you want a puzzle you can put down and pick up, at your own pace, with an answer you can be sure of. Start with a classic sudoku, or the 4×4 and 6×6 grids on our sudoku for kids page for younger players.
- Chess if you want an opponent: another person, a club, a rating that moves with your results.
- Both, if you like each for different moods. And if what you miss in sudoku is the opponent, our Multiplayer Sudoku puts two players on one screen, taking turns on a shared grid, either racing two clocks or scoring the value of each digit they place.