Onitama
Play Onitama against the computer, plus the card geometry: every card you hand over has exactly the opposite forward bias for your opponent.
Pick one of your two cards, then a piece, then a square. Capture the enemy master, or walk your own master onto their arch — the marked square on their back row. Then the card you played goes to them and you take the spare. Everything runs in your browser; nothing is uploaded.
A card's forward bias is exactly reversed when it crosses the table
Your opponent reads every card upside down, so its forward offsets become their backward ones. The bias it gives them is therefore exactly minus the bias it gives you — not approximately, but summing to zero for all sixteen cards. Rotation cannot change how many squares a card reaches, only which way they point.
| Card | Forward | Backward | Bias for you | Bias once it is theirs |
|---|---|---|---|---|
| Crab | 1 | 0 | +1 | -1 |
| Elephant | 2 | 0 | +2 | -2 |
| Mantis | 2 | 1 | +1 | -1 |
| Crane | 1 | 2 | -1 | +1 |
| Boar | 1 | 0 | +1 | -1 |
The other 11 cards are perfectly balanced and cost nothing either way. But Crab, Elephant, Boar have no backward offset at all, which means that once handed over they have no forward one — they advance you and can only retreat your opponent. And Crane is the only card in the deck with a negative bias, so handing it over gives away a card that advances them.
Which kills the obvious strategy of hoarding the good cards and playing the weak ones. Strength and handover cost are the same quantity with opposite signs, so the card that gains you most ground is exactly the one that costs them most — refusing to play it is refusing to advance.
And seven cards have no counterpart in the deck
Turn a card through 180° and you get the move set your opponent will hold. Sometimes that rotation is another card in the deck, so the pattern stays inside the game's vocabulary. Often it is not.
| Group | Cards | Count |
|---|---|---|
| Unchanged by rotation | Goose, Rooster, Monkey | 3 |
| Rotate into each other | Mantis, Horse, Ox, Crane, Eel, Cobra | 6 |
| Rotation is not a card | Tiger, Dragon, Frog, Rabbit, Crab, Elephant, Boar | 7 |
Seven of sixteen — the largest of the three groups, though short of a majority. For those seven, handing the card over gives your opponent a movement pattern that exists nowhere else in the deck: there is no card you could ever hold that moves the way a handed-over Tiger moves for them.
Is it worth playing with that in mind?
Two otherwise identical one-ply opponents, one docking a move for how much reach the card will give away and one ignoring it entirely. Over 800 games the mindful side won 52.3% playing Red and 55.3% playing Blue — an average of 53.8%.
A few points rather than a landslide, which is about right: the card matters, but not as much as not losing your master. Both opponents are one ply deep with no search — Onitama rewards seeing several exchanges ahead, which neither attempts, so read these as a comparison between two habits rather than a measure of good play.
How to use
- Pick one of your two cards, then a piece, then a square it can reach.
- Capture the enemy master, or walk your own master onto their arch, to win.
- The card you play then goes to your opponent, and you take the spare.
- Your opponent reads every card upside down, so its forward moves become their backward ones.
- Watch which cards you hand over as much as which move you make.
Frequently asked questions
What happens to the card you play in Onitama?
It goes to your opponent. You take the spare card in its place, so the five cards in play cycle between the two of you and every card you use is one you are lending out.
How much does handing a card over actually cost?
Exactly as much as it gained you, in forward terms. Your opponent reads the card upside down, so its forward offsets become their backward ones and its bias for them is precisely minus its bias for you — the two sum to zero for all sixteen cards.
Which cards are safest to hand over?
Crab, Elephant and Boar. They have no backward offset at all, so once rotated they have no forward one: they advance you and can only retreat your opponent. Crane is the opposite and the only card in the deck with a negative bias — one step forward against two back — so handing it over gives away a card that advances them.
Should I just hoard the strong cards?
No, and the geometry is why. Strength and handover cost are the same quantity with opposite signs, so the card that gains you the most ground is exactly the one that costs your opponent the most. Refusing to play it is refusing to advance.
Do all the cards have a counterpart in the deck?
No. Three are unchanged when rotated — Goose, Rooster and Monkey — and six form three mirror pairs. The remaining seven, the largest group though not a majority, rotate into patterns that appear nowhere else, so there is no card you could ever hold that moves the way a handed-over Tiger moves for your opponent.
Does thinking about the handover actually win games?
A little. Two otherwise identical one-ply opponents, one docking a move for the reach it gives away and one ignoring it, played 800 games: the mindful side won about 54 per cent overall. A few points rather than a landslide — the card matters, but less than not losing your master.
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