Havannah
Play Havannah in your browser, plus a measured answer to which of its three winning shapes actually happens — and why the ranking inverts.
Click any empty cell to place a stone. Nothing ever moves and nothing is captured. You win by building a group that does any one of three things: joins two corners (a bridge), touches three edges (a fork), or encloses at least one cell (a ring — the enclosed cell can be empty or hold either colour). Everything runs in your browser; nothing is uploaded.
Which of the three actually happens? It inverts.
"Which shape wins Havannah" has no answer that does not name a board size. Fill boards at random and count what finishes them, and the ranking turns completely upside down as the board grows — from the bridge being the usual result to the ring being the usual result.
| Side | Cells | Bridge | Fork | Ring | Playouts |
|---|---|---|---|---|---|
| 4 | 37 | 54.8% | 38.6% | 6.6% | 900 |
| 5 | 61 | 33.4% | 48.4% | 18.2% | 900 |
| 6 | 91 | 21.2% | 42.5% | 36.3% | 900 |
| 7 | 127 | 12.7% | 32.5% | 54.9% | 6,000 |
| 8 | 169 | 6.3% | 22.6% | 71.0% | 6,000 |
| 10 | 271 | 1.2% | 7.5% | 91.3% | 4,000 |
On the smallest board a ring is a curiosity at 6.6%. On the tournament-size board it is the commonest finish at 71.0%, beating the bridge by 11 to one — and at side 10 by 78 to one. The reason is that a bridge has to cross the whole board and that distance grows with the side, while a ring is purely local and only needs a loop.
Both trends are clean: the bridge share falls at every single step and the ring share rises at every single step. The fork is the interesting one — it does neither, peaking in the middle of the range, because it is the shape that is neither fully long-range like a bridge nor fully local like a ring.
What that measurement is, and what it is not
This needs saying plainly, because it is the boundary of the result. Those 18,700 playouts are random fills of the board. They describe the shape of the space — how easy each pattern is to stumble into without trying — and not what strong players do. A real opponent watches for rings and blocks them, and that is exactly the pressure random play cannot represent.
So the honest reading is not "most real games end in rings on a big board". It is that ring-avoidance becomes a much larger share of what you have to watch as the board grows, and bridge-blocking a much smaller one.
One bookkeeping note. A single stone sometimes completes two shapes at once — 82 of 900 finishes on the small board, 20 of 4,000 at side 10. Rather than picking a favourite, those are counted once under each shape, so the columns count shape completions rather than games and can exceed the number of playouts.
Worth keeping the folklore in view: the ring is often described as the rare, exotic win. On a small board that is right — 6.6% at side 4. Carried across to the board people actually play on, it is badly wrong. A claim about one board size was never a claim about the game.
How to use
- Click any empty cell to place a stone; nothing ever moves and nothing is captured.
- Win with a bridge: one group touching two of the six corners.
- Or a fork: one group touching three of the six edges, corners not counting.
- Or a ring: one group enclosing at least one cell, empty or occupied by either colour.
- Try the same position on different board sizes to see which shape starts threatening.
Frequently asked questions
What are the three ways to win at Havannah?
A bridge is a single group of your stones touching two of the six corners. A fork is a single group touching three of the six edges, where corner cells do not count as edge. A ring is a group enclosing at least one cell — and the enclosed cell can be empty or hold a stone of either colour, including your own.
Which winning shape is the most common?
There is no answer that does not name a board size, because the ranking inverts. Filling boards at random, side 4 finishes as roughly 54 per cent bridge and 6 per cent ring; side 8 is about 6 per cent bridge and 71 per cent ring; side 10 is 1 per cent bridge and 91 per cent ring. A bridge has to cross the whole board and that distance grows, while a ring is local and only needs a loop.
Does that mean most real games end in rings?
No, and the distinction matters. Those figures come from random fills, so they describe how easy each pattern is to stumble into rather than what strong players do — a real opponent watches for rings and blocks them. The honest reading is that ring-avoidance takes up more of your attention as the board grows, and bridge-blocking less.
Is a ring still a ring if it surrounds your own stone?
Yes, and this is the case implementations most often get wrong. If the enclosed cell holds a stone of the ring’s own colour it joins the group, so a detector that just floods in from the edge looking for unreachable cells sees nothing and misses the loop. Solid blobs are common, so getting this wrong undercounts rings badly.
What board size should I play?
Side 8 is the usual tournament size and side 10 is common too. The small boards here are worth a game or two mainly to feel how differently they behave: on side 4 you are mostly racing for corners, while on side 8 the ring is the shape most likely to catch you out.
Does this send anything anywhere?
No. The game and the playout survey both run entirely in your browser and nothing is uploaded.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.