Halma
Play Halma against the computer, plus measured jump-chain lengths and why the longest one found keeps growing with the sample.
Click one of your pieces, then a highlighted square. A move is either one step to a touching square, or a jump over any single adjacent piece — yours or theirs — into the empty square beyond, and jumps chain as far as they go. Nothing is ever captured. You win by filling the far camp exactly. Everything runs in your browser; nothing is uploaded.
Jumping is not a trick, it is most of the game
Across 400 random games, of the 4,716,396 moves that were available to play, 41.4% were jumps rather than single steps. You are not waiting for the occasional chance to hop — you are choosing between them nearly every turn.
| Jumps in the chain | Times it was offered |
|---|---|
| 1 | 737,631 |
| 2 | 578,880 |
| 3 | 357,116 |
| 4 | 174,157 |
| 5 | 71,628 |
| 6 | 25,180 |
| 7 | 7,751 |
| 8 | 2,014 |
| 9 | 480 |
| 10 | 80 |
| 11 | 10 |
The longest chain is a moving target, not a number
Eleven jumps was the longest that turned up in 400 games — and also at 50, 100 and 200 games. Four sample sizes in a row agreeing is exactly what a ceiling looks like. It was not one.
| Games sampled | Moves offered | Longest chain found |
|---|---|---|
| 25 | 297,482 | 10 |
| 50 | 591,958 | 11 |
| 100 | 1,180,188 | 11 |
| 200 | 2,357,123 | 11 |
| 400 | 4,716,396 | 11 |
| 800 | 9,427,416 | 13 |
| 1,600 | 18,903,403 | 13 |
So 13 is a longest-so-far and not a maximum. That is worth saying out loud, because the natural way to write this page would have been to sample 400 games, see eleven four times running, and print "the longest possible chain is eleven". Doubling the sample found thirteen.
A search allowed to place the obstacles anywhere — and so to build the friendliest ladder it can — only reaches 11 in 200,000 tries. Real games beat random scattering, which makes sense: a Halma position is full of the loose diagonal lines chains feed on, and noise is not.
And the endgame is not about advancing
You win by filling the far camp exactly, and that is a different problem from getting there. An opponent scored on how far forward it pushes each piece — which sounds like the entire game — finished 0 of 60 games. Rescored on distance to the nearest camp square still empty, the same opponent finished 60 of 60, in a mean of 49 plies. Advancing is not arriving, and the last few pieces are where Halma is actually won.
The opponent on this page is one ply deep with no search — Halma rewards building jump ladders several moves ahead, which it does not attempt. A live check of 12 self-played games runs on every build and all of them still finish, in a mean of 51 plies.
How to use
- Click one of your pieces, then a highlighted square.
- A move is one step to a touching square, or a jump over an adjacent piece into the empty square beyond.
- Jumps chain as far as they go, and you may jump your own pieces as well as your opponent’s.
- Nothing is ever captured — jumped pieces stay where they are.
- Win by filling the far camp exactly.
Frequently asked questions
How much of Halma is jumping?
Most of it. Across 400 random games, of the 4.7 million moves that were available to play, 41.4 per cent were jumps rather than single steps. You are not waiting for an occasional chance to hop — you are choosing between chains nearly every turn.
What is the longest jump chain possible?
Nobody here knows, and that is the honest answer. Eleven jumps was the longest found in 400 games, and it was also eleven at 50, 100 and 200 games — four sample sizes agreeing, which looks exactly like a ceiling. Doubling the sample to 800 games found thirteen. So thirteen is a longest-so-far, not a maximum.
Do longer chains get rarer?
Yes, smoothly, by roughly a factor of two or three at each step: 737,631 single jumps, 578,880 doubles, 357,116 triples, and so on down to ten chains of eleven jumps. There are no bumps in the decay.
Can you build a longer chain by arranging the pieces yourself?
Surprisingly, no. A search allowed to scatter obstacles anywhere it likes only reaches eleven in 200,000 attempts, while real games reach thirteen. Halma positions are full of the loose diagonal lines chains feed on, and random noise is not.
Is Halma just about racing forward?
No, and this is where it catches people. You win by filling the far camp exactly, which is a different problem from getting there. An opponent scored purely on pushing pieces forward finished 0 of 60 games; rescored on distance to the nearest camp square still empty, the same opponent finished 60 of 60. Advancing is not arriving.
Does this send anything anywhere?
No. The game and the chain study 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.