How is the game played?

Two to six players, one counter each and one die. Everyone starts off the board and takes turns to throw and move that many squares along the numbers. Land at the foot of a ladder, or on a go-forward square, and move on; land on a snake's head, or a go-back square, and move back; land on a miss-a-turn square and sit out your next turn. The first counter to reach the last square wins, by whichever finishing rule you printed.

How can a board be impossible to finish?

A die shows at most six, so six snake heads on consecutive squares form a wall no throw can clear. Every counter that reaches the squares before it is sent back sooner or later, for ever. It can be subtler: if a ladder happens to carry some counters over the wall, the last square is reachable and the board looks fine, but anyone who misses that ladder is trapped. Both cases are caught by checking, for every position a counter can reach, whether the finish can still be reached from it.

Why does needing an exact throw make the game so much longer?

Because of where the waiting happens. A counter one square from the end needs a one, which comes up one throw in six, so it waits six turns on average for that single square. Add the squares before it and an empty track gains a little over four turns from the rule alone. Bounce-back is longer still when a snake sits near the end, since a throw that is too high can come back down onto it.

Is there any skill in it?

None. No player ever makes a choice, which is why the whole game can be solved in advance and why it works for players too young to make one. The only decisions are the ones made before the first throw: how many snakes, which finishing rule, and who goes first.

How much is going first worth?

A few points on a long board and a great deal on a short one. With two players on the seeded thirty-six-square board the first to throw wins 51.8% of games; on the hundred-square board from the 1993 paper it is 50.8%. Make the game quick enough to finish in eight rounds and the first of three players wins 42% of the time.

Snakes and Ladders Board Generator

A roll-and-move board is the simplest game there is to print: a numbered track, one die, and a handful of squares that send a counter forwards or back. It is also easy to get wrong in ways nobody notices until the game is on the table — a board with too many snakes that runs for an hour, or one where the squares before the finish make the ending drag. This draws a fresh board at the size you choose, with as many ladders, snakes and miss-a-turn squares as you ask for, and then does the part a hand-drawn board cannot: it works out how many turns a game on that exact board takes on average, the fewest it could take, and how much going first is worth. Before any of that it checks the one thing that can make a board unplayable — that the last square can still be reached from everywhere a counter can get to.

Board

Style

Ladders

Between 0 and 4 on this board.

Snakes

Between 0 and 4. These are what make a game long.

Miss-a-turn squares

Between 0 and 3 on this board.

Finishing

Aim for this many turns (optional)

Leave empty to take the first board drawn. With a number, 24 boards are drawn and the nearest is kept.

Players

Seed (optional)

The same seed and settings rebuild the same board. A seed makes a board repeatable; it is not a secret and has no cryptographic strength.

Paper size

Print size

Margin

Millimetres of blank edge, 5 to 40.

Turn the paper sideways

How to print this, or save it as a PDF

There is no PDF to download, and there does not need to be. Open the print command in your browser and choose “Save as PDF” as the destination. The page addresses and dates a browser normally prints across the top and bottom are already kept off.
Set the scale to 100%, not “fit to page”. This sheet is already the exact size of the paper you chose, so anything that resizes it makes every measurement on it wrong.
Leave the paper size in the dialog set to the same one you chose here.

A numbered board, its special squares, and how long a game on it will take, will appear here.

What this generator does

Lays a numbered track back and forth up the page, places the squares that move a counter, and prints the result with the rules that go with it. The same board is then treated as what it mathematically is — a set of positions and the chances of moving between them — and solved, so the page can state the average number of turns, the shortest possible game, the point by which nine games in ten are over, and each seat's chance of winning. Nothing else here prints a game: the board game picker suggests a kind of game to play and the bingo card generator prints cards for a caller's game, while the Markov chain simulator runs a chain you describe state by state. This builds the chain from a board and gives you the board.

How to use this tool

Choose the size of the board and whether jumps are drawn as snakes and ladders or written in the squares.
Set how many squares send a counter forward, how many send it back, and how many cost a turn.
Pick how the game finishes — this changes the length more than anything else on the page.
Press the button, and read the line above the board for how long a game will take.
If that is too long or too short, change the counts, or type a number of turns to aim for.
Choose the paper and print. The rules for that board print underneath it.

Understanding the controls

Board: Twenty squares up to a hundred, always a full rectangle so the track has no ragged last row. Length grows faster than size: an empty thirty-six-square track takes 15 turns with an exact throw to finish and an empty hundred-square one takes 33, before a single snake is added.
Style: Snakes and ladders draws each jump across the board, always from one row to another, climbing or dropping up to roughly half the board's height. Written in the squares prints go forward and go back instructions of one to three squares instead, which keeps every move local and leaves the board clear to write on — the usual form for a classroom game.
Ladders, or go-forward squares: How many squares send a counter forward. Each one shortens the average game, though only for a counter that happens to land on it: with the seed used in the examples, four ladders take the empty thirty-six-square track from 15.0 turns to 12.0.
Snakes, or go-back squares: How many squares send a counter back. These are what make a game long. With the seed used in the examples, four snakes and no ladders average 21.3 turns on thirty-six squares, against 12.0 for four ladders and no snakes and 17.7 for four of each.
Miss-a-turn squares: A counter that lands on one sits out its next turn. Each costs exactly one turn when it is hit, so a few of them lengthen a game gently and predictably, where a snake's cost depends on how far it drops.
Finishing: Whether a throw that is too high still wins, is wasted, or bounces the counter back from the end. This is the largest single lever on the page. The same seeded board takes 10.6 turns when any throw that gets there wins, 17.7 when an exact throw is needed, and 21.7 with bounce-back, where an overshoot can land on a snake.
Aim for this many turns: Left empty, the first board drawn is the board. With a number, twenty-four boards are drawn at your settings and the one whose average is nearest is kept. It is the nearest of twenty-four, not a guarantee: if the counts you chose cannot produce that length, change the counts.
Players: Changes nothing about the board — only the figures quoted for it. More players means somebody finishes sooner, so the game is shorter in rounds though longer in total throws.
Seed (optional): Type anything and the same settings give the same board again, which is how every table in a room can be handed an identical game or a board can be reprinted next term. A seed is a repeat word and not a secret: it is not cryptographic, and anyone who knows it can rebuild the board.

Worked examples

Thirty-six squares, four ladders, four snakes, exact throw to finish — seed rainy-day: Ladders 4 to 13, 8 to 25, 16 to 24 and 26 to 32; snakes 7 to 5, 9 to 3, 23 to 18 and 35 to 17. One counter takes 17.7 turns on average, the fewest possible is four (throwing 4, 3, 6, 6), half of solo runs are over within 14 turns and nine in ten within 33. With two players somebody finishes after about 11.7 rounds, and the first to throw wins 51.8% of the time.
The same board and seed under the other two finishing rules: Any throw that reaches the end wins: 10.6 turns on average, and the first player's share rises to 53.7%. Bounce back from the end: 21.7 turns, and nine games in ten take up to 43. Nothing on the board moved; only the last few squares are played differently.
Thirty squares, written in the squares, three forward, three back, two miss-a-turn, any throw finishes — seed rainy-day: 2 forward 1, 7 forward 3, 8 back 3, 17 back 1, 20 back 2, 22 forward 2; miss a turn on 15 and 27. One counter takes 9.7 turns on average and at least five. With three players a game lasts about 8.1 rounds, and the seats win 42.0%, 32.4% and 25.6% of the time — on a board this quick, the order of play matters a great deal.
Aiming for twenty turns on the first board's settings — seed rainy-day: Twenty-four boards are drawn and the nearest kept: ladders 3 to 10, 16 to 34, 20 to 26 and 24 to 28; snakes 18 to 8, 19 to 15, 22 to 1 and 35 to 17, at 19.6 turns on average.

Common use cases

A different board for every rainy afternoon, rather than the one in the cupboard everybody knows by heart
A classroom game sized to the time available — a ten-minute board for the end of a lesson, not a forty-minute one
A track to write questions or vocabulary into, with the forward, back and miss-a-turn squares already placed
A worked example for a probability lesson: the same board under three finishing rules, with the three different lengths
Handing every table the identical board from one seed, so no group can blame the layout

How this generator works

The squares are numbered along a path that runs left to right along the bottom row, right to left along the next, and so on up the page, so each square sits beside the one before it and a counter never has to cross the board to continue. Special squares are then placed one at a time, alternating forward and back so neither gets first pick, and every rule about them is applied as each is chosen rather than checked afterwards: no square is given two jobs, a ladder always ends on a higher row and a snake on a lower one, and nothing starts or ends on the last square. One thing cannot be settled square by square, so it is checked on the finished board: from every position a counter can reach, the last square must still be reachable. That fails when snake heads sit on six squares in a row, because no throw of a die clears six; a counter behind such a wall can never finish. With the numbers offered here a wall is very unlikely, and the check runs on every board regardless. The length of a game is then worked out, not estimated. Where a counter goes next depends only on where it stands and what is thrown, so the average number of turns from each square satisfies one equation per square, and solving them together gives the figure exactly. The same figure is then worked out a second, unrelated way — by following the whole spread of possible positions forward one turn at a time and adding up the chance the game is still going — and the board is passed as checked only if the two agree. The method was also run on the hundred-square board analysed in a 1993 paper in The Mathematical Gazette, where it returns that paper's published answer of 39.2 turns on average, and the shortest game of seven turns that is widely quoted for that board.

Randomness and fairness

Chance decides where the special squares go and nothing else: each jump takes a free square picked at random and an end picked at random from the squares it is allowed to reach. Everything quoted about the board afterwards — the average length, the shortest game, the seat-by-seat chances — is calculated from the finished layout and involves no further draw. The positions come from your browser's cryptographic random source unless you give a seed, which replaces it with a repeatable one. That is there for reproducibility, not secrecy.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

One six-sided die, thrown once per turn. Many families let a six earn another throw; that rule shortens a game and is not included in any figure here.
Counters start off the board and enter on the first throw, so a throw of one lands on square one.
A jump is taken once. A counter carried to the end of a ladder or a snake stays there until its next turn, and no jump ever ends on the start of another.
Players do not interact. Two counters may share a square, and nobody is sent back for being landed on.

Limitations and good to know

The squares carry their numbers and the game's own instructions and nothing more. Questions, words or pictures cannot be typed into them, which is what a language-class board usually wants; the instruction style leaves most squares empty with room to write.
Snakes and ladders are drawn as straight runs between the centres of two squares and are not routed round each other. They can cross each other, and a long one runs across squares it has nothing to do with; the square numbers are printed on top of them so every square stays readable.
The figures are for one six-sided die and the rules printed under the board. A house rule — another throw on a six, two dice, sending a counter back when it is landed on — changes the length, and none of those is modelled.
Aiming for a length picks the nearest of twenty-four boards. With counts that cannot reach the number asked for, the nearest may still be several turns away, and the page reports what it got instead of the number you typed.
The largest board is a hundred squares and every board is a rectangle. Spirals, loops and tracks that fork are different games and are not drawn.

Common mistakes

Reading the average as how long the game will take: It is the average of a very lopsided spread. On the seeded example the average is 17.7 turns, half of runs finish within 14, and one in ten is still going after 33. Plan for the nine-in-ten figure if the game has to fit a slot.
Adding snakes to make a short board last longer: Change the finishing rule first. Requiring an exact throw added seven turns to the seeded board without touching a square, and it lengthens the game for everybody equally, where a snake punishes whoever happens to land on it.
Assuming the board is fair because everyone plays the same squares: Whoever throws first wins more often, and on a short board by a lot — 42% against 26% between the first and third seats in the thirty-square example. Let the youngest go first, or play twice and swap the order.

Practical tips

For a first game with small children choose any throw finishes. Waiting for an exact number on the last few squares is the part they find unfair.
If the printed board looks crowded, drop to fewer ladders and snakes or move up a board size — at the largest counts on a hundred squares the drawings do cross each other.
A coin or a button works as a counter, and a seeded board can be printed again if one goes missing with the game half finished.

Privacy and your data

The board is drawn, checked and solved entirely in your browser. The only thing you can type is a seed and a target number of turns; neither is stored, sent anywhere or included in any usage count, and nothing about the board you made leaves the device.

Snakes and ladders is a traditional game that nobody owns. Every board here is an original layout drawn at random, not a copy of any published board, and this page is not affiliated with any commercial edition.

Frequently asked questions

How is the game played?: Two to six players, one counter each and one die. Everyone starts off the board and takes turns to throw and move that many squares along the numbers. Land at the foot of a ladder, or on a go-forward square, and move on; land on a snake's head, or a go-back square, and move back; land on a miss-a-turn square and sit out your next turn. The first counter to reach the last square wins, by whichever finishing rule you printed.
How can a board be impossible to finish?: A die shows at most six, so six snake heads on consecutive squares form a wall no throw can clear. Every counter that reaches the squares before it is sent back sooner or later, for ever. It can be subtler: if a ladder happens to carry some counters over the wall, the last square is reachable and the board looks fine, but anyone who misses that ladder is trapped. Both cases are caught by checking, for every position a counter can reach, whether the finish can still be reached from it.
Why does needing an exact throw make the game so much longer?: Because of where the waiting happens. A counter one square from the end needs a one, which comes up one throw in six, so it waits six turns on average for that single square. Add the squares before it and an empty track gains a little over four turns from the rule alone. Bounce-back is longer still when a snake sits near the end, since a throw that is too high can come back down onto it.
Is there any skill in it?: None. No player ever makes a choice, which is why the whole game can be solved in advance and why it works for players too young to make one. The only decisions are the ones made before the first throw: how many snakes, which finishing rule, and who goes first.
How much is going first worth?: A few points on a long board and a great deal on a short one. With two players on the seeded thirty-six-square board the first to throw wins 51.8% of games; on the hundred-square board from the 1993 paper it is 50.8%. Make the game quick enough to finish in eight rounds and the first of three players wins 42% of the time.