Ludo Dice Roller

Every Ludo board in every house in India eventually loses its die. It goes under the sofa, into the sofa, or into a younger sibling's pocket, and the game stops dead. This roller exists for exactly that moment — but since we were building it anyway, we made it genuinely fair and put the numbers on screen so you can watch the randomness behave.

How to use it

Pick one die or two, then press Roll. Ludo uses a single die, so leave it on one for a normal game. Two is there for Backgammon, Monopoly, Business, and the handful of Ludo house rules that let you roll two dice and split the movement between tokens.

Under the dice you get your last twelve results, and under that a live breakdown of how often each face has come up this session. That second panel is the interesting one, and it is the part almost no other dice roller shows you. Roll twenty times and the bars will look lopsided — one face at 30%, another at 5%. Roll two hundred times and they start converging on 16.7%. Watching that happen is the clearest possible demonstration of why a bad run in a real game is not evidence of anything.

Where the randomness actually comes from

Most online dice rollers call Math.random(), multiply by six, and round. That is fine for a toy, but Math.random() is not a cryptographic source and its quality varies between browsers. This roller uses the Web Crypto API instead — the same random source browsers use to generate encryption keys.

There is a subtler problem underneath that, and it is worth explaining because it is where most implementations quietly go wrong. Crypto gives you a random byte: a whole number from 0 to 255. That is 256 possible values, and 256 does not divide evenly by 6 — it gives 42 remainder 4. If you just take the remainder, faces 1, 2, 3 and 4 each have 43 byte values mapping to them while faces 5 and 6 only have 42. The die is biased toward the low numbers. It is a small bias, around a quarter of a percent, but it is real and it is permanent.

The fix is rejection sampling: discard any byte of 252 or higher and draw again. 252 is the largest multiple of 6 that fits in a byte, so what remains divides perfectly and every face gets exactly a 1-in-6 chance. It costs a re-draw about 1.5% of the time and nothing else. That is what this roller does on every single roll.

Your physical die is probably less fair than this one

People trust the plastic die in the box more than a screen, and that instinct is backwards. A cheap injection-moulded die has three separate sources of bias built into it.

The pips are drilled. Each pip removes a little material, and the faces do not have equal numbers of pips. The 6 face has six holes drilled into it; the 1 face has one. That makes the 6 side fractionally lighter, which very slightly favours 6 landing face-up — the light side floats to the top. Casino dice solve this by filling the pips with a plug of equal density, which is why they cost what they do and why they look flat rather than dimpled.

The corners are rounded unevenly. Board game dice are tumbled to soften the edges, and tumbling is not a precision process. Any asymmetry in the rounding changes how the die rolls.

There is mould flash. The seam where the two halves of the mould met leaves a raised line, usually shaved off by hand or machine, never perfectly. On a well-used family Ludo die, add a decade of chips and wear on whichever corner tends to hit the floor.

None of this makes your board game unplayable. It does mean that if fairness is what you care about, a correctly built digital roller wins.

The bad-luck run, in numbers

The single most common complaint in Ludo is not being able to roll a six to open a token. Here is the actual shape of it. Each turn you have a 5-in-6 chance of not rolling a six, which is 83.3%. Over six consecutive turns that compounds to 0.833 to the sixth power — about 33.5%.

One player in three, in a typical four-player game, will genuinely sit through six turns without opening. Over ten turns the chance of still being stuck is around 16%. Over fifteen turns it is roughly 6.5% — uncommon, but across a few evenings of Ludo it will absolutely happen to you, and it will feel personal. It isn't. We go through the rest of this maths, including capture odds by distance, on the Ludo dice probability page.

House rules for when the die is genuinely gone

If you would rather not pass a phone around the table, families have solved this for decades. The most common fix is a slip of paper: six numbered scraps in a cup, drawn and replaced each turn. Note that this is drawing with replacement, so it is a fair substitute — if you forget to put the slip back you have accidentally invented a completely different game.

Another is the coin ladder: flip three coins and read heads as 1 and tails as 0 to get a number from 0 to 7, re-flipping on 6 and 7, then add one. That is rejection sampling again, done by hand — the same trick this page uses in software.

What most people reach for instead is a phone. That is what this page is for, and unlike an app it needs no install and works on whatever device is nearest.

How the dice work in the Party Ludo app

When you play a multiplayer match in the app, the dice are not rolled on your phone — a phone-side roll would be trivial to tamper with. They are decided by the server using a commit-reveal scheme: the server commits to the outcome before you roll and reveals the seed afterwards, so the result can be verified and could not have been changed after seeing your move. There is no difficulty adjustment, no rubber-banding, and no weighting by player. Read more on playing Ludo online.

Frequently asked questions