Ludo capture odds: about 1 in 28 two-player games end without one

Ahmed Moaz · 10 October 2026

Yes, a Ludo game can finish with nobody ever sent home. Anyone who plays Ludo with friends knows the sting of it, so it is fair to ask how often it never happens. In 10,008 simulated two-player games on the Ludo engine I build for Boardit, run on 29 September 2026, 353 ended without a single Ludo capture. That is 3.5%, or about one game in 28. With three players it happened in 2 games out of 10,008. With four, it never happened.

The 1 in 28 is not the surprising part. The surprise is that the simplest model of random events predicts far fewer quiet games. The size of that gap says something about how captures arrive.

The count from 30,024 simulated games

The run put 30,024 complete games through the live rules engine, 10,008 at each table size, with a seeded die. Every seat was a scripted test player. In each game all seats but one followed a plain rule: take a capture or a finish if one is there, otherwise bring a piece out, otherwise move the furthest piece. The remaining seat used a scoring rule for a separate test.

A capture means landing on a lone rival piece and sending it back to base. Some tables call it a Ludo kill.

The median game lasted 70 rounds at two seats, 95 at three and 120 at four, where a round is one turn for every seat.

What a Poisson model predicts for a Ludo capture count

Statisticians reach for the Poisson model when they count events in a fixed stretch. NIST's statistics handbook describes it as a model for the number of events in a given time interval. Its formula gives the probability of zero events as e to the power minus λ, where λ is the average count.

Ludo makes a tidy Poisson distribution example. Set λ to the two-player mean of 4.42 captures. The chance of a game with none is then e^-4.42, which is 1.2%. Across 10,008 games, that predicts about 121 quiet games.

The simulation produced 353. That is nearly three times the textbook figure.

Why the real count has more zeros

A Poisson count assumes every game shares one underlying capture rate. Ludo games don't. Some runs of the dice keep the two armies apart for long stretches; others bring them together again and again.

Pool games with different rates and the count spreads out more than a Poisson model allows. Statisticians call this overdispersion. It shows at both ends of the range: more empty games, and more crowded ones. The Poisson model puts the 90th percentile at 7 captures. The simulation's 90th percentile is 8.

The usual repair is the negative binomial distribution, which adds one number for the extra spread. I fitted it to two figures only: the mean of 4.42 and the 3.5% share of empty games. The fitted variance is about 7.5, against 4.4 for Poisson. Then I checked it against two figures it never saw. It predicts a median of 4 captures and a 90th percentile of 8, and the simulation recorded exactly 4 and 8.

Why does Ludo online with 4 players almost never end at zero?

At three seats the mean jumps to 14.1 captures. Poisson's chance of an empty game is e^-14.1, about 1 in 1.3 million. The simulation found 1 in 5,004. The same pattern holds: far rarer than at two seats, far commoner than the simple model says.

At four seats the mean is 30.0, and the Poisson chance of zero is roughly 1 in 11 trillion. Not one of the 10,008 games ended at zero. Each extra player adds four more pieces that can end a throw on yours, and the ludo statistics move fast as a result. Two-player Ludo is the only version where a peaceful game is a real possibility.

Can you win Ludo without capturing?

Yes. All 353 quiet two-player games still finished with a winner, because nobody needed a capture to get home. A capture sends a rival back, but it is not a condition of winning under the Ludo rules the engine uses.

So how many captures in Ludo should a pair expect? In this run, half the two-player games had four or fewer, and nine in ten had eight or fewer. That spread is the real lesson of the ludo probability here: the average hides a long tail at both ends.

Questions the run leaves open

This ludo simulation used computer players, not people, on one engine version. Most seats took every capture offered, so an empty game here means no capture ever came within reach of those seats. A human table that sometimes declines a capture should see quiet games at least as often, but I have not measured that. The run also does not record why a given game stayed quiet. The extra spread is measured; the explanation for it is a reasonable guess, not a finding.

Ahmed Moaz builds Boardit, a free browser game site. Drafted and reviewed with AI help; facts checked against the game's code.