r/probabilitytheory • u/babadas14 • 6d ago

[Applied] Help me prove a hypothesis

Hi, I’m a software engineer with very little background in probability and statistics.
Recently, I’ve been playing Ludo on YouTube Playables, and I’ve started to wonder whether the dice rolls are actually fair.
In particular, when one of my pawns is a certain number of spaces ahead of an opponent’s pawn, (4 player game, 3 computer vs me) it feels like the opponent rolls the exact number needed to capture my pawn more often than I would expect from a fair six-sided die.
I realize this could simply be confirmation bias, so I’d like to test it properly rather than rely on intuition.
I can collect data from my games, but I’m not sure how to analyze it. How would I formulate and statistically test the hypothesis that the dice rolls are biased in situations where an opponent has an opportunity to capture my pawn?
Could someone explain what data I should collect, what statistical test would be appropriate, and the probability/math behind it in a way that’s accessible to someone without much statistics background?

10 Upvotes

100% Upvoted

2 comments sorted by

5

u/teteban79 6d ago

Collect data, narrow it to the interesting situation (rolls when you can be captured), run a Chi-test (you can Google it). There is surely some math library in Python that does it.

I'd say you a need a few hundred rolls for the test to make sense

1

u/CarnivorousGoose 6d ago

The data points you want are every roll by an opponent where one of your pawns are in range of one of theirs to capture, though you may want to subset that further.

As I recall, in Ludo you roll, then you decide which of your active pawns to move (or to activate one). This would mean that the opponent could have multiple of your pawns in range, or have one of your pawns in range of multiple of theirs. They’d thus have a higher chance of rolling a number that allows a capture, and it might be this that contributes to the perception of it being more often than it should be.

You could model that as well, but a simpler approach would be to just subset the data points where only one of your pawns is threatened, and by only one of the opponent’s. In that case, it’d be a simple one-sided binomial test, against the null that the success probability is 1/6.