Analysis

observations from the runs

At very low sample counts the numbers are still swinging hard. After 25 tournaments Argentina sits at 28% while Spain is only at 8%. France has zero wins in the first 10.

Convergence

title odds vs number of simulated tournaments · same seed
10%20%30%101001k10k100k17.511.68.57.14.84.24.13.52.82.82.82.6

The noise falls off with the square root of the number of simulations. By 10,000 runs the curves have already flattened.

At the full 100,000 the Monte Carlo error on a ~17% title probability is roughly ±0.12 percentage points — small next to the uncertainty coming from the model itself.