When you start with a tiny number of stakeholders with tiny stakes, large deviations will be likely.
The share-of-ownership sequence for a given stakeholder is essentially a random walk with step size decreasing like 1/n. Since variance of such a walk is the sum of individual variances, the variance for such a walk scales like Sum (1/n)^2, which remains bounded.
If you have N initial coins, the standard deviation in the limiting distribution (as number of allocations goes to infinity) is approximately 1/sqrt(N). In your largest starting allocation you have only N=30, and so the standard deviation in the limit is ~0.18. Since you have only 3 participants the 50% threshold is only 1 standard deviation from the starting values.
So basically what you’re seeing is an artifact of starting with tiny toy values. More realistic starting conditions (such as a thousand participants with up to a thousand coins each) will yield trivial deviations even over quadrillions of steps. The probability that any one participant would ever reach 50% via minting (or even a coalition of a hundred of them) is utterly negligible.
When you start with a tiny number of stakeholders with tiny stakes, large deviations will be likely.
The share-of-ownership sequence for a given stakeholder is essentially a random walk with step size decreasing like 1/n. Since variance of such a walk is the sum of individual variances, the variance for such a walk scales like Sum (1/n)^2, which remains bounded.
If you have N initial coins, the standard deviation in the limiting distribution (as number of allocations goes to infinity) is approximately 1/sqrt(N). In your largest starting allocation you have only N=30, and so the standard deviation in the limit is ~0.18. Since you have only 3 participants the 50% threshold is only 1 standard deviation from the starting values.
So basically what you’re seeing is an artifact of starting with tiny toy values. More realistic starting conditions (such as a thousand participants with up to a thousand coins each) will yield trivial deviations even over quadrillions of steps. The probability that any one participant would ever reach 50% via minting (or even a coalition of a hundred of them) is utterly negligible.
[edited]