Suppose there are $n$ elements with value 1 initially.
In each iteration, two elements will be randomly selected and merged together. The values are added up and the total element size shrinks by 1. For example, after the 1st iteration, there are $(n-2)$ 1s and 1 element with value 2.
My question is how to estimate/approximate the distribution of the $(n-i)$ values after the $i$-th iterations. Here $n$ is at least 100k. From my intuitive, I think it would be like a normal distribution. Could anyone help me?
Thanks!