Hector,
This topic was created almost 3 years ago, and it was just an idea, I didn't even tried to code it to see if it works, because I found that you actually don't have to code or run million spins to see if an idea can work.
This one is a looser because spins are independent from previous and partitions are equally likely.
I stopped with this topic for another reason: people want you to test everything for them and to give them the solution on the golden platter. In fact you are the first person who actually posted a results for it.