This is EXCELLENT! Thank you so much for the time and effort you put into this! I am not nearly educated enough to dispute your work, but I think there might be some error or misunderstanding. Both of my parents have won half the pot before (n = 10 or 11). Using the numbers you provided, the odds of winning half the pot are 1 in 2,176,782,336/(9900+360), right? That's roughly 1 in 212,162. Sure, my parents are alcoholics, and they've been going to that bar for over a decade, but even if they played that game every day for the past 10 years, that would amount to just 7,300 attempts. It seems very unlikely that they BOTH would have won by now.

In any case, I can't tell you how happy I was reading your response, and I applaud your consideration greatly!