Not sure I'm doing it exactly right, but I'm getting somewhere around 31!, maybe a bit more than 10^34. I'm trying to plug some formulas into wolframalpha to estimate when there would be a 50% chance of two matching shuffles. Same with the card shuffles, you have to compare your most recent shuffle with all the ones before to see if there is a match. Each person added to the room has to compare their birthday to all the prior birthdays to see if there is a match.
Compare against 1 then 2 then 3 all the way up to 22.don't compare against yourself and add them up to 253. Correct me if I'm wrong, the 23 people are comparing there birth dates to each other for comparisons which is 253. I don't think this is comparable to the random permutations of a randomly shuffled deck of cards. In a room of just 23 people, there is a 50-50 chance that at least 2 people share a birthday.
