Correction to slips of paper problem
The probability is actually C(1224,8)/C(1225,9) and this is indeed exactly 9/1225. In fact it is
(1224*1223*...*1217/8!)/(1225*1224*...*1217/9!) = 9/1225.
Notice that this is the same result as the card game because only 1 other player can have AA. It works for other hands as long as we are GIVEN that only one other player has that hand, such when we make this approximation when we have KK and we only consider one player having AA. As soon as we consider that more than 1 other player can have this hand, this won't be the same. For example, in this game 6 other players could have AA when we have KK. So this should not be considered a general model for a card game.
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