Join Date: Feb 2006
Posts: 24,647
Because there are still 5 cards to come. I mean, the answer is, it is because it is.
If you just look at the chance of an A or K coming and forget for a minute about other situations (straights, 2 pairs the counterfeit the underpair, etc, etc) then we have this:
There are 48 unknown cards. 6 of them are an A or a K so we need to count how many board there are with no A and no K, vs how many total boards.
There are C(48, 5) total boards and C(42, 5) of them have no A or K.
so that's 1712304 total and 850668 of them with no A or K.
That comes out to 49.6% of boards without an A or K
The C(n, k) thing, if you're not familiar with it, is a short hand for "number of ways to choose a subset of k items from a total of n items, where order is not important". In this case it's just used to express how many ways to make a board with a given property.