What are the odds of everyone's first up card in an eight -handed seven card stud poker game being either a king or an ace?

If my math is right, and it probably isn't, there's approximately a 0.00000013% chance. Here is the math one might consider: Essentially you are looking to deal 8 cards out of a 52 card deck, order being irrelevant.

So that would be 52!/{(52-8)! * (8)!} = 752,538,150 possibilities And you are looking for ONE of those possibilites 1 / 752,538,150 = 0.000000001328836285575690 So as a percentage, 0.00000013% would seem correct.