I'm going to make an attempt at that math:
I'll start with King-Small:
King small was dealt out to "find the button" the formula to find the odds of that is:
4 kings out of 52 cards in a deck. The chance of dealing a single King is 52 / 4 which equals 0.0769 or 7.7%
Small cards are 2's through 8's which are 7 cards types out of 13 card types. The chances of dealing a small card is 0.5384 or 53.8%
The chances of being dealt King-Small as the first two cards dealt is (0.0769 x 0.5384) x 2 which equals 0.0828 or 8.3% - I have to mulitply the end result by 2 because their are two possible ways to be dealt King-Small: the King being dealt first and the Small being dealt first; I hope that makes sense.
Lets just forget the rest of the cards because King-Small was in every one of our hands. Forget the Ace of Spades, forget all that just focus on the King-Small being dealt 8 times in a row using 4 hole cards once we started playing.
At least one of us was dealt King-Small eight times in a row given only 4 cards total at a time.
All we have to do is add the percentages together:
0.0828 + 0.0828 equals 0.1656 or 16.6%
So there is a 16.6% chance of one of us getting dealt King Small each hand. I think I just take this number and apply the Exponentiation of 0.1656 to the power of 8 which equals
1.000000e-6 <-- lol this is what this online calculator gave me and I don't know what it means.
My math could be way off I haven't ever really done anything like this before.
-Sab