Originally Posted by Joe Slick
I'm sure I have the exact percentage at home, or can figure it out here at work, but time doesn't allow it right now.
I guess I couldn't let this go until I figured it out. It's been almost 40 years since my advanced statistics course at xPI so this probably isn't as pretty as it could be.
The odds of pairing exactly one card with the first card of the flop is (6/50) x (44/49) x (43/48) x (42/47) x (41/46) or approximately 7.69%.
The odds of pairing exactly one card with the second card of the flop is (44/50) x (6/49) x (43/48) x (42/47) x (41/46) or the same 7.69%.
Because the card can be paired in any of the five positions, the percentage is 5 x 7.69% or approximately 38.45%.
That means that the chance of two pair (AAKK), trips (AAA, KKK), full house (AAAKK, KKKAA), and quads (AAAA, KKKK) is 48.75-38.45 or 10.30%.
Looking at my Excel spreadsheet, it looks like the odds of pairing exactly one of these cards on the flop is almost 29%.
If anyone finds fault with MY math, please attribute it to getting ooooooooolderrrrrr.