What are the odds of getting quadded when you have the highest full house on the table? I would reckon it's very rare, but I have done it once to an opponent.

I have seen it on TV a few times

Based on hand independent it is 0.000256 (quad) * 0.0017 (boat) = 0.00000044

From the boat there are 45 cards out and need to match the pair on the board
So the odds of getting quadded are:
(2/2) / (45/2) = 0.00101 = 0.1%
Which also = 2/45 * 1/44

Highest or lower boat is immaterial. Quads beat a full house.

• What about a board like AKKKx and you hold an ace? The risk of someone holding a K is much higher than that. Commented Mar 26, 2016 at 19:11
• @J.-E.Pin OK, what about a board like AKKKx? You are welcome to run those numbers. I just don't think OP would have asked the question in that manner if the board tripped. A lone ace would not be the highest full house on that table. Commented Mar 26, 2016 at 19:39

There’s zero chance of quads if u have “the better” full house. Meaning queens full of 3s. Vs 3s full of queens. The boat 3s full of queens can b beat by quads

• Just a comment here to highlight this is incorrect. A player could have something like pocket kings, vs pocket 3s with a board of K33XX. To say there is a zero chance of quads against a full house is totally incorrect.
– Grinch91
Commented Nov 8, 2023 at 9:54