Originally Posted by sense
Me and my brother made a bet on the odds of hitting a bad beat jackpot at our local casino here in the inland empire.
To qualify for jackpot, it has to be aces full or better vs. Quads , straight flush or royal.
He says the chances of this happening are less than 1 in 500,000. I say the chances of this is greater than 1 in 500,000.
Were not mathematicians and can't find a exact answer.
Can anyone help?
I did a lot of work on bad beat jackpots years ago for a cardroom client. Also, this page
from the highly respected wizardofodds site lists the results of extensive simulations. I would have to do some more work to make sure that my exact calculations are in line with the wizard's simulations to within experimental error. My calculations are for more restrictive conditions than yours. However, I think we can both agree now that the odds for your case are far better than 1 in 500,000.
Do both players have to use both hole cards? Do you have to hold a pair for quads? Can the aces full use 3-of-a-kind on the board?
Even under the most restrictive conditions for aces-full beaten by quads or better where the quads must hold a pair, and a full house cannot use 3-of-a-kind on the board, the wizard gives a probability of 0.00004579 or just 1 in 21,839. Removing the conditions of having to hold a pair for quads, and allowing a 3-of-a-kind on the board for aces full, but still using both hole cards, he gives 0.00016964 or just 1 in 5895.
EDIT: To clarify, these are the probabilities for the whole table, with 10 players. It is about 10 times less likely per person.