Poker Math Question

[Dan2]

marksalot300 wrote:

Here's one for all you math gurus. This might be the wrong place to
post it because this isn't a VP question, but I thought maybe you'd
like a challenge.

A casino has a "bad beat" jackpot in the live Hold 'em games. Payoff
isn't important, just curious what the odds are of this happening. Losing hand must be full house (aces over tens) or better. Winning
hand must be 4OAK or better. Both hands must use both of their hole
cards to form the hand.

Sorry, but there are too many variables. How many players in the game? Does an aces-full hand have to have at least one ace in the player's hand? Does a four-of-a-kind hand have to have a pair in the player's hand? (These are common requirements.)

Then you would have to assume that every player who is dealt a hand with any potential for the jackpot stays in for the river card, or at least until it becomes clear that a jackpot is not possible, and that just doesn't happen in a real game. For example, you're dealt a pair of tens, which has jackpot potential, so you stay to see the flop, but it comes A-K-8 suited. There's a bet, so you drop out (it would be stupid to stay). The turn and river cards are both tens (there is roughly one chance in 1000 of this happening). The other player shows pocket aces, so it would have been a jackpot (four tens beating aces full of tens).

With that information and assumptions, someone who is interested could figure it out. I'm not interested because the assumptions don't make sense. With more realistic assumptions, an approximation could be made, but even if the players followed your assumptions exactly, the calculation would still be only an approximation unless a shuffling machine is used. I was a poker dealer instructor at Casino Gaming School for several years, and I have rarely seen a dealer who shuffled the cards well.

Dan

···

--
Dan Paymar
Author of best selling book, "Video Poker - Optimum Play"
Editor/Publisher of VP newsletter "Video Poker Times"
Developer of VP analysis/trainer software "Optimum Video Poker"
Visit my web site at www.OptimumPlay.com

"Chance favors the prepared mind." -- Louis Pasteur

[marksalot300]

Dan -

     I can see how the unstated variables could wreak havoc with
trying to calculate such odds. The only things I can really respond
to are that there was no requirement for which cards were "in the
hole", only that they must both be used to form the hand, and that I
could find out what the maximum number of players would be in the
game. That would be a good guess as most of the Detroit hold 'em
games seem to run waiting lists almost all the time.

- Brian in MI

marksalot300 wrote:
>Here's one for all you math gurus. This might be the wrong place

to

>post it because this isn't a VP question, but I thought maybe you'd
>like a challenge.
>
>A casino has a "bad beat" jackpot in the live Hold 'em games.

Payoff

>isn't important, just curious what the odds are of this happening.
>Losing hand must be full house (aces over tens) or better. Winning
>hand must be 4OAK or better. Both hands must use both of their

hole

>cards to form the hand.

Sorry, but there are too many variables. How many players in the
game? Does an aces-full hand have to have at least one ace in the
player's hand? Does a four-of-a-kind hand have to have a pair in

the

player's hand? (These are common requirements.)

Then you would have to assume that every player who is dealt a hand
with any potential for the jackpot stays in for the river card, or

at

least until it becomes clear that a jackpot is not possible, and

that

just doesn't happen in a real game. For example, you're dealt a

pair

of tens, which has jackpot potential, so you stay to see the flop,
but it comes A-K-8 suited. There's a bet, so you drop out (it would
be stupid to stay). The turn and river cards are both tens (there

is

roughly one chance in 1000 of this happening). The other player

shows

pocket aces, so it would have been a jackpot (four tens beating

aces

full of tens).

With that information and assumptions, someone who is interested
could figure it out. I'm not interested because the assumptions

don't

make sense. With more realistic assumptions, an approximation could
be made, but even if the players followed your assumptions exactly,
the calculation would still be only an approximation unless a
shuffling machine is used. I was a poker dealer instructor at

Casino

Gaming School for several years, and I have rarely seen a dealer

who

···

--- In vpFREE@yahoogroups.com, Dan Paymar <Dan@O...> wrote:

shuffled the cards well.

Dan

--
Dan Paymar
Author of best selling book, "Video Poker - Optimum Play"
Editor/Publisher of VP newsletter "Video Poker Times"
Developer of VP analysis/trainer software "Optimum Video Poker"
Visit my web site at www.OptimumPlay.com

"Chance favors the prepared mind." -- Louis Pasteur