$Bad Beat Jackpot$

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$Bad Beat Jackpot$

I play poker at a casino in Pennsylvania. There is a progressive bad beat jackpot that accumulates until two players meet the requirements to win it. The minimum hand necessary to qualify is quad 5s and the qualifying hand needs to be beat by a higher qualifying hand. Both players must use both hole cards. If everyone at the table folds except for two players, please tell me how many different hands there are where each player has a bad beat qualifying hand BUT against each other there is no possibility of hitting the bad beat (example: pocket 10's against jack 10 suited). Please also tell me how many hands there are where there IS the possibility of hitting the bad beat. I am making the assumption that the solver of this problem knows something about poker. I look forward to hearing from you.

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Philip G Dooman

13

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First, you need to calculate the total number of ways two players can be dealt two-hole cards from a standard 52-card deck, where both have hands that qualify for the bad beat jackpot (i.e., as you mentioned, each has at least quad fives).

Then, calculate how many of these qualifying combinations lead to a situation where a bad beat is possible and how many do not.

You can classify hands into three categories:

Straight flushes (including royal flushes)
Quads with a pocket pair
Quads without a pocket pair. (you would not include this because both hole cards need to be used and should start with a pocket pair)

See table below for the details of different combinations of hands between player 1 and player 2 that can result in a bad beat.

You know that quads with a pocket pair require the matching pocket pair to appear in the community cards. And quads without a pocket pair require the community cards to have trips.

Having quads in community cards would not work for the bad beat jackpot, since no player would be able to use both of his hole cards to beat the other hand.

Bad Beat Combinations Calculation:

Player 1	Player 2	Bad Beat Count
Straight Flush	Straight Flush	1,578,720
Straight Flush	Quads (PP)	787,200
Quads (PP)	Quads (PP)	531,360



Total Cases	2,696,880

All Combinations Calculation:

There are 2,321,768,327,288 total combinations of dealing cards for a No Limit Texas Hold'em (NLHM) game with 2 players.

This is:

$\frac{\frac{52\times 51\times 50\times 49 \times 47 \times 46 \times 45 \times 43}{4} }{5!} $

This includes the cards burnt before flop, before turn and before river.

Non-Bad Beat Combinations Calculation:

From the total combinations, subtract the combinations where a bad beat can occur.

The result gives the number of cases where a bad beat is not possible:

$2,321,768,327,288 − 2,696,880= 2,321,765,630,408 $

Chances of the bad beat jackpot to occur with the requirements you mentioned:

$0.000141 $ percent

Naturelover

68

Philip G Dooman

0

Hello, I think I didn't describe the parameters accurately. Minimum qualifying hand is quad 5's and quads means using both hole cards so please dont include combinations involving 3 cards on board and one in your hand. What I need is the number of hands that qualify for the bad beat but cannot hit the bad beat when paired against other bad beat qualifying hands. Pocket 5's against 5 6 suited would be an example.
Philip G Dooman

0

Starting hand is drawing dead vs starting hand Ace 2 ace 3 Ace 4 Ace 5 Ace 3 Ace 4 Ace 5 Ace 6 Ace 4 Ace 5 Ace 6 Ace 7 Ace 5 Ace 6 Ace 7 Ace 8 Ace 6 Ace 7 Ace 8 Ace 9 Ace 7 Ace 8 Ace 9 Ace 10 Ace 8 Ace 9 Ace 10 Ace Jack Ace 9 Ace 10 Ace Jack, Ace Queen Ace 10 Ace Jack Ace Queen, Ace K
Naturelover

0

OK, updated the table and numbers, to exclude combinations where 3 cards from the community cards are used. Does the approach and detail make sense? Let me know.

$Bad Beat Jackpot$

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