Implied odds of the bad beat jackpot

At my local poker room there's a bad beat jackpot. A certain amount is taken from the hand [I don't know how much it is] and this funds the jackpot.

In the short time I've been playing the bad beat jackpot (BBJ) is usually around $10,000 - $20,000. One time it got up over $60,000. When it's high the poker room is busier.

The jackpot is awarded when quads or better beats Aces full of tens or better. The rule is also that both players have to use both of their cards to form the winning and losing hand. The payout is losing player gets half the BBJ, winning hand gets 25%. The remaining 25% is shared among other players at the table.

A hand came up one time where a player 3 bet on an early position raise and two callers. The big reraise ended up chasing everyone out and the player made over $20 on the hand. At the time the BBJ was around $60,000.

After the hand a regular in the poker room suggested to the player who 3bet that there may have been some consideration to slow playing, i.e. just overcalling with the premium hand. That would have ensured a multiway pot and possibly got others in. With a premium hand it had a better chance of cracking the BBJ.

So the regular's point was that the BBJ was so large that the implied odds of cracking the BBJ were enough to be possibly more worthwhile than the big 3bet which would most likely just win the hand preflop.

It's an interesting concept because in a way it violates the principle of table stakes; which all of modern poker is built on. Although it violates table stakes in a good way. You still can't lose or be forced to call more than the amount in front of you on any hand. So table stakes still holds on the downside. On the upside though it becomes possible to win money which is not on the table at the beginning of the hand.

Afterward I thought about it some more over the next few weeks. Then I realized that it should be possible to quantify the implied odds of the BBJ.

I wanted to determine the chance of being on the losing side of the BBJ. I quickly realized you would need to be dealt AA to have a measurable chance of being in a BBJ hand. Since you only need Aces full of tens then it's relatively not too unusual to form the losing side of the BBJ.

In this example Hero is holding Aces UTG in a 10 player game. I want to calculate the chance that this will be a BBJ hand.

I believe the most likely scenario is that Hero and another player holding a pocket pair flop a set. Then Hero goes on to make full house 10 or better. The other player hits the 1 outer to make quads. This doesn't account for other scenarios such as quads over quads or losing to a straight flush. However it should be at least an approximation.


Part one, chance to form the losing BBJ hand starting with Aces

In this case Hero flops a set and then makes a full house.

The chance then of being on the losing side of the BBJ is

(1 / 8.5) * (1 - ((40 / 47) * (36 / 46))) * (1 / 3) = 0.0130960802

So dealt Aces there's about a 1.3% chance of ending up with a hand that can be a losing BBJ hand.


Part Two, another player is dealt a pocket pair. Villain flops a set and makes quads

In this example Hero is dealt Aces UTG at a 10 player table. I used my preflop overpair equation that I derived in the past to determine the probability that someone else at the table has a lower pocket pair. The chance of an underpair to AA is the same as the chance of an overpair to 22. So using the overpair equation I determined there is a 39% chance someone has a pocket pair.

The chance then of someone at the table having a pair, flopping a set and making quads is then

0.396140781 * (1 / 8.5) * (1 - ((44 / 45) * (43 / 44))) = 0.00207132435

About 1 in 500.



So multiply part one and part two to determine the chance then that the BBJ will go on this hand. That comes out to.

0.0130960802 * 0.00207132435 = 2.71262298 × 10^-5

Which is 1 in 36,864.



So that's not very good. Even if you account for other ways for the BBJ to form such as straight flush or more than one opponent being dealt a pocket pair then the best you can hope for is probably around a 1 in 20,000 chance of being on the losing end of the BBJ when starting with Aces.


From there then we can determine the implied odds of the BBJ when dealt Aces preflop. Being a bit generous and setting it at 1 in 20,000.

If the BBJ is $60,000 then the implied odds of the BBJ is about $1.50.

If the BBJ is $100,000 then the implied odds of the BBJ is around $2.50.


So we have determined that the BBJ must be extremely large in order to create enough implied odds to alter your preflop strategy to slow play instead of 3 bet. It would have to be around $400,000 - $500,000 + to even come into your thoughts.

Of course people at the table who have already folded or were going to fold anyway would prefer you slow play Aces against a preflop raise. They want to freeroll for a slice of the 25% of the BBJ that goes to the others at the table.