Bad Beat Jackpot Calculations

[snoopdarr]

I'm familiar with the idea of progressive jackpots, applied to video poker, giving the game positive expectation when they reach some high number. But I haven't seen any work on what number various BBJP would have to reach for that .05 or $1 dropped out of every pot to show a positive expectation?

The variables: your contribution to the jackpot (per hand), the probability of the jackpot hand occuring.

The question I haven't seen a lengthy analysis on is the probability of hitting certain jackpots. Remember that they are all a certain hand OR BETTER beat. Is simulation the only way to go about figuring those odds? If so, what simulation software will permit me to do this? Has this work already been done and I just haven't found it?

[KneeCo]

I recommend Dr. Brian Alspach's articles on the subject in his great Poker Digest.

Mainly, I would point toward these three articles:1, 2, 3.

In the conlcusion (article 3), the author cautions against the use of simulation for calculating Bad Beat Jackpot probabilities:
[ QUOTE ]
When I told a local player about these calculations, his reaction was that he could find them easily by just running many simulations. One has to be careful with this approach. We are talking about events with very low probabilities. First of all, one must run the simulation an immense number of times. For example, the probability of a bad beat qualifying semi-deal in hold'em with four deuces as the minimum qualifier is just about spot on at one in a hundred thousand. Even 10,000,000 trials gives you only about a seventy percent chance of being accurate within ten percent of the true expectation of 100 successes. Another problem with simulations is that very low probability events may be badly measured because of a poor quality random number generator.

[/ QUOTE ]


EDIT: Hey! I'm an addict! (how true!)

[snoopdarr]

Yeah, I had already considered that part about simulations... I figured it would be a very robust simulator with a excellent random number generator that I'd leave running for a few days or however long it took [img]/images/graemlins/smile.gif[/img]

But thanks for these links! These odds will be nearly dead-on in typical BBJP games, where people will play any pair and any suited connector or 1-gap. The odds of hitting each BBJP are:
4 of a kind (2 PP required): 1-250,000
4 8's or better beat: 1-155,000
4 of a kind beat: 1-93,000
Aces full of Kings beat: 1-71,000
Aces full of Queens beat: 1-42,000
Aces full of Jacks beat: 1-24,000
Aces full of Tens beat: 1-16,000

How much do you contribute to the BBJP every hand? How the money is distributed isn't relevant, just the amount you put in, and the potential jackpot. Typical B+M takes $1 out of the pot, PP takes $0.50. But you only pay when you win a pot. What % of pots do you win? Can I assume a random 10%, i.e. the BBJP contribution per hand in B+M would be 0.10, and 0.05 on PP. Does this look right? Now I just have to figure out what % of the BBJP you stand to win if you know one hits on your table, which will give what the BBJP has to be for you to break even on the drop.


P.S. Vegas Dream on NES destroys Vegas Stakes on SNES.

[snoopdarr]

Ok, now for the final bit - what do the jackpots have to be for your .10 or .05/hand to break even, in theory. If you hit the BBJP many times, you stand to win 10% of the jackpot each time (1/10 50%, 1/10 25%, 8/10 3.125%). So the BBJP has to be 10 times your contribution times the odds. I used a .05/hand for PP's BBJP, and .10 for the other potential B+M BBJPs. In conclusion:

4 of a kind (2 PP required): $250,000
4 8's or better beat: $77,500
4 of a kind beat: $93,000
Aces full of Kings beat: $71,000
Aces full of Queens beat: $42,000
Aces full of Jacks beat: $24,000
Aces full of Tens beat: $16,000

This isn't as interesting as I thought.