Holdem probabilities using both hole cards

Hi guys.

I run a poker platform in Asia and I have been searching all over the internet for the below information to no avail, I will give some background information to what I am trying to do so that it is not just a what is the answer to 1+1 then someone answers 2 and I say thank you.

Firstly, I am no maths major but I understand the basics certainly not at a university level, I majored in finance.

I am trying to implement a Jackpot system NOT a bad beat jackpot system.

Basically, in a round of holdem poker whenever the pot reaches X big blinds (BB) the system will take Y BB from the pot and place it into the jackpot pool.

I have now encountered the following:

1) I am having trouble finding the probability of any hand hitting (must use BOTH HOLE cards, in the case of four of a kind must use BOTH HOLE cards and needs to be a pocket pair)
- royal flush
- straight flush (not including royal flush)
- four of a kind

There are many readily available articles and websites detailing probabilities for 5 card poker and 7 card poker (holdem) but none with odds relating to what I wrote above making use of BOTH HOLE cards.

The reason why I wish to know these probabilities is so that I can estimate dealing how many hands of holdem I can expect each of the above 3 scenarios to happen then I can estimate how much jackpot rake I have taken.

2) Our jackpot system does not contain bad beat jackpot as those are too rare and not enticing for players, rather the jackpot pool that we are implementing simply pays out a % of the pool eg,

- royal flush 50%
- straight flush (not including royal flush) 25%
- four of a kind 5%

My second question is how should I setup these percentages to ensure that over the long run (statistically) that the jackpot grows over time, ie, the max values for each type of hand (quads, straight flush, royal flush) that I can payout so that the pool keeps growing. I would not want the jackpot pool to become smaller and smaller because then it would not be enticing over a long period of time.

We are thinking about taking and placing into the jackpot pool：

1/2 BB when if the pot is between 15BB and 30BB
1 BB when if the pot reaches 30BB or more

As you can see the maximum we can take from a pot is 1 BB.

Would greatly appreciate some help on the 2 questions I have above.

Thanks everyone.

To answer your question is impossible to do exactly.
variables....

1. How often will your pots reach 15 BB? how often 30 BB?
2. Do your players fold quickly? Or all stay in to see the river? (Obviously somewhere in between, but I'm sure different areas sway one way more than the other)
3. Will the bonus be big enough to sway player strategy? If you have 4 to a royal but you know an opponent already has 4 of a kind, will you pay to see the river? (extreme example...)
4. Maybe I missed this, but is this a jackpot that will be zero house edge? The house never takes any of the money?

Hi, thanks for your reply：

1. How often will your pots reach 15 BB? how often 30 BB?

Let's assume we take 1BB max every 20BB and 20BB occurs 30% of the time.

2. Do your players fold quickly? Or all stay in to see the river? (Obviously somewhere in between, but I'm sure different areas sway one way more than the other)

Let's assume for calculation purposes, all stay to see the river.

3. Will the bonus be big enough to sway player strategy? If you have 4 to a royal but you know an opponent already has 4 of a kind, will you pay to see the river? (extreme example...)

Assume Jackpot bonus do not change poker strategy.

4. Maybe I missed this, but is this a jackpot that will be zero house edge? The house never takes any of the money?

The reason why I asked for max % payouts for each category is so that I can calculate the house edge while allowing for the jackpot to grow naturally.
So for example if you tell me that the straight flush payout max should be 25% then I structure it so that when straight flush hits, player gets 22% and house gets 3% or something like that.

Thanks a lot.

When people wake up here there will be someone with the math skills that will likely give you the answer. It is probably easily findable how often a player gets 4 oAK, SF, or RF in holdem using both hole cards assuming they all stay to the river. The rest of the math shouldn't be too difficult.