# Video Poker Probabilities

I developed a Video Poker software. Its working fine "Jacks Or Better"

Now i want to improve it with statistics.I want the software to suggest which cards to hold to get the best possibility of a gain.

I know that holding $5$ cards in different way create $32$ scenarios.

What i want is to calculate the probability for each one of these $32$ scenarios :

1. Royal Flush
2. Straight Flush
3. Four Of A Kind
4. Full House
5. Flush
6. Straight
7. Three Of A Kind
8. Two Pairs
9. Jacks Or Better

I got the solution for Jacks or Better when nothing is hold ...

its: $13C1 * 4C2 * 12C3 * (4C1)^3 * \frac4{13}$

But whats the probability when my hand is

$JS - 2C - 6D - 7H - 10H$ and i hold $JS$.

Is it possible to develop a formula for each of $9$ ( Special Hands ) for a given scenario ?

When nothing is selected is easy. But when you hold 1 , 2 or more cards depending what you want to achieve its very difficult for me ...

Please , i am struggling with it for a week and got formulas just when holding nothing ...