Video Poker Probability

Hi WOV,

How I calculate the probability to get each of the hands in video poker? it makes me trouble because we can hold some cards in the first hand and change them to something else.
And also i want to knew what is the exactly probability for each of the option.

For just 5 cards i knew how to do the math
For example:
Jack's or better = [combin(4,1)*combin(4,2)*combin(12,3)*combin(4,1)*combin(4,1)*combin(4,1)] / combin(52,5)
2 pairs = [combin(13,2)*combin(4,2)*combin(4,2)*combin(11,1)*combin(4,1)] / combin(52,5)/
.
.
.
Royal Flash = 4 / combin(52,5)

thanks ahead WOV,
Regards,
Stam.

Hello, and welcome to the forums!

For 5-card (results of the deal), it really is that simple. How many occurrences out of 52 choose 5.

As for final hands (results of the draw), it’s “not so simple”, as it depends on all of the hold decisions. Are you playing perfect strategy, basic strategy, “ploppie” strategy, or channeling your VP chakras? Which game are you playing? Almost every game has a different strategy than every other game (except for “ploppie”?). If either perfect or basic was your answer, then the work has been done for you! Enter the pay table into the VP Analyzer on wizardofodds.com, and divide the number of combinations for your hand by the total combinations. The first chart of the output is for perfect strategy, and the second chart is for basic strategy. If you prefer to or have to calculate this yourself, then you must write a program (or tweak an existing one) to analyze your game’s pay table. It really is this complicated. Maybe someone else has a shortcut…

Video Poker Analyzer

Hello,

I spoke about perfect strategy,

For example in a perfect strategy in Jack's or Better is there 356,447,740,914 combination to get a pair of Jacks.or up,
and 41,126,022 comibations to get a Royal Flush out of 1,661,102,543,100 combinations

So i want to know what is the way and the calculate to get to this numbers?

Thanks ahead

Quote: BleedingChipsSlowly

Video Poker Analyzer
link to original post

edit: formatting

Quote: stam36

Hello,

I spoke about perfect strategy,

For example in a perfect strategy in Jack's or Better is there 356,447,740,914 combination to get a pair of Jacks.or up,
and 41,126,022 comibations to get a Royal Flush out of 1,661,102,543,100 combinations

So i want to know what is the way and the calculate to get to this numbers?

Thanks ahead
link to original post

The answer is, "The long way," although there are some shortcuts involved.

There are 2,598,960 different possible 5-card deals, but actually only 134,459 "unique" ones. For example, a Royal Flush in spades is the same as one in hearts, so there's no need to check both of them separately; also, there are 24 hands of 9-8-8-6-3 where the 9, 6, 3 and one of the 8s are four different suits and the other 8 is the same suit as the 3.
For each one, start with what it would pay if you held all 5 cards.
For each of the 5 ways to draw 1 card, take the average of the 47 hands you get when you replace the discard with each of the 47 cards remaining in the deck.
For each of the 10 ways to draw 2 cards, take the average of the 1081 hands you get when you replace the two discards with each of the 1081 different pairs of cards in the deck.
Do the same for the 10 ways to draw 3 cards, the 5 ways to draw 4 cards, and the 1 way to draw 5 cards; whatever play has the best average is the strategy for that hand.

Techncially, the total number of possible results = 2,598,960 (hands) x 1,533,939 (number of 5-card hands in the 47-card deck. The number you are seeing (1,661,102,543,100) is this x 5 / 12 because the other numbers are reduced to make them as small as possible while still being integers.