Poker Probabilities for 6-10 Cards

Somebody suggested that I add a table to WoO for poker probabilities with 6-10 cards. Before I go live with that, if anybody would like to check my work, please do! To start, here is what I get for six cards. Straights, flushes, straight flushes, and royal flushes must make use of all cards. For example 89TJQK would be a straight, but 89TJQA would not. Once somebody agrees with me on this, and hopefully somebody will, we'll move onto 7 cards.

Hand	Combinations
Royal flush	4
Straight flush	32
Four of a kind	14,664
Full house	165,984
Flush	6,828
Straight	36,828
Three of a kind	732,160
Two pair	2,532,816
Pair	9,884,160
Garbage	6,985,044
Total	20,358,520

I'm not a poker player, so maybe I don't understand. Or maybe I just shouldn't comment. However, it seems it would be more useful to know the probability of the various 5-card hands given that you have 6 or more cards to work with, such as the 7 cards of Hold-em. How often do you have to use more than five cards in one hand (not split into two hands)?

Gotta agree with Doc. What is the point of a six card straight? But on the other hand why bother with 6 cards to begin with. We play with 5 or 7 no?

Quote: Doc

I'm not a poker player, so maybe I don't understand. Or maybe I just shouldn't comment. However, it seems it would be more useful to know the probability of the various 5-card hands given that you have 6 or more cards to work with, such as the 7 cards of Hold-em. How often do you have to use more than five cards in one hand (not split into two hands)?

Point taken. I may do that next, but the math will be very messy.

Quote: DeMango

We play with 5 or 7 no?

Well, draw poker would give you 8, not all available at the same time (or maybe even 10, depending on the local rules.) As I said, I'm not a poker player, so I don't know all the variations that might be out there. Apparently, the Wizard is considering hands for a very different kind of game that I don't know about.

Quote: Wizard

Somebody suggested that I add a table to WoO for poker probabilities with 6-10 cards. Before I go live with that, if anybody would like to check my work, please do! To start, here is what I get for six cards. Straights, flushes, straight flushes, and royal flushes must make use of all cards. For example 89TJQK would be a straight, but 89TJQA would not. Once somebody agrees with me on this, and hopefully somebody will, we'll move onto 7 cards.

Must.... go... to.... bed...... Don't even think about it.
I'll check after work tonight.

Arrrrg finaly. I agree. Fullhouse gave me the most problems, until I realized that I wasn't counting 2 trips.

Thanks! I'm away from my computer with the 7-card numbers, but I'll post those by Monday morning at the latest. If you wish to work ahead, by all means, don't let me stop you.

On another topic, I have an easy paying project. It has to do with a baccarat side bet. Send me a message via the contact form if you're interested.

Quote: Wizard

Thanks! I'm away from my computer with the 7-card numbers, but I'll post those by Monday morning at the latest. If you wish to work ahead, by all means, don't let me stop you.

You're welcome. I should have 7 card numbers about this time tomarrow.

Quote:

On another topic, I have an easy paying project. It has to do with a baccarat side bet. Send me a message via the contact form if you're interested.

Message sent.

Ok I woke up early so I did it before work

Hand	Combinations
Royal flush	4
Straight flush	28
Four of a kind	22,4848
Full house	3,473,184
Flush	6,832
Straight	131,040
Three of a kind	6,589,440
Two pair	32,123,520
Pair	63,258,624
Garbage	27,977,040
Total	133,784,560