Poker Probabilities for 6-10 Cards

8 cards

Hand	Combinations
Royal flush	4
Straight flush	24
Four of a kind	2,529,462
Full house	45,659,328
Flush	5,120
Straight	458,724
Three of a kind	42,172,416
Two pair	282,625,200
Pair	295,206,912
Garbage	83,880,960
Total	752,538,150

How would a full house be composed out of 6 cards? Also, how about a new combo , three of a kind-three of a kind.

Actually, I'm still confused on the purpose of this whole topic. Can someone tell me what poker game it is that requires a player to use six, eight, ten cards in a hand?

I dont think there is one. I think someone maybe asked about the probabilities of 6-10 card hands.

Thanks Miplet for the 7-card and 8-card numbers. I agree with the 7-card numbers. However, beg to differ on some of the 8-card numbers. Let's look at a four of a kind. I think you are counting hands like Ah As Ac Ad Kd Qd Jd Td as a four of a kind, when it should be a royal flush.

As I mess with the other 8-card hands, it gets pretty messy for three of a kind and two pair. I think going through 7 cards the most I should bother you for. For the rest, I'll probably write a looping program.

Quote: Ibeatyouraces

How would a full house be composed out of 6 cards? Also, how about a new combo , three of a kind-three of a kind.

A 6-card full house could be something like KKKQQQ or KKKQQJ. It is the best 5-card hand you can make using 6 cards.

Got it. I assumed the hand had to make use of all cards, no "kickers". For example with 8 cards a full house would be five of a kind + three of a kind. I just couldn't see it be done with 6 cards.

Quote: Wizard

Thanks Miplet for the 7-card and 8-card numbers. I agree with the 7-card numbers. However, beg to differ on some of the 8-card numbers. Let's look at a four of a kind. I think you are counting hands like Ah As Ac Ad Kd Qd Jd Td as a four of a kind, when it should be a royal flush.

Quote: Wizard

Straights, flushes, straight flushes, and royal flushes must make use of all cards. For example 89TJQK would be a straight, but 89TJQA would not.

These seem contradictory. For 7 cards I have As Ac Ad Kd Qd Jd Td as a three of a kind based on the second quote, but by the first quote it should be a royal.

Quote: miplet

These seem contradictory. For 7 cards I have As Ac Ad Kd Qd Jd Td as a three of a kind based on the second quote, but by the first quote it should be a royal.

You're absolutely right. Let me redo my math and get back to you.

Quote: Doc

Actually, I'm still confused on the purpose of this whole topic. Can someone tell me what poker game it is that requires a player to use six, eight, ten cards in a hand?

And now, even seven cards?

Quote: Ibeatyouraces

I dont think there is one. I think someone maybe asked about the probabilities of 6-10 card hands.

That is indeed what the initial post seems to indicate. I'm just curious why anyone would ask that question and why it would warrant this much work on the part of the Wizard and miplet. Doesn't there exist some limit on how esoteric an issue will be exhaustively investigated by a geek (not counting Trekkies)? I thought that suggested there might actually be a real-world use for this info. Perhaps that notion reflects a personal bias drawn from a career in applied rather than basic research.

I have no clue either. Someone already did an analysys using 5 of 8-10 cards here. What we are doing is using all cards for the cards for royal flush, straight flush, flush, and straights, but only 5 cards for the other hands.