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#1
12-19-2018, 09:04 AM
 septimus Guest Join Date: Dec 2009 Location: The Land of Smiles Posts: 18,397
Six-card poker: Hand rankings

There are a wide variety of poker games. In seven-card stud you get seven cards. In Texas Hold'em you get either 2 cards or 7 cards, depending on how you count them. In Big Jacoby you finish with six cards. But in all these variations your hand value is determined by your best five cards.

Why not score based on six-card hands? Is it because the list of hand rankings would get too cumbersome? It is the goal of this thread to rank the possible 6-card hands.

The following list is roughly in increasing probability of getting the hand with six random cards from a 52-card deck. (Tie-breaking is shown for 5-card straight-flush since the 6th card might extend the straight, etc.)
• 6-card straight flush
• 5-card straight flush
• with a 6-straight
• with a 6-flush
• ** (6-straight and 5-flush "should" rank here)
• with a pair
• ordinary
• 6-straight and 5-flush
• Monster Boat: Quads and a Pair
• Big Boat: Two Triplets
• 5-straight and 5-flush
• 6-flush
• Four-of-a-kind
• 6-straight
• Three pair
• 5-straight and pair
• 5-flush and pair
• 5-flush
• Ordinary Boat: Triplets and a Pair
• 5-straight
• Triplets
• Two pair
• No pair
• One pair

A 6-straight with 5 in same suit is actually much less likely than an ordinary straight flush but I've demoted it to reduce confusion. The '5-straight and pair' is only very slightly less likely than '5-flush and pair.' Would it be less confusing to reverse these ranks? With six cards, One Pair is more likely than No Pair but should the hands be ranked that way?

Comments? (If ranking the 6-card hands is too tedious, feel free to hijack and discuss 4-card poker instead.)
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andros had more faith in an American jury than I had; and he was right. I'm happy to lose a bet and hope this trend continues.
#2
12-19-2018, 09:19 AM
 OldGuy Charter Member Join Date: Dec 2002 Location: Very east of Foggybog, WI Posts: 5,136
I'm not sure why 5 straights and 5 flushes are even a thing. You get no credit for a four flush (with or without a pair) in regular 5 card poker.
#3
12-19-2018, 09:26 AM
 septimus Guest Join Date: Dec 2009 Location: The Land of Smiles Posts: 18,397
Okay. But note that, in a 6-card deal, opposite to a 5-card deal, 5-flush is harder to get than an ordinary full house. 6-Flushes and 6-Straights would be very rare.
#4
12-19-2018, 10:40 AM
 Snarky_Kong Guest Join Date: Oct 2004 Posts: 7,905
Quote:
 Originally Posted by septimus Okay. But note that, in a 6-card deal, opposite to a 5-card deal, 5-flush is harder to get than an ordinary full house. 6-Flushes and 6-Straights would be very rare.
I'm with OldGuy. In addition I wouldn't want flush+pair or straight+pair to be hands either, although I'm less convinced of that.
#5
12-19-2018, 11:03 AM
 Chronos Charter Member Moderator Join Date: Jan 2000 Location: The Land of Cleves Posts: 81,267
I think that it's inherent in the notion of "straight" and "flush" that they involve all of the cards. And yes, this makes those hands less likely, at the same time that the match-based hands become more likely: What of it? It's a variant; we expect things to be different.

And if you require all of the cards to be in a straight or flush, then that also eliminates the possibility of having a pair with either, so that's a non-factor.
#6
12-19-2018, 11:51 AM
 septimus Guest Join Date: Dec 2009 Location: The Land of Smiles Posts: 18,397
4-flushes count in Cribbage. (And 3-straights for that matter.)
#7
12-19-2018, 12:17 PM
 Snarky_Kong Guest Join Date: Oct 2004 Posts: 7,905
Quote:
 Originally Posted by Chronos And if you require all of the cards to be in a straight or flush, then that also eliminates the possibility of having a pair with either, so that's a non-factor.
Of course.
#8
12-19-2018, 01:35 PM
 DPRK Guest Join Date: May 2016 Posts: 2,645
Quote:
 Originally Posted by septimus ...feel free to hijack and discuss 4-card poker instead....
I don't know if 4-card poker is a thing, but three-card brag definitely is. (Wherein a straight beats a flush, as expected.)
#9
12-19-2018, 01:43 PM
 septimus Guest Join Date: Dec 2009 Location: The Land of Smiles Posts: 18,397
There's some sort of 3-card poker variant played here in rural Thailand but I've never even tried to learn the rules. The weird dice game called 'Hi-Lo' is already enough excitement for me.
#10
12-19-2018, 06:19 PM
 DPRK Guest Join Date: May 2016 Posts: 2,645
OK, this report describes Primero, which I have never personally seen played, but you have to bet on a hand with four cards. From lowest to highest, you can make

numerus: 2 or 3 cards from the same suit
primero: one card from each suit
supremus: highest possible numerus (67A, since the cards go face cards - 2 - 3 - 4 - 5 - A - 6 - 7)
fluxus: flush
chorus: four of a kind

So no pairs or straights; high cards are worth more than low cards.

Last edited by DPRK; 12-19-2018 at 06:20 PM.
#11
12-21-2018, 05:18 AM
 septimus Guest Join Date: Dec 2009 Location: The Land of Smiles Posts: 18,397
I may as well post some calculated percentages. 5-card poker usually isn't played with just 5 cards of course: by "7 cards" I show the chances in Texas Hold'em for a player who always stays for the final showdown. Similarly "8 cards" shows the chances for the possible 6-card best hands when dealt 8 altogether. (I've combined related hand types compared with the earlier list of hand rankings.)

.................5_cards...7_cards..........||..........6_cards...8_cards

No_Pair...........50.1%.....17.4%...........||...........32.5%......7.1%
One_Pair..........42.3%.....43.8%...........||...........47.8%.....31.4%
Two_Pair...........4.75%....23.5%...........||...........12.1%.....28.4%
Triplets...........2.11%.....4.83%..........||............3.60%.....5.12%
5-Straight.........0.39%.....4.62%..........||............1.60%.....6.57%
5-Flush............0.20%.....3.02%..........||............0.98%.....5.86%
Ord-Boat...........0.14%.....2.60%..........||............0.81%.....5.09%
Three-Pair...........--........--...........||............0.30%.....6.69%
6-Straight...........--........--...........||............0.18%.....2.51%
Four-of............0.024%....0.17%..........||............0.068%....0.22%
6-Flush..............--........--...........||............0.034%....0.67%
Two-Trips............--........--...........||............0.0061%...0.16%
Monster-Boat.........--........--...........||............0.0046%...0.12%
5-StraightFlush....0.002%....0.031%.........||............0.0089%...0.077%
6-StraightFlush......--........--...........||............0.0002%...0.0048%

Notes:
(a) As shown, 5-Straight Flushes are not hugely more common with 6 cards compared with 5. In the 8-card Hold'em game, they're less than thrice as likely as in regular Hold'em.
(b) Similarly the Ordinary Full Boat is less than twice as likely.
(c) The extra two cards lead to changes in the relative odds. A straight is almost as likely as Triplets in the 7-card column — contrast this with 5-card. Of course they won't be so likely in real Hold'em — players are much more likely to play a pocket pair than a 2-card possible straight!

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