5 OAK and Other Ranking Mysteries in Poker

Recently, I have been playing some Dealer's Choice home poker; in these games wild cards are the norm, but never are Jokers used, at least in my experience.

It's always bothered me a bit to have 5 of a kind outrank a royal flush in poker hands with wild cards, but I had accepted that on the assumption that if you crunched the numbers, you'd find 5 OAK was in fact the hardest hand to achieve. Sometimes not hard exactly, for at least one player, if there are enough wild cards!!

But now I have even more doubts about that. In the pdf linked below, looking at the charts, the indication for 5 card stud poker using jokers is that a royal flush is indeed slightly more likely than 5 OAK, though nearly the same. However, using deuces wild, a 5 OAK is *not* as rare as a royal flush. Again, declaring some rank as the wild card seems to be the norm by far, so in fact it might be more proper to declare the RF as highest ranking hand.

Notice there are other anomalies, such as in deuces wild, 4 OAK being dominatingly the most common hand in competition with the more rare flushes and full houses - all against the notion the more rare hand should rank highest ... but never mind that for this post.

It occurs to me that things might revert to more expected distributions with 7 card stud, but the math for that would just about be sure to be a clusterF if I tried to sort that out.

I am thinking about declaring that the RF will the highest ranking hand when it is my turn in Dealer's Choice. Is there something I am missing here? Would it have to be 5 card stud to claim a good reason to do so?


http://www.meteor.iastate.edu/~jdduda/portfolio/492.pdf

Your problem is that you’re thinking about royals as if they were an independent item. They are not. They are merely the best straight flush.

When lumped in with the other straight flushes, a SF is far more common than a 5oak.

For further thought, if you were to put a steel wheel on the rank list, where would you put it???

OG & DJ

OG,

Another, "Anomaly," with Deuces Wild Five-Card Stud, as you put it, is that Two Pair is a more rare hand than a 3OaK. The reason why, of course, is that if a hand has a Deuce it is automatically not going to be a 2P regardless of the other cards in the hand. I don't think that would qualify as a good reason to make 2P the higher ranking hand of the two.

When it comes to home poker (and VP, in many cases) most hand rankings comport themselves to agree as closely as possible to the hand rankings in a game such as Jacks or Better. Wilds throw a monkey-wrench into the thing not just by making many hands significantly more likely, (so hands drop off of VP rankings) but also by creating hands that cannot exist in JoB. What you will notice is that, with exception to Four Deuces, every other hand is ranked in the same order as it would be in Jacks or Better for non-Wild hands.

I wouldn't have a 5OaK outrank a Royal in Wild Stud unless it was only being played with one Joker. If one Joker in Stud, the 5OaK becomes substantially more difficult to achieve as I believe the linked chart spoke to Stud with two Jokers.

Anyway, "Dealer's Choice," means you can do whatever you like! I once played with a guy who would call Five Card Draw, Deuces Wild, except Natural hands ALWAYS beat Wild hands by rank. In other words, if you had trip-sixes with a Deuce and I had trip-threes au natural, my hand would be better than yours. JUst the way he liked to play.

I think that games try to base themselves as closely to JoB as possible, which was of course based on the hand rankings of straight or draw poker, games that existed long before Video Poker machines. They just adapted other VP and Poker games to fit the Jacks or Better mold rather than adapting the hand ranking mold to fit the new games and variations. Eliminating Wild hands, the concept of RF-SF-4OaK-FH-Flush-Straight-2P-JoB/1P holds for most, if not all, other games in terms of rankings.

DJTeddyBear,

I would argue that Royals are an independent item, but I see your point. Video Poker certainly treats them as an independent item. Further, they are known not only as the best possible straight flush, but also separately designated as the best possible poker hand in straight or draw poker with no wilds. Royal Flushes are separately listed on almost all, if not all, probability tables. You don't see something like Four Aces listed separately above other 4OaKs, even though it is obviously so.

Finally, in a game with Wilds, a, "Natural Royal Flush," generally ranks highest while there is no separate designation for, "Natural Straight Flush."

A SF is more common, but a Royal isn't. Why lump them in together? I maintain that a Royal is commonly accepted as a hand of special designation, while recognizing that it is technically a form of SF.

Aces behave as either the highest card in the deck for Video Poker or (most) other Poker games, or as the lowest card in the deck. When used for the purposes of High Cards, Pairs, Two Pair, Trips, Flushes (not SF), FH's or Quads, Aces automatically rank the highest. Aces only rank low when they are being used for the purposes of forming either a Straight or a Straight-Flush, in conjunction with 2-3-4-5, obviously.

In almost all official competitive poker, an A-5 straight is recognized as the lowest possible straight because straights are designated by way of the highest-ranking card, which is the five in that hand. For the same reason, an A-5, SF, or Steel Wheel, constitutes the lowest-ranking SF because the highest-ranking suit is the five. Once again, the Ace is being used as a low card.

The only game I know of in which an Ace-Straight is second-highest, or Ace SF is second-highest, is Pai-Gow Poker. Some casinos don't even do that anymore.

I've never heard of a steel wheel. Any idea of it's origin?

Quote: billryan

I've never heard of a steel wheel. Any idea of it's origin?

I know that, "Wheel," refers to any A-5 straight, whether it be a straight flush or not. The wheel is also known as, "The Bicycle," which may be after the popular card manufacturer whose existence goes back to pre-1900. From, "The Bicycle," may have come, "The Wheel." "Steel," would represent strength, of course, and the Steel Wheel, as a straight-flush, is the best possible A-5 straight. "The Wheel" is also the best possible hand in California Lowball (The Wheel or Steel Wheel) because Straights and Flushes do not count as any special designation in that game thereby making A-5 (any) the best possible hand.

A little more searching found what I was looking for in 7 card:

I am to credit Durango Bill who further says:
"Computer program and data by Bill Butler"
http://www.durangobill.com/Poker_Probabilities_7_Cards.html

7 card poker probabilities with Deuces (2’s) wild

Poker Hand...................Nbr. of Hands.........................Probability
_______________________________________________________________________

5 of a kind ......................609,760..................................0.00455778
Royal Flush......................399,484.................................0.00298602
Other SF...........................1,552,732.............................0.01160621

So it appears that a player can not only claim the right to do so per "dealer's choice", but can also say putting in the rule "Royal Flush beats 5 OAK" conforms to the reality that the former is harder to achieve than the latter, 5 card or 7 card either one. As pointed out, not true of SFs in general. But this confirms something I had suspected all along.

In 7 card the anomaly that a Full House or a Flush is harder to get than 4 OAK disappears, see link.

PS: note that the chances for a RF are quite real using wild cards, the above translates to 1 in 334.89

The anomaly partially disappears. The FH remains more likely than a Flush and Trips more likely than 2P.