POKER RANKS OF HANDS AND ODDS

Last updated 02-02-02

Contents:

Rank of Hands

• The High Poker Game
• Lowball Poker
• High/Low Poker
• 3 Card Poker
• The Rank of the Ace

Odds of Poker

• Number of Hands Possible
• Odds of Draw Poker Improvements
• Odds of 7 Card Stud Improvements

Wild Cards

• How it Affects the Odds
• Ranking the Five of a Kind

HIGH POKER- RANK OF HANDS

In poker, the object of the game is to get the highest ranked hand over your opponents' hands.

Rank of hands from highest (best) to lowest (worst) with no wild cards:

• Straight Flush (e.g., J-10-9-8-7 of the same suit. If the Ace is the highest card in the straight then it is called a Royal Flush and is the highest hand possible.)
• 4 of a Kind (e.g., J-J-J-J-7)
• Full House (a 3-of-a-kind with a pair. E.g., 10-10-10-K-K)
• Flush (any 5 cards of the same suit. E.g., 3-5-9-10-K all in clubs)
• Straight (any 5 cards in sequence and unsuited. E.g., 8-7-6-5-4 unsuited.)
• 3 of a kind (e.g., 7-7-7-5-J)
• Two pair (e.g., 5-5-Q-Q-A)
• Pair (e.g., A-A-4-6-K)
• Single High card (e.g., 4-5-8-10-Q of differing suits. The Queen is the highest card.)

LOWBALL POKER- RANK OF HANDS

In this form of poker the "lowest" hand wins. Per Hoyle's rules, all straight and flush issues are ignored (very important) and the Ace is considered low for all evaluations of poker hands. This makes the best low as 5-4-3-2-A regardless of suit.

So if the Ace is low then a pair of deuces is higher in rank than a pair of Aces and the pair of Aces would win over the deuces. Similarly, a pair of deuces beats threes, beats fours, beats fives,... You get the idea.

Rank of Lowball hands from lowest (best) to highest (worst) with no wild cards:

• Sequenced or non sequenced hands with no pairings with the Bicycle (5-4-3-2-A in the same or differing suits) being the lowest hand possible.
• Pair
• Two pairs
• 3 of a kind
• Full House
• 4 of a kind

Since there are no straight or flush issues then a 3-of-a-kind beats a Full House with nothing in between these two ranks of hands.

HIGH/LOW POKER- RANK OF HANDS

Hoyle's rules also address the issue of rank of hands in High-Low poker. In the book "According to Hoyle" by Richard L. Frey, the high hand follows the standard ranks in high poker but the best low hand becomes 7-5-4-3-2 unsuited. This seems to challenge the concept of Lowball's rank of hands. Well, since the game is playing both high and low hands together the Ace is evaluated as a high ranked card in both the high and low hand. That means a high card can't be part of the best low hand. Also you must consider the straight and flush issues for high poker. For that reason you must consider them in the low hand as well. Thus you have the 7-5-4-3-2 unsuited as the best low hand in High-Low poker. Confused? I don't blame you. But if you think about it long enough it does make sense.

BUT...Many players will play the Ace both ways in a High/Low game which then makes the best low 6-4-3-2-A unsuited. I decided to add this paragraph after an email from a player requesting clarification of a low hand in High/Low poker. Because the odds of obtaining a 7-5-4-3-2 are the probably the same as the latter it becomes a bit trivial. Always remember to declare the value of the Ace when playing the High/Low game to avoid any confusion. So, comparing the rank of hands for the Low Hand is just the reverse of the High hand ranks.

Rank of Low hands from lowest (best) to highest (worst) with no wild cards:

• Single unpaired cards (6-4-3-2-A unsuited where Aces are low; 7-5-4-3-2 unsuited where Aces are high only) being the lowest hand possible.
• Pair
• Two pair
• 3 of a kind
• Straight
• Flush
• Full House
• 4 of a kind
• Straight Flush

Evaluating a low hand can also be confusing (as pointed out to me in the email example sent to me). "Which is the lower hand? A-2-3-6-7 or A-2-4-5-7?" He and his friends were split over who had the lowest hand. Their dilemma was that the 3 was lower than the 4 but the 5 was lower than the 6. So who has the lowest? The 7-5-4... hand. Why? Remember to begin the evaluation of cards from the highest card and work down. In their situation they were starting at the Ace and working up the rank. It's easy to make that mistake.

3 CARD POKER

3 Card poker is similar to 5 Card poker with less ranks due to obvious reasons. Ranked from highest to lowest.

• Straight Flush
• 3 of a Kind
• Straight
• Flush
• Pair
• High Card

Note that a Straight beats a Flush in 3 Card poker due to the odds (see below). Some people consider straights and flushes optional in 3 Card poker effectively eliminating 3 ranks. Best to declare the ranks before playing.

THE RANK OF THE ACE

In poker the Ace can be considered a High or a Low card depending on the game being played. Most people only view the Ace as a High card but if you scrutinize the very meaning of the Ace, it is a single value card (a value of ONE). In Hoyle's Rules of Games Second Revised Edition, the Ace ranks high in the high poker hand as a single card, within pairings, straights, and flushes. The Ace is considered low when evaluated in a low straight (5-4-3-2-A, called a "Bicycle" or a "Wheel"). This is the only time where the Ace is considered low (unless your game specifically states the value of an Ace as low within a high poker game). My best advice to all who play is whenever in doubt clarify these choices prior to the start of your game.

ODDS IN POKER

So, what are your odds in getting a desired hand? Do you want to know? Well first let's look at how many hands are possible from a 52 card deck.

For 3 Card Poker:

From Hoyle's Rules of Games, It doesn't help much to know the chances of being dealt a straight flush, a full house, or even a pair. But it does help to know the odds against improving any particular hand. That does make sense. I'd rather know if I can improve my hand against the players around the table. So let's look at some of these odds.

For Draw Poker, no wild cards:

For 7 Card Stud Poker, no wild cards:

WILD CARDS AND HOW IT AFFECTS THE ODDS

It is inevitable. There will be a wildcard game played at least once during the night at your party. (Did I say once? I meant a dozen.) Why? Because everyone wants to obtain a better hand and wild cards will give them those high powered hands. Wildcards will make them feel better. It will give them a reason to stay in and keep betting to build the pot. So what does that mean to the odds? Means a lot if you're a statistician. Wild cards will always change the odds. When you introduce them into the game, the possible number of specific hands increases which, in turn, improves the odds of obtaining those high powered hands. It also introduces the Five of a Kind into card ranks.

Calculating the odds with wild cards is beyond the scope of this site. Rather I would direct you to the Neo-Tech site, particularly Appendix D, for those odds. I have found their site to have the best information regarding odds on poker. They also have a graphical chart (though it is fuzzy, you can make it out) showing how the ranks relate to each other as you go from no wild cards to one wild card to 4 wild cards. It's eye-opening.

So why play with wild cards? The variety, excitement, whatever. A bunch of the games and variants listed in this site have varying numbers of wild cards, whether it's just Jokers or your lowest hole card, maybe it's the Suicide King and One-Eyed Jacks, or it's every other red card on the third Friday of the month... (WHOA! That's beyond where I draw the line). Some players refuse to play games with wild cards. It would be sacrilegious to the purity of the game. I don't blame them. When it comes to wild cards I suggest to use them sparingly. The most I would ever play is 8 total (such as in Baseball). And that's pushing it. I try not to rely on a lot of wild card games throughout the night. I try to mix several good straight poker games in to help "cleanse my soul", so to speak.

In any event, you will have to make the determination as to how you will deal with wild cards in your game. As I have dug deeper into the wild card issue, I find more permutations with the ranks and odds. It's become a blur of lines and numbers.

RANKING THE FIVE OF A KIND

Not only do wild cards increase the possible number of hands of all ranks they will change the order of the rank of hands should there be too many wild cards. There are many people who believe that with wildcards the five of a kind is now the highest hand possible and that it beats a Royal flush. If you did the math (which I will not get into on this site), it's true for one wild card added such as the joker. For a total of four wild cards available to use, the odds against obtaining a five of a kind are lower than obtaining a Royal Flush. But, for the same criteria, the odds against obtaining a five of a kind are greater than obtaining a straight flush. When the game calls for two named wild cards (total of eight wild cards) the odds change even more. With that many wild cards you are more likely going to see those five of a kind hands regularly (Go ahead and flash back on a few games of Baseball you played in the past. How many five of a kind hands do you remember?)

From Hoyle's Rules of Games, When wild cards are used, five of a kind are the highest ranking hand. Ties become possible for four of a kind, full houses, or three of a kind.

In the book "The Oxford Guide to Card Games" by David Parlett, he writes Another peculiarity is that the highest hand is five of a kind, making five Aces absolutely unbeatable. As it is considered unethical to be able to bet on absolute certainty, in species of Poker where such high hands actually occur players prefer to rank the five of a kind between fours and a straight flush. (Though it would satisfy mathematics as well as principles to rank it between a King high straight flush and a Royal flush.)

Who's right? Well, they both are. When it comes to wild cards most everybody will stick by the ranks of straight poker as the guideline and rank the five of a kind as the highest hand beating a Royal flush. It really is too confusing to try and figure out a new order of rank when you call multiple wild cards. It's just easier to let the issue go for most players. To see what the wild cards do to the ranking of poker hands check out the Neo-Tech's Poker Odds page. (See link below).

(Side note: I do believe that I will attempt the topic of wild cards with my friends. Since I was schooled in engineering my logic demands that I pursue it. I am leaning towards the five of a kind to rank BELOW the Royal flush for 2 or more wild cards in the deck because I do understand the logic in the odds. It may not be the accepted practice but what the hell. And if any player pulls a natural Royal straight flush in any 4 or more wild card game that I'm dealing then that player deserves the pot.)

Just to reiterate my disclaimer: I am not a professional poker player. I'm just a part-time home poker player who likes to get together with the neighbors once a month to play a little nickel ante poker. These pages are the only the opinions of a rookie poker player. It doesn't reflect the opinions of the web host and their associates. It is only intended to provide some basic information on the ranks of hands and some helpful odds in poker. Some information was taken from Hoyle's Rules of Games, Second Edition, and According to Hoyle (odds on poker hands). The odds information is considered common knowledge and can be recalculated on a computer thus it is not considered plagiarism. If you have any comments, corrections, or additions please email me with your thoughts. I'll be the first to admit that I'm wrong on an issue provided there is evidence backing up someone's claim. Please don't ask me about calculating specific odds of hands. I'll only redirect you to the Neo-Tech web sites or suggest you buy a book. I don't remember all that much from my statistics class from my college days and I'll be damned if I can ever find that book. So just enjoy a good poker game with friends. Drink a homebrew and relax.

Back to Main

This website is hosted for free by . Get your own Free Website now!