Winning Poker Hands in Order: A Brief Guide |

Winning Poker Hands in Order: A Brief Guide

| By Roy Rasmussen | Category: Games

Whether you’re playing five-card draw, seven-card stud, texas holdem, or most other variants of poker, the rules for what makes a winning hand are usually the same. There are a few notable exceptions, like stripped-deck five card draw and lowball, but even in these exceptions, the mathematical laws of probability govern how cards are ranked. Here is a brief guide to the ranking hierarchy of winning poker hands in order.

The Mathematics Behind Poker

In plain English without going into technical details, the underlying mathematical principle behind poker is that the more combinations of coincidences a hand depends on, the less likely that hand is, and the higher it ranks.

Standard Odds of Hands from Lowest to Highest

A hand where no cards match does not depend on anything other than the hand being dealt, so no pairs is the most likely combination. Out of 2,598,960 possible standard hands, the odds of getting a hand with no pairs is about 50%. Because of this, a hand with no pairs ranks lowest. When this is highest type of hand at play, under normal rules, the high card wins. For example, A-K-7-6-2 would beat A-K-7-5-3 because 6 is higher than 5.

A hand where two cards match is the next most likely combination, so a pair ranks next highest. There is a 42.25% chance of drawing a hand with one pair.

After this there is a marked drop in odds. The next most likely combination is two matching pairs, so two pairs is third highest. There is only a 4.75% chance of drawing two pairs.

Three cards matching is next most likely, making three of a kind rank next. There is a 2.10% chance of drawing three of a kind.

After this, the odds drop below 1%. The next most probable combination is five cards from any suit forming a numeric sequence, for a straight. There is only a 0.39% chance of drawing a straight.

Next is a combination of any five cards from the same suit, for a flush. There is a 0.20% chance of getting a flush.

The next possible scenario is a combination of three of a kind and a pair, for a full house. The odds of a full house are 0.14%.

From here the odds continue to drop below a tenth of a percent and then dip dramatically. The next most likely is four of a kind. The odds of four of a kind are 0.024%.

Then there can be a straight where the cards are all from the same suit and form a flush, for a straight flush. The odds of being dealt a straight flush are 0.0015%.

Finally a straight can be formed by all the face cards in a suit, for a royal straight flush. The odds of a royal straight flush are 0.000154%.

And last but not least, when a joker is added to the deck, it is possible to combine four aces with the joker for five of a kind aces. The odds of five of a kind aces are about 0.0000348%, or one in every 2,869,685 deals.

The Standard Ranking

Based on these odds, when the joker is not at play, the standard ranking from highest to lowest hand is:

Royal straight flush
Straight flush
Four of a kind
Full house
Flush
Straight
Three of a kind
Two pairs
Pair
High card with no pairs

Variations

There are a few notable exceptions to this standard ranking system.

The first is when a joker is added to the standard ranking system. In this case, the house rules may count five of a kind aces higher than a royal straight flush.

A second major exception is when five-card draw is played with a stripped deck, where either 20 or 16 cards have been removed from the deck, depending on the number of players. This alters the odds of different hands being dealt. As a result, a flush is ranked above a full house.

A third exception is lowball. In lowball, the lowest-ranking hand wins. Different variants of lowball have different ways of determining which card ranks lowest.

Worthy Resources

The Official Rules According to Hoyle
Poker Rules