Poker Combinatorics: How to Extract Maximum Information from Cards

Most recreational players start learning poker by diving into the rules. A crucial part of these rules is understanding poker combinations. Poker terms, gameplay, mandatory bets, and more are important, but what’s a poker game without knowing the core hand rankings?

Among card games, Texas Hold’em leads in popularity. This is due not only to its simple rules but also to the wealth of training materials, including strategies, charts, and mathematical calculations. Before diving into those, you need to understand how hands are played and the combinations in Texas Hold’em. This is explained in detail below.

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Poker Combinatorics: Texas Hold’em Rules

Before we explore how to calculate combinations in poker, let’s start with the basics—the rules. A Texas Hold’em hand can involve 2 to 10 players. Each player takes a seat at the table relative to the dealer button, which moves one position clockwise after every hand.

Players in the small blind (SB) and big blind (BB) post mandatory bets called blinds, forming the initial pot. Then, the main game begins, consisting of four stages, or streets:

After each card-dealing phase, a betting round follows where players place bets, increasing the pot. Available actions are detailed later in this article.

The winner is the player who shows the strongest combination at the final stage (showdown). Their hierarchy is outlined below.

Not every hand reaches showdown, though. Sometimes, the winner is determined differently—the last player to put the bet in takes the chips.

To win pots more often, tools like HisHands can be a game-changer. This service offers pre-mined hand history databases from top poker rooms. With thousands of cash game and tournament hands on tough opponents, you can use this data to your advantage, building a profitable long-term game.

High Card

We begin poker combinatorics with the weakest possible hand. At showdown, players may find no one has even a pair. In this case, they compare their highest card. The player with the higher rank wins the pot. For example, [5d][8c][Th][Qs][2h] loses to [5d][8c][2h][As][9h].

Pair

This hand consists of two cards of the same rank and three unrelated cards. The pair’s strength depends on its rank. For instance, [5d][5c][3h][8s][10h] loses to [7d][7c][3h][8s][10h]. If comparing [10d][10c][2h][5s][9h] vs. [10d][10c][2h][5s][Jh], the player with the jack wins due to the kicker (explained below).

Two Pair

Also called a “doper” in Texas Hold’em, this hand includes two cards of one rank, two of another, and a kicker. When both have two pairs, players compare the higher pair’s rank first, then the lower pair if tied, and finally the kicker if both pairs match. For example, [3d][3c][5h][5s][10h] beats [3d][3c][5h][5s][7h].

Three of a Kind (Set)

This hand is easy to remember: three cards of the same rank plus two unrelated cards. For example, [5d][5c][5h][6s][10h] is a set of fives. It beats lower-ranked sets and loses to higher ones. If opponents have sets of the same rank, the kicker’s rank decides the winner.

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Straight

A straight is five cards of different suits in sequential order, like [7d][8c][9s][Jc][Qh]. To resolve disputes, compare the highest card in the sequence. For instance, [8c][9s][Jc][Qh][Kd] beats [7d][8c][9s][Jc][Qh].

When an ace starts the sequence, it counts as one. The lowest straight, called a “wheel,” is [As][2c][3h][4d][5c]. It loses to any other straight.

Flush

A flush is five cards of the same suit, not in sequence. Flushes of spades, hearts, diamonds, or clubs are equal in value. To settle disputes, compare the highest card in the flush. If tied, move to the next highest card, and so on, until a winner is determined.

Full House

This hand combines a pair and three of a kind. To decide a winner, compare the three-of-a-kind ranks first. If they’re equal, compare the pair’s rank. For example, a full house with three kings loses to one with three tens, even if the opponent has two aces.

Four of a Kind (Quads)

Quads consist of four cards of the same rank and one unrelated card, like [Kd][Kc][Kh][Ks][2h]. This is one of the strongest hands, with high odds of winning, except on dangerous boards that allow stronger combinations. The fifth card matters only if both players have quads of the same rank. Otherwise, the higher-ranked quads win—e.g., [3d][3c][3h][3s][2h] loses to [10d][10c][10h][10s][2h].

Straight Flush

A straight flush is five sequential cards of the same suit, like 6 to 10 of spades. Its strength depends on the highest card in the sequence. The player with the higher top card wins the pot in a dispute.

Royal Flush

The strongest hand in Texas Hold’em. It is a Ten to Ace straight flush, like [10h][Jh][Qh][Kh][Ah]. Spade, club, heart, and diamond royal flushes are equal in value. A royal flush guarantees victory, but experienced players don’t chase it—it’s extremely rare.

What Is a Kicker in Texas Hold’em?

A kicker is the highest card not part of the main combination. It matters only in situations where players have same combinations, determining who wins the pot.

Kickers apply to hands using four or fewer cards, so flushes and straights don’t have them. Some hands, like sets (two kickers), can involve multiple kickers.

Hand Rankings in Different Games

Each poker variant has unique rules, often affecting how combinations are formed. Below are the specifics for popular poker types compared to Texas Hold’em.

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Omaha Hi-Lo and Stud Hi-Lo

In these games, the pot splits at showdown: one half goes to the strongest hand, the other to the weakest (low). For low hands:

• Cards above eight aren’t allowed. The ace always counts as one.
• The best low hand is A-2-3-4-5.
• Disputes for low hands are settled by comparing the highest card. The lower rank wins half the pot.

If no player has a qualifying low hand, the entire pot goes to the player with the best high hand.

Lowball Poker

This game focuses on low hands. Key rules:

• Flushes and straights are the worst hands, as are pairs and sets.
• The best low hand is 2-3-4-5-7 of different suits.
• The ace is always high, so there’s no “wheel” in this game.

Short-Deck Poker

Also known as 6+ Hold’em or Texas 6+, this game uses a 36-card deck, excluding twos to fives. This changes hand rankings:

• The lowest straight is A-6-7-8-9.
• A flush beats a full house.
• A straight is weaker than a set (in some rooms).

Texas Hold’em Combinations: Concept and Formation

In poker, combinations refers to card groupings that form specific hands. Building the strongest possible hand in a given deal is the simplest way to win. Alternatively, tactical moves can push opponents to fold before showdown.

In Texas Hold’em, you can use any number of pocket cards (or none) and common cards to form a hand. The board is always shared. If no player can improve the board with their pocket cards, the pot is split equally among active players (split pot).

Poker Betting Rounds Step-by-Step

Betting rounds follow a set order under Texas Hold’em rules:

1. Preflop, the player to the left of the big blind acts first, with action moving clockwise. Postflop, the small blind starts, followed by clockwise actions.
2. Decisions are final once announced, passing the turn to the next player.
3. A betting round ends when all players have matched contributions to the pot. If a player refuses to call a bet or raise, he must fold.

Types of Texas Hold’em

Poker rooms offer tables that differ not only in blind sizes or player numbers but also in betting formats.

Limit Poker

Marked as FL (Fixed Limit), these tables set strict bet sizes:

• Lower limit: The minimum and maximum bet/raise on preflop and flop.
• Upper limit: The minimum and maximum bet/raise on turn and river, double the lower limit.

This allows larger bets on later streets.

Pot-Limit Poker

Marked as PLH or PL, the maximum bet is limited by the pot size. Each contribution to the pot increases the maximum bet size.

No-Limit Poker

The most popular format, marked NL, has no cap on bet sizes. Players can raise any amount or go all-in.

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Poker Betting Rules: Actions in Betting Rounds

Combinations are vital, but bets are just as crucial. They let you inflate pots with strong hands or push opponents out with weak ones.

Available actions:

• Bet: A wager at least the size of the big blind to stay in the hand.
• Fold: Discarding cards, forfeiting the chance to win the pot.
• Check: Passing without betting, staying in the hand without adding chips.
• Call: Matching the previous player’s bet to continue.
• Raise: Increasing the opponent’s bet to pressure folds or grow the pot.
• All-In: Betting your entire stack.

How to Win at Texas Hold’em: Basic Strategy

Knowing rules and combinations isn’t enough to win. A strategy is key to staying profitable long-term.

Tips for building a strategy:

1. Choose a playing style: Beginners should opt for a tight style to minimize risks.
2. Adjust hand ranges: Select appropriate ranges for each table position.
3. Learn poker math: Calculate probabilities, outs, pot odds, and more for better decisions.
4. Master basic tactics: Learn moves like stealing, check-raising, 3-betting, slow-playing, and others.
5. Understand bankroll management: Pick suitable stakes and manage your funds wisely.

Don’t rush into real-money games. Practice theory at play money tables to eliminate risks. Once confident, move to real games and try freerolls—MTTs with no buy-ins. Held in all poker rooms, they offer $50-$100 prize pools.