Poker Probabilities! Complete List of Hand Probabilities in Texas Hold’em and Calculation Methods

Whether in online poker or live poker, knowing the probability of poker hands forming is important for winning consistently.

The probability of hands forming in Texas Hold’em is as shown in the probability table below:

Hand	Probability on Flop	Probability by River
Royal Straight Flush	0.00015%	0.0032%
Straight Flush	0.0014%	0.027%
Four of a Kind	0.0024%	0.16%
Full House	0.14%	2.6%
Flush	0.2%	3.25%
Straight	0.39%	4.62%
Three of a Kind	2.1%	4.83%
Two Pair	4.75%	23.5%
One Pair	32%	43.8%
High Card	50%	17.4%

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Why Understanding Probability Is Important in Poker

Understanding probability in poker is extremely important.

That’s because understanding probability eliminates wasteful battles and allows you to aim for maximum profit when you’re in an advantageous position.

In poker, no matter how skilled you are, it’s not a game you can win 100% of the time.

The probability of cards coming in your starting hand is the same for beginners, and it’s not that ‘advanced players have stronger cards.’

However, after many battles (or sometimes even in a single battle), advanced players’ win rates become higher than beginners’ or intermediate players’.

That’s because they think about probability at each phase and avoid battles when there’s a high chance of losing.

If you don’t understand probability, there’s a risk of becoming easy prey for advanced players.

Therefore, understanding probability is extremely important for improving at poker.

Also Learn Poker Terminology

As stated above, probability is important in poker, but equally so is learning specialized terminology.

Beginners need to study poker to improve, but for that you need to know at least some specialized terminology to understand what books and videos are saying.

Therefore, work on memorizing terms in order from those most frequently used.

Poker Probability Basics

First, let’s roughly cover the basics of poker (Texas Hold’em) probability — starting hand and hand appearance probabilities.

For those who don’t yet know the poker rules, the article ‘Thorough Explanation of Poker Rules‘ explains in detail, so please use it as a reference.

Let’s dive in.

① Starting Hand Combinations

The starting hand — the initial cards in a game — is composed of 2 cards dealt from a 52-card single deck.

The combinations are found with the combinatorics formula 52C2 taught in high school math, for a total of 1,326 combinations.

When researching starting hand probabilities, remember that this 1,326 becomes the denominator of calculations.

② Poker Hand Probabilities [Probability Table Included]

The probability of poker hands completing by the showdown stage (after the river, comparing hand strengths) is as shown in the table below:

Hand	ハンド	確率
Royal Straight Flush		0.0032％
Straight Flush		0.027％
Quads (Four of a Kind)		0.16％
Full House		2.6%
Flush		3.25％
Straight		4.62％
Three of a Kind (Set)		4.83％
Two Pair		23.5％
One Pair		43.8％
High Card		17.41％

A common pattern for beginners just starting poker is aiming for a flush or full house — which are hard to complete from weak hands — and losing to one pair or two pair.

If you understand the difficulty of hand appearance numerically, you can avoid engaging in unreasonable battles from the start.

Poker hands are explained in detail in the following article:

③ Starting Hand Probabilities

Next is an explanation of the probability of the 2 starting hand cards dealt at the start of the game.

Basically, starting hands are determined with the following probabilities:

Starting Hand	Probability
Pocket Pair	~6%
Suited	~24％
Connector (Suited Connector)	~4％
Other	~66％

Also, starting hands are explained in detail in the following article too, so please also take a look:

Pocket Pair

Getting 2 cards of the same rank initially is called a pocket pair.

For example, getting a 9 of clubs and a 9 of diamonds.

The appearance probability of a pocket pair is approximately 6%.

Since one pair is already formed at the start, it boasts a fairly high win rate at the pre-flop stage.

Suited

Suited — 2 cards of the same suit — come as your initial hand approximately 24% of the time.

Since you can complete flush — the strong hand of 5 cards of the same suit — the hand can fight better than mismatched cards.

Connector (Suited Connector)

2 hole cards with consecutive ranks like 7-8 or Q-K are called connectors.

The appearance probability of a suited connector — same suit and consecutive ranks — is approximately 4%, and an unsuited connector’s appearance rate is approximately 12%.

Connectors are easy hands to complete straight — the hand of 5 consecutive ranks.

Other

And the appearance probability of hands like A-J off-suit (not suited) that don’t easily lead to specific hands is approximately 66%.

Remember that 2 out of 3 times you’ll get a hand like this.。

Each Poker Hand’s Probability and Details [Texas Hold’em]

In the previous section we introduced probabilities centered on starting hands. Here we introduce each poker hand’s probability and details.

Probability of Royal Straight Flush: 0.0032%

(Appearance rate approximately 0.0032%)

Royal Straight Flush is the strongest hand made with cards from 10 to A of the same suit, with an appearance rate below 0.01%.

It’s extremely rare, and completing it at a poker room sometimes earns you the accumulated jackpot as a bonus. Also, online poker platforms like GGPoker also give bonuses.

Probability of Straight Flush: 0.027%

(Appearance rate approximately 0.027%)

A hand completed by connecting 5 consecutive ranks of the same suit, with an appearance rate of 0.027%.

Probability of Quads (Four of a Kind): 0.16%

(Appearance rate approximately 0.16%)

The appearance rate of quads — collecting 4 of the same rank — is 0.16%.

But since the appearance rate is below 1%, you won’t see it without considerable luck.

Probability of Full House: 2.6%

(Appearance rate approximately 2.6%)

Full house — completed from a combination of 2 cards of the same rank and 3 cards of the same rank — appears with approximately 2.6% probability.

Since it’s still only 2.6% with all cards open to the river, you won’t see it frequently, but if you play a game for a long time, someone will naturally complete it.

Probability of Flush: 3.25%

(Appearance rate 3.25%)

The appearance rate of flush — collecting 5 cards of the same suit — is approximately 3.25%.

Since the opponent can fully have a chance of completing it too, you need to be wary when community cards (the face-up cards shared by all players) match in suit.

Probability of Straight: 4.62%

(Appearance rate approximately 4.62%)

A hand completed when 5 consecutive ranks regardless of suit, with an appearance rate of 4.62%.

As shown in the image, a straight using A-2-3 can be made, but K-A-2 cannot, so be careful.

Probability of Three of a Kind (Set): 4.83%

(Appearance rate approximately 4.83%)

Three of a Kind (Set) — collecting 3 of the same rank — has an appearance rate close to 5%.

When the starting hand is a pocket pair, it becomes easier to complete, so even with a 2 or 3 pocket pair, some players join the game aiming for a three-of-a-kind comeback.

Probability of Two Pair: 23.5%

(Appearance rate approximately 23.5%)

Two Pair — completing 2 separate sets of matching ranks — has an appearance rate of approximately 23.5%.

Since it can be completed fairly frequently, even if you’ve completed one pair, there are many cases where the opponent completes two pair on the river and reverses.

Probability of One Pair: 43.8%

(Appearance rate approximately 43.8%)

The appearance probability of one pair is approximately 43.8%, boasting a dramatically higher probability than no-hand high card.

Therefore, even if you have one pair, if the game continues to showdown, there’s a high chance the opponent has also completed one pair — be careful.

Probability of High Card: 17.41%

(Appearance rate approximately 17.41%)

The appearance probability of high card — no hand — is approximately 17.41%.

When you can judge from the opponent’s actions that they have a high card, you can challenge showdown even with a high card.

However, high card vs. high card is decided by the simple numerical strength of the hole cards, so avoid high card battles with weak cards.

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11 Important Probabilities in Poker Strategy [Calculation Methods Also Introduced]

Until now we’ve introduced basic poker probabilities.

However, in actual play, the ‘2% rule’ is used in a very large number of situations.

The 2% is the approximate possibility of drawing 1 out (a card that completes a stronger hand when drawn) from the flop onwards, used to quickly calculate hand completion rates during a game.

However, this is a method for briefly judging the possibility of drawing cards in a short time, and you must not forget that the actual chance of drawing a card is lower than calculated due to factors like being dominated (the card you want is in the opponent’s hand).

Below, let’s look in more detail at specific situations.

① Probability of Getting One Pair by the River

First, let’s look at the probability of one pair completing from the flop.

For example, if you have a 7 of hearts and Q in your hand.

To complete one pair, you need to draw a 7 or Q that’s not hearts, so there are a total of 6 outs.

2% × 6 cards gives an approximately 12% chance of drawing the outs, and with 2 chances on turn and river, one pair completes with approximately 24% probability.

② Probability of Getting One Pair on the Flop

By the way, the probability of getting one pair on the flop is 32%.

The 2% rule is applicable at the turn and river stages, so it doesn’t become 12% × 3 cards (flop) = 36%.

At 32% probability, it appears 1 in 3 times, so remember that there’s a sufficient chance the opponent completes one pair at the flop stage.

③ Probability of Two Pair on the Flop

Also, the possibility of two pair completing on the flop is approximately 2%.

Even two pair, which exceeds 20% appearance rate by the river, almost never completes at the flop stage.

Therefore, joining a pre-flop battle aiming for two pair with weak cards tends to lead to a loss.

④ Probability of Two Pair on Flop Developing into Full House or Better

When two pair is complete on the flop, full house completes if you draw 4 outs on turn and river.

The calculation is 4 cards × 2% × 2 times for approximately 16% probability.

Once full house is complete, it’s almost impossible to lose on hands.

⑤ Probability of Middle Connector Becoming a Flop Straight

The possibility of a middle connector like 7-8 — with consecutive ranks — becoming a flop straight is approximately 1.3%.

Since the completion probability is very low, even against a player who frequently uses connectors aiming for straights, there’s not much to fear at the flop stage.

⑥ Probability of Middle Connector Becoming Open-End or Gutshot on the Flop

Also, the probability of a middle connector forming an open-end — one card away from completing a straight (forms like 5-6-7-8 or 7-8-9-10) — is approximately 9%.

On the other hand, gutshot (a state where the middle rank is missing like 5-6-8-9) completes with approximately 16.8% probability.

Open-end with 8 outs (2 types × 4 cards) has 2 chances on turn and river, and straight completes with 32% probability, so many players play it.

⑦ Probability of Suited Becoming Flush Draw or Flush on the Flop

The probability of a suited hand becoming a flush or flush draw (one card away from completing flush) is approximately 12%.

Here, let’s also learn how to calculate flop probabilities.

The total number of combinations at flop stage is 50C3 = 19,600 combinations drawing 3 cards from 50 remaining cards after the starting hand, and this number becomes the denominator for probability calculations.

The combination of flush is drawing 3 cards from 11 cards of the same suit remaining in the hand, so 11C3.

Also, flush draw has the combination of drawing 2 same-suit cards which is 11C2, and multiplying by the combination for the remaining 1 card (39 cards = 50-11), so 11C2 × 39 combinations.

(11C3 + {11C2 × 39}) ÷ 19,600 × 100% = 11.97%

We were able to calculate the possibility of a suited hand leading to flush or flush draw on the flop.

⑧ Probability of Flush Draw Becoming a Flush

The probability of a completed flush draw on the flop becoming a flush by the river is 36%.

The number of same-suit cards remaining at the flush draw stage is 9, so the formula is 9 outs × 2% × 2 times.

The completion rate isn’t bad, so be careful when the same-suit cards are lined up in the community cards at the flop stage.

⑨ Probability of Pocket Pair Becoming a Set or Quads by the River

Next is the probability of a pocket pair being strengthened to set or quads between turn and river.

Set draws 2 outs over 2 chances for an 8% completion probability.

Meanwhile, quads requires drawing 1 out in 1 chance at river on the premise that set has been completed, so completion probability is 2%.

⑩ Probability of Pocket Pair Becoming a Set or Quads on the Flop

Also, the probability of a pocket pair becoming a set on the flop is approximately 12%, and the possibility of quads is approximately 0.2%.

Since set completes more than once every 10 times, some players will at least check the flop cards even with a weak pocket pair.

⑪ Probability of Winning with AA / Probability of Losing to AA

AA (Pocket Aces) is an extremely powerful hand, and the win rate in a heads-up situation against a random hand is 85.3%. Conversely, the probability of losing with an AA hand is approximately 15%.

Poker Probability Calculators (Apps) Compatible with Texas Hold’em

There are 2,598,960 combinations (formula: 52 ÷ (5 × 47)) of playing cards used in poker. Memorizing or calculating them each time would be hard.

Here we introduce probability calculators (apps) that easily produce probabilities.

[Recommended for iPhone / iPad]

• Poker Keisanki (Calculator) (free)
•  Poker Odds Calculator (paid)

[Recommended for Android]

• Poker Calculator (free)
•   Poker Odds Keisanki (free)

To perform probability calculations faster and apply them in real play, it’s important to actually play while calculating. For those who want to accumulate more experience, online poker is recommended!

For information on which online poker platforms are easy to practice at, see the following article:

Situations Where the Concept of Poker Probability Becomes Important

The situations where the concept of poker probability becomes important are as follows:

• In the midst of tournament bubble line
• When reading the opponent’s bluff in ring games
• When making probability-based plays to put your balance in the positive

Let’s check each.

In the Midst of a Tournament’s Bubble Line

Where the probability element in poker must be particularly conscious is when you are in the midst of the bubble line in a tournament.

This is because being in the midst of the bubble line means winning gets prize money while losing could mean losing everything.

For example, if you hold AA and face an all-in from the chip leader, how should you handle it?

If the opponent has a suited connector (other than AK), the win rate is approximately 80%.However, turning it around, there’s a 20% chance of losing everything — so at bubble lines and other moments where prize money is on the line, calmly analyze probabilities and be able to take actions like folding even with AA.

When Reading the Opponent’s Bluff in Ring Games

Also, knowing probability can be used when reading the opponent’s bluff.

That’s because when the opponent is clearly making strange moves, you can think about the probability of the hand rank the opponent holds being valid.

For example, if you can see through the probability of nuts-class forming, there’s no problem no matter what playing the opponent does.

However, when reading bluffs, also always incorporate the following items as ‘variables’ in play.

The variables here are where the game’s unpredictability lies, so note that they exist beyond probability.

Also Combine Player Reads

When reading bluffs in ring games and beyond, you also need to combine player reads.

The reason is that if you can properly read people’s habits, you can not only read bluffs but also convert to exploiting.

If the probability of the opponent making a pot overbet when bluffing is 100%, you just need to follow the opponent’s bluff to make them release chips.

By combining the player-read element, you can also enjoy battles beyond probability.

However, player reads can only be done because you know the base probabilities, so always start by acquiring probability knowledge.

Also Consider the Opponent’s Play Style

You also need to properly consider the opponent’s play style.

Since poker play styles vary — tight-aggressive, loose-aggressive, or rock — when the opponent’s hand is shown, properly memorize it along with their playing.

For example, with a tight-passive player, they might follow your bets as long as they can, and you end up losing.

In that case, quickly checking to receive a free card would be more profitable than reading the bluff.

When Making Probability-Based Plays to Put Your Balance in the Positive

Knowing probability directly leads to knowing expected value, and you can always make plays that are profitable for yourself.

All advanced players and poker pros know probability, so consider that other skills develop from a backbone of expected value.

In particular, clutch plays test something like fundamental strength based on how familiar you’ve become with poker probabilities, so get into the habit of always calculating.Also, know about hand range charts for whether to play. Hand range charts are introduced in detail in the article ‘Texas Hold’em Hand Range Chart [Poker Basics]‘.

Master Basic Probabilities to Improve Your Win Rate in Poker

This article introduced poker probabilities.

The probability of each hand at showdown is as follows:

Hand	Probability
Royal Straight Flush	~0.0032%
Straight Flush	~0.027%
Quads (Four of a Kind)	~0.16%
Full House	~2.6%
Flush	~3.25%
Straight	~4.62%
Three of a Kind	~4.83%
Two Pair	~23.5%
One Pair	~43.8%
High Card (Bust)	~17.41%

The especially important point to keep in mind is the 2% rule.

The probability derived by the 2% rule is nearly equivalent to win rate, and being able to calculate your current win rate allows odds calculations such as how far you can bet.

For example, in a game with a payout of 5x or more, you can make judgments like ‘since my win rate is above 20%, it’s a balanced bet against the risk’ and go ahead with call or raise.

Being able to judge whether odds are appropriate or not is the shortcut to leaving the beginner level.

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