Poker

Poker Probabilities – Simply Increase Your Chances Of Winning

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Being knowledgeable about poker probabilities can instantly improve your overall experience. You can make ideal decisions that increase the “ odds ” of your success and differentiate you from ill-informed players at the table.

Calculating poker probabilities – advantages

A complete understanding of poker odds and how they are calculated is essential for anyone wanting to improve their poker skills. Below are some of the key benefits when calculating poker odds:

  • Better Decisions: Help you make optimal decisions about how to play in each moment.
  • Risk Assessment: Risk assessment allows players to weigh the potential rewards and risks associated with different scenarios.
  • The advantage over opponents: An advantage over is achieved through a better understanding of probabilities compared to opponents.
  • Avoid costly mistakes: Identifying low-probability hands reduces the chances of you making bad plays.

The formula for calculating the chance of winning in poker

Before you try to calculate the odds of winning in poker, you need to calculate your “outs,” which are the cards that can strengthen your hand. Subtract your outs from the total of the deck’s unknown cards.

Formula for calculating the chance of winning in poker

Here are two calculations to help you with your chances of winning:

First calculation:

  • Identify Unknown Cards: Total cards minus known cards.
  • Subtract Outs: Unknown cards minus your outs equals the number of bad cards.

Second calculation:

  • Ratio formation: Establish a ratio of bad cards to good ones (outs).
  • Determine the odds: This ratio indicates the chances that your hand will improve.

The 4-2 rule for quickly calculating the odds of winning in poker

The 4-2 rule offers a direct approach to quickly determining the likelihood of a better hand while sitting at the poker table.

To find the percentage outcome of getting one of your outs to the river on the flop, simply multiply your current number of outs by 4. To learn more about the basic poker rules that support these calculations, explore our related content. Multiply the number of outs by 2 on the turn to determine the probability of advancing on the river.

This provides a quick and straightforward way to evaluate the strength of your hand during intense play, allowing you to make faster and better decisions.

Example of quick calculations using the 4-2 rule:

Situation Outs calculation Result (%)
After flop 9 9 outs × 4 36 %
After Turn 9 9 outs × 2 18 %

 

In short, if you have 9 outs after the flop (e.g. a flush), your chances of getting a hand by the river are about 36%. If you still have nine outs after a failed flush on the turn, the probability of getting a flush on the river drops to about 18%.

Consistent poker probabilities at a glance

It is essential to understand consistent poker probabilities to make timely and effective decisions at the table. Learn how to make money in poker by familiarizing yourself with these odds and efficiently determining the value of a call.

poker

The probabilities in this overview therefore provide a momentary assessment of your chances of winning given various possible draws after the flop and turn.

Overview of the winning probabilities in poker

Poker Hand Outs Odds (Nach Flop) Odds (After Turn)
Gutshot Straight Draw + Flush Draw 12 1.2:1 2.8:1
Flush Draw 9 2:1 4.1:1
Open-Ended Straight Draw 8 2:1 4.8:1
Two overcards 6 3:1 6.7:1
A pair withdraw to two pair of three of a kind 5 4:1 8.2:1
Gutshot straight draw 4 5:1 10.5:1
Eine Overcard 3 7:1 14.3:1
Set Draw 2 11:1 22:1

 

Preflop & Postflop Probabilities

Preflop is the phase in Texas Hold’em in which players evaluate their initial two-card hands before the community cards are revealed. Learn from the best poker players how to approach this phase strategically.

Postflop, on the other hand, refers to the phases that occur after the first 3 community cards (the flop) and allow players to assess the strength of their hand about the evolving board.

Since you need to know these phases well, we will also explain to you in the next sections how you can calculate the preflop and post-flop poker odds:

Preflop probabilities

In Texas Hold’em, preflop probabilities provide a clear understanding of the potential strength of a player’s first two-card hand. Notable probabilities include those associated with Aces or Kings.

There is a 0.45% probability of receiving Aces (AA), which occurs approximately every 221 hands, and a 0.90% probability of receiving Kings (AA, KK), which also occurs every 111 hands .

This information is particularly important because it has a huge impact on your strategy before the community cards.

Table: Preflop hand probabilities

Poker Hand probabilities Every umpteenth time
Axis (AA) 0.45 % 221
Aces or Kings (AA,KK) 0.90 % 111
Ace King (AK) 1.21 % 83
Ace King or Queen and better (AK, QQ, KK, AA) 2.56 % 39
One pair (AA to 22) 5.88 % 17
Cards of the same color (95 in Hearts or Q9 in Diamonds) 23.53 % 4
Cards of the same color (A in hearts and K in clubs) 70.59 % 1.4
2 picture cards (A to 10 – KQ, QT or AJ) 14.33 % 7
2 low cards (9 to 2 – 98, 72 or 43) 33.79 % 3
Suited Connectors (89 in Herz oder QJ in Caro) 3.92 % 26

Postflop probabilities

Understanding post-flop probabilities is just as important for the correct strategic approach once the flop is revealed.

In this phase, players have the opportunity to observe the development of their hand as 3 community cards are added, increasing the transparency of potential hand strengths.

A clear understanding of starting hand probabilities makes it easier to decide whether to continue placing bets, fold, or change strategy in light of evolving card dynamics.

To help you calculate post-flop poker probabilities , we will explain what different hands look like in the following sections:

Unpaired starting hand

With unpaired starting hands, such as Ace-King or Ace-Queen, everyone pays attention to the post-flop probabilities.

The probability of getting a pair on the flop is 28.96%, but that doesn’t automatically guarantee a successful hand. It’s important to be extra careful when choosing poker starting hands, especially when paying attention to probabilities – as this potentially optimizes post-flop results.

Table: Postflop probabilities for unpaired starting hands

Poker Hand probability All X hands
A few flops 28.96 % 3
Flop a pair or better 32.43 % 3
Two pairs or better flop 3.47 % 29
Drilling or better flopping 1.35 % 74
Full house or better flop 0.10 % 980

Pair as starting hand

Entering the game with a pair in hand presents unique opportunities and dangers. Approximately 11.76% of hands contain a failed set, which is once every nine hands.

However, the probability of receiving a full house is significantly lower at 0.73%. These numbers suggest that lower pairs (like 22-66) could be dangerous. In bad situations, it may be advisable to fold preflop to avoid expensive post-flop commitments.

Table: Postflop probabilities for an initial pair

Poker Hand probability All X hands
Flop a set or better 11,76 % 9
The full house flop 0,73 % 136
Quads the flop 0,22 % 445

Cards of the same color as the starting hand

By using cards of the same color as your starting hand, you can strategically increase your chances of getting a flush or flush draw on the board.

While this strategy sometimes relies on intuition, it is backed by considerable probabilities: the probability of getting a flush draw is 10.94% and the probability of getting a complete flush on the flop is 0.84%.

In addition, the probability of losing at least one card of the same suit to get a backdoor flush draw is comparatively high at 46.63%.

Table: Postflop probabilities for starting hands of the same color

Poker Hand probability All X hands
Flush draw the flop 10,94 % 9
Flush the flop 0,84 % 119
Flop a card of the same color (backdoor flush draw). 46,63 % 2

Connectors like Starthand

Connectors, which are adjacent cards of different suits, provide the opportunity to form straight draws or complete straights on the flop. However, the usability of these hands is often limited.

Therefore, you should also be careful with these hands, preferably from positions such as the big blind without prior advances, or when the better position and game dynamics justify the investment given the pot odds.

Table: Postflop probabilities for connectors

Poker Hand probability All X hands
Flop any straight draw (e.g. a gunshot). 26,00 % 4
Flop an open-ended straight draw 9,60 % 10
Straight flop 1,31 % 77

Calculating Pot Odds – When Should You Play a Hand?

The pot odds play a central role in poker strategy as they provide guidance when deciding whether to call your opponent’s bet based on the possible winnings.

By comparatively analyzing the pot odds and your own calculated odds of winning the hand, you can determine the financial viability of the call.

For example, if your opponent places a bet of €10 in a €40 pot, the cumulative winnings will be €50, giving odds of 5:1. This is a favorable call if your odds of winning are 4:1; Statistically you would win 1 out of 5 times, which would pay off over time.

If the pot only contains €20 and the stake remains at €10, the odds drop to a ratio of 3:1. Since the overall odds are less than your chances of winning, it is not profitable to call in this situation.

This strategy allows you to effectively minimize risks and optimize your returns by taking advantage of statistical advantages.

Poker probabilities for preflop all-in

Preflop all-in is a very high bet, which often draws the attention of the entire table to you. It appears particularly common as a strategy to force opponents out of the pot, or in the final stages of a tournament where high blinds force players to make daring moves.

Poker probabilities for preflop all-in

Knowing when and with which cards to go all-in can have a significant impact on your success in a tournament.

The decision to bet all your chips can be influenced by the quality of your hand compared to your opponents’ likely holdings. Below you will find an overview of various scenarios with the corresponding showdown probabilities:

Showdown probabilities

scenario probabilities
One pair vs two higher cards (Coinflip) 46 % (33 vs QTs) to 57 % (QQ vs AKo)
A pair against a higher and a lower card 68 % (99 vs A8o) to 73 %
A pair against two lower cards 77 % (QQ vs T9s) to 89 % (QQ vs 72o)
A pair against a higher card and a card of the same rank 60 % (55 vs 65s) to 70 % (JJ vs AJo)
A pair against a lower card and a card of the same rank 81 % (77 vs 76s) to 95 % (JJ vs J40)
Two higher cards against two lower cards 58 % (Q9o vs 76s) to 71 % (JTs vs 62o)
High and low card versus two cards in between 51 % (K7o vs 89s) to 63 % (K4s vs 95o)
Better kicker 53 % (A5o vs A2s) to 76 % (QJs vs Q3o)
Interlocked cards 56 % (A9o vs T8s) to 66 % (K9s vs Q6o)

 

In an all-in scenario, these probabilities inform players about the relative strength of their hands. For example, the probability of winning with a pair against a higher card and a lower card is significantly higher than many might expect, at 68% to 73%.

Calculating poker probabilities – this is how it works

To navigate the intricacies of the game of poker, it is essential to master the mental calculations that allow you to pragmatically calculate the probabilities of winning a particular hand.

The first step is to understand several basic terms that are particularly important once you calculate odds in poker:

  • Outs: These are the remaining cards in the deck that have the potential to strengthen your hand to the highest possible position in the game. It is important to know your outs to make further calculations.
  • Odds: The odds or odds indicate the calculated probability of winning the hand. This is determined by the correlation between the number of outs in your hand and the number of unknown cards remaining.
  • Unknown Cards: In a standard poker game with a 52-card deck, numerous cards remain invisible or “unknown” throughout the hand. Unknown cards are cards that you do not have in your hand or that are not visible on the table at the start of the game.
  • Bad cards: Bad cards are also unknown cards, but they have the potential to strengthen your opponent’s hand and thus endanger your chances of winning. They do not represent outs for your hand and therefore influence the probability calculations against you.

With these definitions in mind, you can determine your poker probabilities in just two steps:

  1. Identify Your Outs: Choose your outs by identifying the remaining cards in the deck that will be beneficial to you.
  2. Calculate the Odds: Apply the formula (unknown cards: outs) to identify bad cards. This then reflects the probability of the following card forming a hand.

Calculating Outs – Example

To illustrate the calculation of probabilities in poker, consider the following scenario: You are holding stock cards of the same suit, specifically the 10-9 in spades.

After the flip that reveals the Ace of Hearts, Queen of Spades, and 7 of Hearts, you are two hearts away from making a flush. The 2 diamonds are dealt on the turn, which is detrimental to your flush draw.

At the start, the deck in this scenario consists of 13 hearts. 4 hearts are already known to you (2 in your hand and 2 on the board); So you have 9 outs in the deck that could end your flush.

To calculate the probability of winning the hand with a flush on the river, it is important to know these outs.

Example calculation for poker probabilities

Poker tableTo properly apply poker probabilities in a game, we will calculate different situations to try to achieve a flush:

  1. Calculate the unknown cards: Start with a complete deck of 52 cards. After subtracting the two cards in your hand and the 4 visible cards on the board (flop and turn), 46 unknown cards remain in play.
  2. Calculate the bad cards: Subtract the 9 outs (the remaining hearts that can be used to complete your royal) from the 46 unknown cards. This calculation results in 37 cards called “bad cards” that are detrimental to your flush.
  3. Calculate your odds: Divide the number of bad cards by the number of outs to find the chances of getting a flush by the river: 37 bad cards × 9 outs = approximately 4.1, which is a ratio of 4: 1 corresponds. This means that there is about a 20% chance that one of your outs will be the next card drawn.

Chances of winning in Texas Hold’em at a glance

Understanding the probabilities in Texas Hold’em can immediately influence your decisions – and promote more efficient game management in the process.

Below you will find detailed analyses of numerous facets of the game to give you insider tips on Texas Hold’em probabilities:

The best hands in Texas Hold’em Poker

The probability of a first-class starting hand (such as AA or AK suited) is around 2.1%. If you bet exclusively on these hands, you would only play a limited number of hands and potentially miss out on advantageous opportunities.

Are you waiting for a flush?

If you are one card short of a flush after the flop, you will complete your flush by the river 34.97% of the time. This remarkable opportunity can be a justification for further investment in the pot.

“But they were the same color!”

If you play 2 cards based solely on their suitability, the probability of winning increases by just 2.5%. This is a negligible advantage that, barring other better circumstances, shouldn’t affect game action.

Pairs in Texas Hold’em Poker

With a probability of 32.43%, or just over a third, it often happens in the game that one of your basic cards will match the draw.

The right community card

The probability of hitting a minimum of 2 pairs increases to around 50% by the river, providing plenty of opportunity for post-flop improvement.

On the street

If you hold an open straight draw after the flop, the probability of finishing the road to the river increases to 31.5%. This has an impact on the decision about the further course of the hand.

Play the three-of-a-kind correctly

The odds ratio of turning a pair into three of a kind is 7.5:1. Only invest in small pairs when the sum of the odds is in your favor.

Inside street

Pursuing an inside straight (or gutshot) is dangerous; About 9% of the time you will be able to complete the hand to the river.

Over Pair bei Texas Hold’em

About 80% of the time when competing pairs compete, the highest pair wins. When intense betting occurs, the likelihood of opponents holding higher pairs should be taken into account.

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