Probability of Getting a Premium Hand in Poker

Probability calculations are an integral part of the game of poker. All poker players calculate their odds of getting a premium hand such as a pair of aces, kings, or an A-K, as well as the odds of getting a particular out card on the flop, turn, or river.

In this article, we present important statistical calculations.

Why is it important to know the odds?

Knowing the odds of getting the card you need or the odds of your opponents holding certain cards will help you make better decisions and win more hands. Always use statistics to support your decisions.

The number of possible combinations for getting two cards in poker (one deck consists of 52 cards) is 1,326. To calculate the chance of getting a particular pair of cards, count all the possible combinations for that pair and divide by the total number of combinations (1,326) to get the result.

For example:

To calculate the odds of getting a pair of 4s, we count all possible combinations:

  • Pair combination of 4 of Hearts with 4 of Diamonds.
  • Pair combination of 4 of Hearts with 4 of Clubs.
  • Pair combination of 4 of Clubs with 4 of Diamonds.
  • Pair combination of 4 of Spades with 4 of Hearts.
  • Pair combination of 4 of Spades with 4 of Diamonds.
  • Pair combination of 4 of Spades with 4 of Clubs.

There are 6 combinations for getting a pair of 4s out of 1,326 different combinations. Therefore, the calculation is 6 / 1,326, resulting in a 0.452% probability of getting a pair of 4s. Remember, the odds of getting a pair of 4s or any other pair are the same.

Probability of getting a premium hand in Poker

What is The Probability of Getting a Premium Pocket Card From The Dealer?

Everyone hopes to get a pair of aces, kings, or an A-K, premium hands that make playing poker and winning easier. Sometimes, it may feel like you aren't getting a premium hand for a while, affecting your game and leading to desperate moves. So, before losing patience, remember the statistics for getting a premium hand from the dealer:

  • The probability of getting a pair of aces is 0.452% (1 every 220 hands).
  • The probability of getting a pair of aces or kings increases to 0.905% (1 every 110 hands).
  • The probability of getting a pair of jacks or better is 1.8% (1 every 55 hands).
  • The probability of getting any pair is 5.88% (1 every 16 hands).
  • The probability of getting an ace-king suited is 0.302% (1 every 331 hands).
  • The probability of getting an ace-king suited or offsuit increases to 1.21% (1 every 82 hands).
  • The probability of getting a pair of 10s or two strong cards higher than 10 is 14.3% (1 every 6 hands).
  • The probability of getting 2-7 suited or offsuit is 1.21% (1 every 82 hands), the same probability as getting an ace-king.

What we have learned:

The probability of getting any pair is almost 6%, or 1 every 16 hands. There is no difference in the statistics between getting a pair of aces or a pair of 2s. According to the statistics, the odds of getting a premium hand, a pair of 10s or higher, is 1 every 6 hands (Odds of 14%).

So, play with patience and wait for your premium hands. Remember, the probability of getting a premium hand for you and your opponents is the same.

The odds getting pair of aces or kings
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What is the Probability that Our Opponents Hold a Stronger Hand than Us?

Now, we must learn statistics that show the probability of our opponents holding stronger cards than us. The odds may vary if we are playing against one player or a full table, so it's important to always remember the positions and actions of all your opponents before you act.

If we are dealt pocket Aces (A-A), the probability that our opponent(s) will hold:

A pair of Aces – Against one player, the odds are 0.0816% (1 every 1,224 hands), but at a full table, the odds increase to 0.651% (1 every 153 hands). The odds are low and should not significantly impact your decision-making, as you still hold the strongest hand in the poker hand rankings.

If we are dealt pocket Kings (K-K), the probability that our opponent(s) will hold:

A pair of Aces – Against one player, the odds are 0.490% (1 every 203 hands), but at a full table, the odds increase to 3.85% (1 every 25 hands). The odds are not high, but they are significant. After your bet, observe the actions of the players following you; if they do not re-raise, it is unlikely that your opponents hold aces.

If we are dealt pocket Queens (Q-Q), the probability that our opponent(s) will hold:

A pair of Aces or Kings – Against one player, the odds are 0.980% (1 every 101 hands), but at a full table, the odds increase to 7.57% (1 every 12 hands). The odds that your opponent has a stronger hand are significant, so pay attention to the actions of all players on the table.

If we are dealt pocket Jacks (J-J), the probability that our opponent(s) will hold:

A stronger pair than ours – Against one player, the odds are 1.47% (1 every 67 hands), but at a full table, the odds increase to 11.2% (1 every 8 hands). The odds are high, so it's recommended not to bet high and to be cautious about committing to the pot.

If we are dealt an Ace and a King, the probability that our opponent(s) will hold:

A pair of Aces or a pair of Kings – Against one player, the odds are 0.490% (1 every 203 hands), but at a full table, the odds increase to 3.85% (1 every 25 hands).

Learn how to play Ace King in all positions.

probability that our opponents hold stronger hand
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What is The Probability of Getting a Set, Straight or a Flush?

Now, let's consider our odds of strengthening our hand when the flop is revealed. Once we know our chances, it will be easier to decide whether to continue playing the hand or fold.

If we have a pair, what are our odds to get:

A set – 11.8% (1 every 7.5 hands).
Quads – 0.245% (1 every 407 hands).

The probability that a pair becomes a set is low, but it does exist. If you have a low pair, decide whether to keep playing or not based on the bets of the other players.

If we have two suited cards, what are our odds to get:

A flush flop – 0.842% (1 every 118 hands).
A flush draw on the flop – 10.9% (1 every 8.1 hands).

Remember, do not be overly focused on a pair of suited cards, as the odds of getting a flush on the flop are very low. The odds of flopping a flush draw are reasonable but may not justify paying any bet.

two suited cards what our odds to get flush

If we have connector cards (for example 9,10), what are our odds to get:

A straight flop – 1.31% (1 every 76 hands).
Flopping a straight draw – 9.71% (1 every 9.3 hands).

If we have one gapper cards (for example 8,10), what are our odds to get:

A straight flop – 0.980% (1 every 101 hands).
Flopping a straight draw – 7.67% (1 every 12 hands).

In these scenarios, it's not recommended to make any high-risk moves.

The probability of getting quads with two different cards is 0.0102% (1 every 9,799 hands).
The probability of getting a full house with two different cards is 0.0918% (1 every 1,088 hands).
The probability of getting a trio with two different cards is 1.35% (1 every 73 hands).
The probability of getting two pairs with two different cards is 2.02% (1 every 48 hands).

connector cards what our odds to get straight

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