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, a pair of kings or an A-K, etc. All poker players are also calculating the odds of getting a particular out card on the flop, turn, or river.

In this article, we bring you important statistical calculations.

Why is it important to know the odds? The ability to estimate what the odds are of getting the card you need or what the odds are that your opponents hold certain cards will help you to make better decisions and win more hands. Always use statistics to substantiate your decisions.

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

For example:

We want to calculate the odds of getting a pair 4-4, first, we will 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.

We have 6 combinations for getting a pair of 4s out of 1,326 different combinations so the calculation is 6/1326 and the result is 0.452% for getting a pair of 4s. Remember, the odds of getting a pair of 4s or any other pair is equal).

Probability of getting a premium hand in Poker

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

Everyone wants to get a pair of aces, pair of kings, or an A-K, premium hands that, if acquired, makes it easier to play poker and win. Sometimes it feels like you aren't getting a premium hand for a while and it affects your game, resulting in reckless moves out of desperation. So before you lose 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 and up 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 suit is 0.302% (1 every 331 hands).
• The probability of getting an ace-king suit or off suit increases to 1.21% (1 every 82 hands).
• The probability of getting a pair of 10 or two strong cards over 10 is 14.3% (1 every 6 hands).
• The probability of getting 2-7 suits or off-suit 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%, 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, we are supposed to get 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 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 the actions of all your opponents before you act.

If we got pair of Aces, the probability that our opponent(s) will hold:

Pair of Aces Against one player the odds are 0.0816% (1 every 1,224 hands) but, on a full table the odds increase to 0.651% (1 every 153 hands). The odds are low, and it shouldn't interfere with your decision-making. You still hold the strongest hand in the poker hand rankings.

If we got pair of Kings, the probability that our opponent(s) will hold:

Pair of Aces Against one player the odds are 0.490% (1 every 203 hands) but in a full table, the odds increase to 3.85% (1 every 25 hands). The odds are not high but are significant. After your bet, follow the actions of the players following you, if they didn't do a re-raise most likely your opponents are not holding aces.

If we got pair of Queens, the probability that our opponent(s) will hold:

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

If we got pair of Jacks, the probability that our opponent(s) will hold:

Stronger pair than ours Against one player the odds are 1.47% (1 every 67 hands) but in 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 committed to the pot.

If we got an Ace and a king, the probability that our opponent(s) will hold:

Pair of aces or a pair of kings Against one player the odds are 0.490% (1 every 203 hands) but on a full table the odds rise 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 we'll see what our odds are to strengthen our hand when the flop is revealed. Once we know our chances, it will be easier for us to decide whether to continue playing the hand or fold.

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

  • Set 11.8% (1 every 7.5 hands).
  • Quad 0.245% (1 every 407 hands).

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

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

  • Flush flop 0.842% (1 every 118).
  • Flopping a flush draw 10.9% (1 every 8.1 hands).

Remember, do not be blinded by a pair of suit cards because the odds of getting a flush on the flop are very low, the odds of flopping a flush draw are reasonable but do not justify paying any bet.

two suited cards what our odds to get flush

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

  • Straight flop 1.31% (1 every 76 hands).
  • Flopping straight draw 9.71% (1 every 9.3 hands).

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

  • Straight flop 0.980% (1 every 101 hands).
  • Flopping straight draw 7.67% (1 every 12 hands).

For the scenarios mentioned below, It's not recommended to make any high-risk moves.

  • The probability of getting a quad 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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