Odds of getting a pocket pair in texas holdem

Who doesn’t love looking down at their cards and seeing high pocket pairs or that A-K looking right back at them? However, waiting for these premium hands can slow your game down to snail mode, as only 2.1% of hands are premium hands in poker.

The coin-flip

When a player had a pocket pair and another has two over-cards, this is essentially a coin-flip with regards to odds, as it’s pretty even. Odds change slightly if the over cards are suited, which means that the pair wins up to 54% if they’re suited and up to 57% if they’re not.

The illusion of suited cards

We see suited cards and automatically we want to play our 9-4 suited. Keep in mind that suited cards only improve your hand by 2.5%, so don’t be fooled again!

Flopping a pair

32.43% are the chances of making a pair on the flop. That doesn’t mean you should be playing any two cards, as the same odds apply for players with a higher hole cards.

On a flush draw!

Your chances of making a flush after the flop when on a flush draw are at 34.97%! It’s a great feeling when you’re on a flush draw on the flop, and one third of the times, you’ll make the hand!

Hitting the board

This term is used when you tell other players you’ve got something without revealing your hole cards. Your chances of hitting the board on the river are almost 50%.

“I couldn’t fold, I had an up & down straight draw on the flop!”

An up and down straight draw, or an open ended straight draw means that you have eight cards that can complete your straight. You’ll complete your straight 31.5% of the time on the river – and what a sweet feeling that is!

Runner runner!

This is when you need two specific cards to make the desired hand. The chances of that happening are ultra slim, but anything is possible. It’s a 0.3% chance of getting both your desired cards, but if you hit one, your chances increase to 4.55% of hitting the other.

Hitting two pair on the flop

2% is the statistic that you hit make two pairs on the flop, considering that you have different cards in the hole.

Beware of the walking sticks, a.k.a Pocket Jacks

As great as they might look in the hole, pocket jacks are dangerous. Why you ask? Because the chances of a higher card showing up on the flop is at 52%.

It’s all about the kicker

If your pair matches your opponent’s pair but your kicker is weaker, you will win 1/4 of the time, or 24%.

Two Pairs, Over-Pair

If you have a higher two pair than your opponent, your hand will win 80% of the time. With that in mind, be aware of the betting patterns and bet sizes, if you witness big raises, your two pair might be trapped.

Suited connectors

Suited connectors are a joy to look at. They give more options to the player holding suited connectors but they’re vulnerable to over-pairs, but not all suited connectors are worth playing. An over-pair will beat suited connectors around 80% of the time.

Pocket Pairs

The chances of being dealt pocket pairs are at 6%, or once every 17 hands! So be sure to have a clear strategy of how to play your pocket pairs.

Gutshot or inside straight draw

This is a hand not really worth chasing, as it only materialises 9% of the time. You will only have 4 cards that can make your straight, so be careful of how many chips you put in the pot.

“I love playing suited cards, in case I flop a flush.”

Flopping a flush has a very slim chance of happening, with 0.8%. While looking pretty, they are misleading and a cause of lost chips. That’s why it’s a general rule to fold 80-90% of hands when playing poker.

The power of a full house

When having two pair, the chances of making a full house are at 16.74% but when you have three of a kind, your odds of making a full house improve greatly, shooting up to 33.4%.

High vs Low cards

If you tried to make a play with the attempt of stealing the pot or are playing small ball poker (playing a wider set of starting hands) and up against a monster, like A-J, A-Q, or A-K, you’ll still have a 35% chance of winning the hand. 

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My approach would be to start with the case of holding KK against one player, where the chance of them holding a higher pair (in this case, exactly AA) is:

(4/50)*(3/49)

or

(4*3)/(50*49)

if you'd prefer. This comes to

(4*3)/(50*49)

From here, we can extrapolate for the number of players by simply multiplying the above by the number of players, so against 2 players, we are twice as likely to face AA (this ignore card removal, see below), and so we expect this

(4*3)/(50*49)

Similarly, we can extrapolate our chances of facing a larger pair when we ourselves hold a smaller pair by just multiplying by the number of larger pairs. When we hold

(4*3)/(50*49)

[chance of facing AA or KK when holding QQ]
= (8/50)*(3/49)
= 0.0098 (0.98%)

or by simply doubling our original result.

By this method, we can calculate all of the values:

/---------------------------------------------------------------------------------------\
|      |                                    Opponents                                   |
| Hand |    1   |    2   |    3   |    4   |    5   |    6   |    7   |    8   |    9   |
|------+--------+--------+--------+--------+--------+--------+--------+--------+--------|
|  KK  |  0.49% |  0.98% |  1.47% |  1.96% |  2.45% |  2.94% |  3.43% |  3.92% |  4.41% |
|  QQ  |  0.98% |  1.96% |  2.94% |  3.92% |  4.90% |  5.88% |  6.86% |  7.84% |  8.82% |
|  JJ  |  1.47% |  2.94% |  4.41% |  5.88% |  7.35% |  8.82% | 10.29% | 11.76% | 13.22% |
|  TT  |  1.96% |  3.92% |  5.88% |  7.84% |  9.80% | 11.76% | 13.71% | 15.67% | 17.63% |
|  99  |  2.45% |  4.90% |  7.35% |  9.80% | 12.24% | 14.69% | 17.14% | 19.59% | 22.04% |
|  88  |  2.94% |  5.88% |  8.82% | 11.76% | 14.69% | 17.63% | 20.57% | 23.51% | 26.45% |
|  77  |  3.43% |  6.86% | 10.29% | 13.71% | 17.14% | 20.57% | 24.00% | 27.43% | 30.86% |
|  66  |  3.92% |  7.84% | 11.76% | 15.67% | 19.59% | 23.51% | 27.43% | 31.35% | 35.27% |
|  55  |  4.41% |  8.82% | 13.22% | 17.63% | 22.04% | 26.45% | 30.86% | 35.27% | 39.67% |
|  44  |  4.90% |  9.80% | 14.69% | 19.59% | 24.49% | 29.39% | 34.29% | 39.18% | 44.08% |
|  33  |  5.39% | 10.78% | 16.16% | 21.55% | 26.94% | 32.33% | 37.71% | 43.10% | 48.49% |
|  22  |  5.88% | 11.76% | 17.63% | 23.51% | 29.39% | 35.27% | 41.14% | 47.02% | 52.90% |
\---------------------------------------------------------------------------------------/

However, this is not strictly the correct set of values, because the chances of a player making a pair are not mutually exclusive from the chances of another player in the same hand making a pair.

Consider for example a game with 9 players - the chances of a single player getting a pair (without any other information) is

(4*3)/(50*49)

[chance of making 44, 77 or KK] + [chance of making any other pair]
= [(6/46)*(1/45)] + [(40/46)*(3/45)]
= 0.0609 (6.09%)

We have a greater chance of making a pair because other players have already made pairs, which has polarised the deck with regards to pairs. Taking this to its logical conclusion, think about a situation at a 10-handed table where all 9 of your opponents have pairs (AA x 2, KK x 2, QQ x 2, JJ x 2 and TT). Now our chances of making a pair are:

[chance of making JJ+] + [chance of making TT] + [chance of making 22-99]
= [0] + [(2/34)*(1/33)] + [(32/34)*(3/33)]
= 0.0873 (8.73%)

Similarly, sometimes if we know that other players have not made pairs, our chances of making pairs also increases; for example, if we know 3 players hold

(4*3)/(50*49)

(4*3)/(50*49)

(4*3)/(50*49)

[chance of making 99+] + [chance of making 22-99]
= [(18/46)*(2/45)] + [(32/46)*(3/45)]
= 0.0638 (6.38%)

However, if lots of different ranks are known to be in other players' hands, our chances to make a pair will be decreased. For example, if we are in a 10-handed game where we know 6 of our opponents hold

(4*3)/(50*49)

(4*3)/(50*49)

(4*3)/(50*49)

[chance of facing AA or KK when holding QQ]
= (8/50)*(3/49)
= 0.0098 (0.98%)

[chance of facing AA or KK when holding QQ]
= (8/50)*(3/49)
= 0.0098 (0.98%)

[chance of facing AA or KK when holding QQ]
= (8/50)*(3/49)
= 0.0098 (0.98%)

[chance of making 22] + [chance of making 33+]
= [(4/40)*(3/39)] + [(36/40)*(2/39)]
= 0.0538 (5.38%)

For this reason, my simplified approach above is not 100% accurate, because it is not correct to say that if the chance of facing an overpair with KK against one opponent is 0.49%, then it must be double this chance against two opponents - this is flawed because the chance of that second player having a pair is affected by what the first player held. At least that's my understanding.

In any case, the numbers above will certainly be close enough to the "real" figures to be useful to you, and hopefully this answer has helped show you how these numbers are calculated.

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