Odds Of Getting Pocket Aces

In 10mil sets of 3 hands you should get AA 3 times in a row at some point, and for that matter 22 3 times in a row, and it is the same odds to get AA followed by KK followed by 22. Your way is correct in that after the first hand you ask what are the odds that my next two hands will be AA also.

1. Odds Of Getting Pocket Aces Three Times In A Row
2. Odds Of Getting Pocket Aces

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As a poker beginner, you might be already envisioning the money made when you look down at your cards and see pocket aces. While it is true that AA will win more often than not, you still need to understand you will not win every time. So how often can you expect to win with aces?

1. The odds of being dealt any specific pocket pair, such as aces, is 220-to-1 but the odds of being dealt a pair of aces and then someone at the same table being dealt pocket kings is slightly less as the two aces have been removed from the 52-card deck. This means that the odds of someone being dealt a pair of kings when you have aces is 205-to-1.
2. Pre-Flop Poker Probability - 169 Distinct Starting Hands. Now we are getting somewhere. Next we can use the numbers above to work out what the probability of being dealt AA, KK (or in fact any pair) is. This is a case of taking the total number of possible hands and then seeing how many of these are your pair. We will take a pair of Kings as an.

Pocket aces win 85% of the time against one opponent holding the random hand in Texas Holdem. Although the percentage varies greatly depending on the opponent’s hand and the number of opponents. 85% is the odds to win when AA goes all-in preflop. Odds change on later streets.

It might feel unfair when we loose holding the best hand but keep in mind if we are not 100% to win, we will lose sometimes.

Chances of winning with pocket aces preflop

Every time you get dealt a hand in Texas Holdem your odds of getting pocket aces are 1/221, which is roughly 0.9%.

First, let’s check how often do pocket aces win preflop. For better representation, I will take a sample of 100 examples. So next 100 times you receive an AA, 15 times you will lose and win 85 times.

We should not forget about variance. If we experience negative variance (if we are unlucky), then we may lose 30 times and win 70 times only. On the other hand, if we get a positive side of variance (if we are lucky), we could win 95 out of 100 times!

Pocket aces odds for winning when all-in preflop change depending on which hand we are up against. See how well does AA against specific hands in terms of poker percentages (chance to win). For new players to poker, let me elaborate on the table below.

• 72o means any combination of 7 and 2, o after means the hand is off-suit (meaning that suits on 7 and 2 don’t match)
• 22+ means any pocket pair of 2 and higher (which is all pocket pairs from 22 to and including AA)
• T+ means any card T and higher (T, J, Q, K, A)
• JTs stands for JT suites, which means that suits of J and T match
• broadway hands are the hands that include any combination of hands where the lowest card is T or higher (TQ, TJ, AA, KK, TT, AT)

The best hand against aces preflop is 76s or 87s. They both win 22.5% of the time, so still a big underdog, but it is the best you can hope for.

How odds change against more players

The odds of winning reduce if more players are involved in the hand. Against two opponents holding random hands, AA wins 73.5% of the time. Against three, the odds of winning are now merely 64%.

The tool I am using to show you the % is called Equilab. And you can download it for free from Pokerstrategy’s website. Click on Poker Tools in the menu, the software and scroll down to the end where it says Free training software. Make sure you download the one for Hold’em (it’s written only Equilab).

Chances of winning with AA on later streets

In poker, there is more than just preflop. We know four streets. Those are preflop, flop, turn, and river. It’s easy to calculate your odds to win preflop. When it comes to postflop, things start to get more complex. There are many possible flops. In fact 22100 possible flops. Now some of those could be grouped, but that would still leave us with 1755 different scenarios of flops. On turn and river, that number only increases.

So I can’t show you the pocket aces win percentage against those. But I encourage you to download yourself Equilab I linked to above and play around with different flops, turns, and rivers. As a general rule of thumb, more players, the more cautious you need to be. It will be more likely at least one player has something good.

Chances of winning pre-flop with other hands

Pocket aces are the strongest hand in poker. But we shouldn’t ignore others. The second strongest hand in Hold’em are pocket kings followed by pocket queens.

Chances to win with pocket kings

From the table, we can notice that equity (% to win) with KK against random hand preflop is a bit different for some cards and pretty much the same for others. The biggest difference comes from broadway hands and 22+. The difference is because 22+ and broadways also include AA and that crushes us (AA is 82% to win against KK).

KK has 78.5% chance to win preflop against a random hand. So if our opponent holds a random hand they will still win roughly 1 out of five times. 21.5% of the time to be exact.

Important note. In scenarios above for AA and KK, where I compared them to random holding, I assumed the opponent has a random hand he is willing to go all-in with preflop. In real poker games, opponents will not be going all-in with random hands.

Lets now check the case for QQ

Odds Of Getting Pocket Aces Three Times In A Row

Same as for KK our equity with QQ now falls lower, when we are up against broadway hands and pocket pairs.

Lastly let’s check how we do against those hands with AK as many players like to overplay AK.

Many beginner players are shocked when they see how poorly AK does. That’swhere seasoned poker players will make a lot of money from beginners. Any experienced player knows newbie often overplays hands that look nice but don’t do that good against stronger holdings. With QQ our equity was a lot higher for all of the scenarios. Even against the worst combination of 72o, AK is supposed to win only 2 out of 3 times. This means you will lose 32 times and win 62 times. And that is if you run just average. And this if there would be no variance involved.

I will go deeper into the strategy in another article as it is a massive topic on its own. For now, know when the opponent goes all-in preflop, he will have a decent hand unless they are aggressive players willing to bluff their stack. While some players play tighter (they don’t play many hands) than others a good rule of thumb is pocket kings and aces are always strong enough to get all the money in the middle preflop. With QQ we should be good against the majority, but the tightest people. When it comes to AK, it depends on the opponent we are up against. Often it comes down to personal playing style. I prefer to play my AK a bit more passively, and I will not be blindly throwing my stack in the middle to gamble for what is around 50% to win against what opponent wants to go with all-in.

Conclusion

While pocket aces are a definite favorite against any other hand preflop, it doesn’t mean it’s guaranteed to win. Odds change significantly if more players are involved, but at the end of the day, if we get all the money in preflop, we should be happy. In the worst-case scenario, we will have 77.5% to win. When we have either KK or QQ we should still do good. But with AK we need to start being cautiouspreflop.

Related Links

• Ace King vs Pocket Jacks: Winrate and Examples
  
• Odds of Winning With Pocket Kings: Including the Winrate
  

The main underpinning of poker is math – it is essential. For every decision you make, while factors such as psychology have a part to play, math is the key element.

In this lesson we’re going to give an overview of probability and how it relates to poker. This will include the probability of being dealt certain hands and how often they’re likely to win. We’ll also cover how to calculating your odds and outs, in addition to introducing you to the concept of pot odds. And finally we’ll take a look at how an understanding of the math will help you to remain emotional stable at the poker table and why you should focus on decisions, not results.

What is Probability?

Probability is the branch of mathematics that deals with the likelihood that one outcome or another will occur. For instance, a coin flip has two possible outcomes: heads or tails. The probability that a flipped coin will land heads is 50% (one outcome out of the two); the same goes for tails.

Probability and Cards

When dealing with a deck of cards the number of possible outcomes is clearly much greater than the coin example. Each poker deck has fifty-two cards, each designated by one of four suits (clubs, diamonds, hearts and spades) and one of thirteen ranks (the numbers two through ten, Jack, Queen, King, and Ace). Therefore, the odds of getting any Ace as your first card are 1 in 13 (7.7%), while the odds of getting any spade as your first card are 1 in 4 (25%).

Unlike coins, cards are said to have “memory”: every card dealt changes the makeup of the deck. For example, if you receive an Ace as your first card, only three other Aces are left among the remaining fifty-one cards. Therefore, the odds of receiving another Ace are 3 in 51 (5.9%), much less than the odds were before you received the first Ace.

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Pre-flop Probabilities: Pocket Pairs

In order to find the odds of getting dealt a pair of Aces, we multiply the probabilities of receiving each card:

(4/52) x (3/51) = (12/2652) = (1/221) ≈ 0.45%.

To put this in perspective, if you’re playing poker at your local casino and are dealt 30 hands per hour, you can expect to receive pocket Aces an average of once every 7.5 hours.

The odds of receiving any of the thirteen possible pocket pairs (twos up to Aces) is:

(13/221) = (1/17) ≈ 5.9%.

In contrast, you can expect to receive any pocket pair once every 35 minutes on average.

Pre-Flop Probabilities: Hand vs. Hand

Players don’t play poker in a vacuum; each player’s hand must measure up against his opponent’s, especially if a player goes all-in before the flop.

Here are some sample probabilities for most pre-flop situations:

Post-Flop Probabilities: Improving Your Hand

Now let’s look at the chances of certain events occurring when playing certain starting hands. The following table lists some interesting and valuable hold’em math:

Many beginners to poker overvalue certain starting hands, such as suited cards. As you can see, suited cards don’t make flushes very often. Likewise, pairs only make a set on the flop 12% of the time, which is why small pairs are not always profitable.

PDF Chart

We have created a poker math and probability PDF chart (link opens in a new window) which lists a variety of probabilities and odds for many of the common events in Texas hold ‘em. This chart includes the two tables above in addition to various starting hand probabilities and common pre-flop match-ups. You’ll need to have Adobe Acrobat installed to be able to view the chart, but this is freely installed on most computers by default. We recommend you print the chart and use it as a source of reference.

Odds and Outs

If you do see a flop, you will also need to know what the odds are of either you or your opponent improving a hand. In poker terminology, an “out” is any card that will improve a player’s hand after the flop.

One common occurrence is when a player holds two suited cards and two cards of the same suit appear on the flop. The player has four cards to a flush and needs one of the remaining nine cards of that suit to complete the hand. In the case of a “four-flush”, the player has nine “outs” to make his flush.

A useful shortcut to calculating the odds of completing a hand from a number of outs is the “rule of four and two”. The player counts the number of cards that will improve his hand, and then multiplies that number by four to calculate his probability of catching that card on either the turn or the river. If the player misses his draw on the turn, he multiplies his outs by two to find his probability of filling his hand on the river.

In the example of the four-flush, the player’s probability of filling the flush is approximately 36% after the flop (9 outs x 4) and 18% after the turn (9 outs x 2).

Pot Odds

Odds Of Getting Pocket Aces

Another important concept in calculating odds and probabilities is pot odds. Pot odds are the proportion of the next bet in relation to the size of the pot.

For instance, if the pot is $90 and the player must call a $10 bet to continue playing the hand, he is getting 9 to 1 (90 to 10) pot odds. If he calls, the new pot is now $100 and his $10 call makes up 10% of the new pot.

Experienced players compare the pot odds to the odds of improving their hand. If the pot odds are higher than the odds of improving the hand, the expert player will call the bet; if not, the player will fold. This calculation ties into the concept of expected value, which we will explore in a later lesson.

Bad Beats

A “bad beat” happens when a player completes a hand that started out with a very low probability of success. Experts in probability understand the idea that, just because an event is highly unlikely, the low likelihood does not make it completely impossible.

A measure of a player’s experience and maturity is how he handles bad beats. In fact, many experienced poker players subscribe to the idea that bad beats are the reason that many inferior players stay in the game. Bad poker players often mistake their good fortune for skill and continue to make the same mistakes, which the more capable players use against them.

Decisions, Not Results

One of the most important reasons that novice players should understand how probability functions at the poker table is so that they can make the best decisions during a hand. While fluctuations in probability (luck) will happen from hand to hand, the best poker players understand that skill, discipline and patience are the keys to success at the tables.

A big part of strong decision making is understanding how often you should be betting, raising, and applying pressure.
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This 7+ hour course gives you applicable rules for continuation betting, barreling, raising, and easy ratios so that you ALWAYS have the right number of bluffing combos. Take the guesswork out of your strategy, and begin playing like the top-1%.

Conclusion

A strong knowledge of poker math and probabilities will help you adjust your strategies and tactics during the game, as well as giving you reasonable expectations of potential outcomes and the emotional stability to keep playing intelligent, aggressive poker.

Remember that the foundation upon which to build an imposing knowledge of hold’em starts and ends with the math. I’ll end this lesson by simply saying…. the math is essential.

By Gerald Hanks

Gerald Hanks is from Houston Texas, and has been playing poker since 2002. He has played cash games and no-limit hold’em tournaments at live venues all over the United States.