## Those Pesky Aces Got you Blue?

Pocket Aces Racing LLC is very excited to announce the newest member of our stableSamurai’sfirstlady. This mare is in foal to Exaggerator and will comprise our 2021 breeding partnership. This seven-year-old mare is a daughter of First Samurai out of Leinster Lady, by E Dubai. She is a very attractive. 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.

1. With a 3/4 pot bet, you have 7:3 pot odds and need +30% equity to call. With a pot sized bet, you get 2:1 pot odds and need +33% equity to call. With a 2x pot bet, it's 3:2 pot odds and you need 40% equity to call. So, say your opponent has a hand lesser than a flush, like two pair. They bet the pot size on the flop, you may elect to call.
2. The odds of being dealt with any specific pocket pair when playing against a single player, such as aces, is 220:1, with the odds of someone else being dealt pocket kings being significantly lower at 205:1. When playing against nine other opponents, the odds become around 21.8:1, or 1 in 22.8.
3. 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.

There’s a question for the ages, in poker terms. The short answer is “Hah!” but the longer and more careful answer is, “It depends on the game and conditions.”

Slow-playing a pair of pocket aces, particularly under the gun, is often an invitation to trouble, and as you grow in experience at the game, you will invariably run up against a player who never limps under the gun, always raising if he’s going to play – except in the rare case he has pocket aces. The idea, of course, is that he wants someone to raise from late position, so he can come back over the top with a hefty three-bet in an attempt to get lots of chips into the pot before the flop.

Once you encounter this particular breed of player and see this trait, you’ll be able to limp behind with pocket queens, toss them away if other action compels you to, and toss them away for cheap after the flop if you don’t connect for the set. The lesson: Don’t be that type of player, and make your pocket aces so obvious by your position bets.

That said, there are some general rules you can adhere to if that 1-in-229-hand occurrence comes up, and you find yourself staring down at pocket rockets. The general rule is to play them a little bit faster then you might otherwise believe. It’s easy to lose a lot of money with aces, perhaps even easier than it is to win a lot of money with them. So with that in mind:

### First Rule, Don’t Limp

Don’t limp with your aces if you are at a soft, passive (often lower-stakes) table that often sees four or five or six players seeing a cheap flop. Pocket aces play very poorly against a large number of competing hands, and even though they’re a prohibitive favorite against any other single hand, they can often be a large dog against a collection of other hands. Don’t forget it’s the trash that connects to the flop that stays around and plays; the trash that misses folds and disappears from the hand. Coordinated flops like 9-10-J are absolute death for pocket aces in a multi-way pot. Throw them away and lick your wounds quietly.

### Don’t Always 3 Bet

Conversely, don’t always make the automatic three-bet in poker with pocket aces before the flop. When holding pocket aces, you want to limit the field, not destroy it. If there’s a healthy raise pre-flop by an aggressive player, and your image is loose, go ahead and make the three-bet raise and mix it up at will. But another ploy that works well against tighter, more cautious players is called “second-hand low”. This is when an early-position player makes a healthy opening raise – perhaps \$12 or \$15 in a \$1/2 cash game, and you just smooth-call from middle position. This gives a late-position player or one of the blinds the opportunity to look at a half-good hand like A-K and make a three-bet squeeze raise, which should have you dancing in your seat. Don’t do this too often or become too devoted to other subtle tricks, lest you succumb to “fancy play syndrome”, but the occasional subterfuge will improve your game and profit margin.

Use your pocket aces to deny proper pot odds to your opponents. Whether in cash games or tournaments, a situation often arises where you can size your bets in such a way as to ensure a single opponent does not have the proper odds to continue in the hand, even though he may think he does. Imagine a cash-game scenario, playing something as simple as \$1/2, where you and your opponent in a hand both have \$120 in chips. He opens to perhaps \$10, and you, holding pocket aces here, can go ahead and put in an undersized reraise to perhaps \$25 to induce the call. While he is rightly guessing that his \$15 call is worth it when there’s \$38 or more in the pot and your remaining \$95 to potentially still be won, you have the knowledge that your aces are between 3.6:1 and 6:1 favorites heads-up before the flop against any other hand.

The likeliest hand to crack pocket aces is 10-9 suited, but the aces will still win 77% of the time. Play your aces just guarded enough against possible sets and flops that make “ace-cracker” hands work, but most of the time, following up with a sizeable post-flop bet is again the odds-on play. Often, your opponent will flop a flush or straight draw, and you must make it unprofitable for him to pursue that draw – even though many players can’t resist the temptation and will call against the odds anyway. These players are your long-term victims, even if they are paradoxically the ones most likely to crack your aces in any given hand. Such is the nature of poker. We always remember the aces we lose with, but rarely the ones we win with!

### Aces and Drawing Hands, The Crackers

Beware drawing hands in deep-stack situations. A corollary to the above. No matter how pretty your pocket aces look, pocket aces don’t beat straights and flushes. You must drive drawing hands out of the hand, and the only way to do that is to protect your aces with a large bet. Pre-flop that means limiting the field; post-flop that means putting in raises of at least three-quarters of the pot on each round to make sure your opponent doesn’t have the right pot odds to chase those eight- and nine-outers.

### Hitting a Set of Aces

If you’ve flopped a set of aces, there is always a potential straight draw. This might sound odd, but a set of kings is often a far safer hand to slow-play after the flop than is a set of aces. Imagine yourself with a pair of pocket aces, and envision a flop of any three non-paired cards that include an ace. No matter what the other two non-ace cards are, if you let your opponents see the turn for free, a turn card that doesn’t pair the board will always put some sort of straight in play. It might be a highly unlikely holding, such as the big blind holding 4-7 and the board through the turn showing A-5-J-8, but if you’ve let this player see all these cards for free and a 6 comes off on the river (roughly a 1-in-11 chance), you’ve only yourself to blame. You have to charge them something for the dream of making that hand.

No worthy bad beat story ever started with, “I limped with pocket aces….” Enough said.

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.

## Odds Of Pocket Aces Vs Kings

### 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

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.

## Odds Of Pocket Aces Vs Pocket Kings

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. Net entertainment blackjack.

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.

## Odds Of Pocket Aces Three Times In A Row

A big part of strong decision making is understanding how often you should be betting, raising, and applying pressure.
The good news is that there is a simple system, with powerful shortcuts & rules, that you can begin using this week. Rooted in GTO, but simplified so that you can implement it at the tables, The One Percent gives you the ultimate gameplan.

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.

## Odds Of Getting Pocket Aces Two Hands In A Row

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.

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