Important Poker Probabilities

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Poker is a popular card game that combines elements of chance and strategy. There are various styles of poker, all of which share an objective of presenting the least probable or highest-scoring hand. A poker hand is usually a configuration of five cards depending on the variant, either held entirely by a player or drawn partly from a number of shared, community cards. Players bet on their hands in a number of rounds as cards are drawn, employing various mathematical and intuitive strategies in an attempt to better opponents.

How Important Are Your Texas Holdem Poker Hand Pot Odds? Your pot odds inform many of your decisions in Texas Hold'em poker. Of course, but there are other factors as well. It is crucial to study your opponents and observe their tendencies to better appreciate the quality of their bets. Check-raising is an important element of poker, but you must learn how to best implement this strategy if you want to reap its rewards. How to Print Money with Your Flop C-Bets In and Out of Position Discover the best situations for continuation betting while in and out of position. Important poker charts that every player must know. Most poker lovers use poker charts to assist them in playing this game. So, we made a list of the most important poker charts every poker player must know about. Poker means getting the math right for which having a poker chart is good, easier representation. Pot odds, which is the ratio of making or calling a bet compared to the size of the pot, is one of the most essential concepts you need to know to play winning poker. In this reference article, I'd like to explain the concept of pot odds including what it is, how to calculate it, and why it's important to you as a smart poker player. Figuring pot odds (the pot is all the money that has been bet for a single game) is one of the most misunderstood and misused concepts for beginning poker players. In this section, simple and straightforward computations are used.

Given the game's many different forms and various dynamics, poker strategy becomes a complex subject. This article attempts to introduce only the basic strategy concepts.

The fundamental theorem of poker[edit]

The fundamental theorem of poker, introduced by David Sklansky, states: Every time you play your hand the way you would if you could see your opponents' cards, you gain, and every time your opponents play their cards differently from the way they would play them if they could see your cards, you gain.^[1] This theorem is the foundation for many poker strategy topics. For example, bluffing and slow-playing (explained below) are examples of using deception to induce your opponents to play differently from how they would if they could see your cards. There are some exceptions to the fundamental theorem in certain multi-way pot situations, as described in Morton's theorem.

Pot odds, implied odds and poker probabilities[edit]

The relationship between pot odds and odds of winning is one of the most important concepts in poker strategy. Pot odds are the ratio of the size of the pot to the size of the bet required to stay in the pot.^[1] For example, if a player must call $10 for a chance to win a $40 pot (not including their $10 call), their pot odds are 4-to-1. To have a positive expectation, a player's odds of winning must be better than their pot odds. If the player's odds of winning are also 4-to-1 (20% chance of winning), their expected return is to break even (on average, losing four times and winning once for every five times they play such a pot).

Implied odds is a more complicated concept, though related to pot odds. The implied odds on a hand are based not on the money currently in the pot, but on the expected size of the pot at the end of the hand. When facing an even money situation (like the one described in the previous paragraph) and holding a strong drawing hand (say a Four flush) a skilled player will consider calling a bet or even opening based on their implied odds. This is particularly true in multi-way pots, where it is likely that one or more opponents will call all the way to showdown.

Deception[edit]

By employing deception, a poker player hopes to induce their opponent(s) to act differently from how they would if they could see their cards. David Sklansky has argued that winning at poker is often decided by how much one player can force another to change his/her style while successfully maintaining their own strategy.^[2]Bluffing is a form of deception where players bet strongly on a weak hand to induce opponents to fold superior hands. Related is the semi-bluff, in which a player who does not have a strong hand, but has a chance to improve it to a strong hand in later rounds, bets strongly on the hand in the hopes of inducing other players with weaker 'made' hands to fold. Slow-playing is deceptive play in poker that is roughly the opposite of bluffing: checking or betting weakly with a strong holding, attempting to induce other players with weaker hands to call or raise the bet instead of folding, to increase the payout.

Position[edit]

Position refers to the order in which players are seated around the table and the strategic consequences of this. Generally, players in earlier position (who have to act first) need stronger hands to bet/raise or call than players in later position. For example, if there are five opponents yet to act behind a player, there is a greater chance one of the yet to act opponents will have a better hand than if there were only one opponent yet to act. Being in late position is an advantage because a player gets to see how their opponents in earlier position act (which provides the player more information about their hands than they have about his). This information, coupled with a low bet to a late player, may allow the player to 'limp in' with a weaker hand when they would have folded the same hand if they'd had to act earlier. Position is one of the most vital elements to understand in order to be a long-term winning player. As a player's position improves, so too does the range of cards with which they can profitably enter a hand. Conversely this commonly held knowledge can be used to an intelligent poker player's advantage. If playing against observant opponents, then a raise with any two cards can 'steal the blinds,' if executed against passive players at the right time.

Reasons to raise[edit]

Unlike calling, raising has an extra way to win: opponents may fold. An opening bet may be considered a raise from a strategy perspective. David Sklansky gives seven reasons for raising, summarized below.^[1]

• To get more money in the pot when a player has the best hand: If a player has the best hand, raising for value enables them to win a bigger pot.
• To drive out opponents when a player has the best hand: If a player has a made hand, raising may protect their hand by driving out opponents with drawing hands who may otherwise improve to a better hand.
• To bluff A player raises with an inferior or 'trash' hand attempts to deceive other players about the strength of their hand, and hopefully induce a better hand to fold.
• To semi-bluff A player with a drawing hand may raise both to bluff and for value. While technically still a bluff, as the player may not end up with a made hand and is primarily trying to drive out players, the player still has the opportunity to make his or her hand and win the pot if the bluff is called.
• To block Players on drawing hands may put out a 'blocking bet' against players who are likely to bet when checked to, but unlikely to raise when bet into. This is a small bet made on a drawing hand to lessen the likelihood of having to call a larger bet from a player in late position.
• To get a free card: If a player raises with a drawing hand, their opponent may call the bet and check to them on the next betting round, giving them a chance to get a free card to improve their hand.
• To gain information: If a player raises with an uncertain hand, they gain information about the strength of their opponent's hand if they are called. Players may use an opening bet on a later betting round (probe or continuation bets) to gain information by being called or raised (or may win the pot immediately).
• To drive out worse hands when a player's own hand may be second best: A combination protection and probe raise, a player with a strong hand but not the 'nuts' (the hole cards that make the best possible hand given the current face-up cards) may raise, both to induce drawing hands that may improve to the 'nut hand' to fold, while also testing to see if another player has the 'nuts'.
• To drive out better hands when a drawing hand bets: If an opponent with an apparent drawing hand has bet before the player to act, if the player raises, opponents behind them who may have a better hand may fold rather than call two bets 'cold'. This is a form of isolation play, and has elements of blocking and protection.

Reasons to call[edit]

There are several reasons for calling a bet or raise, summarized below.

• To see more cards: With a drawing hand, a player may be receiving the correct pot odds with the call to see more cards.
• To limit loss in equity: Calling may be appropriate when a player has adequate pot odds to call but will lose equity on additional money contributed to the pot with a raise.
• To avoid a re-raise: Only calling (and not raising) denies the original bettor the option of re-raising. However, this is only completely safe in case the player is last to act (i.e. 'closing the action').
• To conceal the strength of a player's hand: If a player has a very strong hand, they might smooth call on an early betting round to avoid giving away the strength of their hand on the hope of getting more money into the pot in later betting rounds.
• To manipulate pot odds: By calling (not raising), a player offers any opponents yet to act behind them more favorable pot odds to also call. For example, if a player has a very strong hand, a smooth call may encourage opponents behind them to overcall or even raise, building the pot. Particularly in limit games, building the pot in an earlier betting round may induce opponents to call future bets in later betting rounds because of the pot odds they will be receiving.
• To set up a bluff on a later betting round: Sometimes referred to as a long-ball bluff, calling on an earlier betting round can set up a bluff (or semi-bluff) on a later betting round. For instance, a player with a strong initial hand may call instead of raise to see the flop cheaply. That flop may not benefit the player, but the player may still have many 'outs' (cards left to deal that could make a strong hand), or even if the odds are slim they can try to bluff. By raising, this scenario may appear to an opponent like a player who has 'limped in' with a weak initial hand, but after the flop now has a strong made or drawing hand. A recent online term for 'long-ball bluffing' is floating.^[3]

Gap concept[edit]

The gap concept states that a player needs a better hand to play against someone who has already opened (or raised) the betting than he would need to open himself.^[4] The gap concept reflects that players prefer to avoid confrontations with other players who have already indicated strength, and that calling only has one way to win (by having the best hand), whereas opening may also win immediately if your opponent(s) fold.

Sandwich effect[edit]

Related to the gap effect, the sandwich effect states that a player needs a stronger hand to stay in a pot when there are opponents yet to act behind him.^[3] Because the player does not know how many opponents will be involved in the pot or whether he will have to call a re-raise, he does not know what his effective pot odds actually are. Therefore, a stronger hand is desired as compensation for this uncertainty. A squeeze play exploits this principle.

Loose/tight play[edit]

Loose players play relatively more hands and tend to continue with weaker hands; hence they do not often fold. Tight players play relatively fewer hands and tend not to continue with weaker hands; hence they often fold. The following concepts are applicable in loose games (and their inverse in tight games):^[1]

Reasons to raise[edit]

Unlike calling, raising has an extra way to win: opponents may fold. An opening bet may be considered a raise from a strategy perspective. David Sklansky gives seven reasons for raising, summarized below.^[1]

• To get more money in the pot when a player has the best hand: If a player has the best hand, raising for value enables them to win a bigger pot.
• To drive out opponents when a player has the best hand: If a player has a made hand, raising may protect their hand by driving out opponents with drawing hands who may otherwise improve to a better hand.
• To bluff A player raises with an inferior or 'trash' hand attempts to deceive other players about the strength of their hand, and hopefully induce a better hand to fold.
• To semi-bluff A player with a drawing hand may raise both to bluff and for value. While technically still a bluff, as the player may not end up with a made hand and is primarily trying to drive out players, the player still has the opportunity to make his or her hand and win the pot if the bluff is called.
• To block Players on drawing hands may put out a 'blocking bet' against players who are likely to bet when checked to, but unlikely to raise when bet into. This is a small bet made on a drawing hand to lessen the likelihood of having to call a larger bet from a player in late position.
• To get a free card: If a player raises with a drawing hand, their opponent may call the bet and check to them on the next betting round, giving them a chance to get a free card to improve their hand.
• To gain information: If a player raises with an uncertain hand, they gain information about the strength of their opponent's hand if they are called. Players may use an opening bet on a later betting round (probe or continuation bets) to gain information by being called or raised (or may win the pot immediately).
• To drive out worse hands when a player's own hand may be second best: A combination protection and probe raise, a player with a strong hand but not the 'nuts' (the hole cards that make the best possible hand given the current face-up cards) may raise, both to induce drawing hands that may improve to the 'nut hand' to fold, while also testing to see if another player has the 'nuts'.
• To drive out better hands when a drawing hand bets: If an opponent with an apparent drawing hand has bet before the player to act, if the player raises, opponents behind them who may have a better hand may fold rather than call two bets 'cold'. This is a form of isolation play, and has elements of blocking and protection.

Reasons to call[edit]

There are several reasons for calling a bet or raise, summarized below.

• To see more cards: With a drawing hand, a player may be receiving the correct pot odds with the call to see more cards.
• To limit loss in equity: Calling may be appropriate when a player has adequate pot odds to call but will lose equity on additional money contributed to the pot with a raise.
• To avoid a re-raise: Only calling (and not raising) denies the original bettor the option of re-raising. However, this is only completely safe in case the player is last to act (i.e. 'closing the action').
• To conceal the strength of a player's hand: If a player has a very strong hand, they might smooth call on an early betting round to avoid giving away the strength of their hand on the hope of getting more money into the pot in later betting rounds.
• To manipulate pot odds: By calling (not raising), a player offers any opponents yet to act behind them more favorable pot odds to also call. For example, if a player has a very strong hand, a smooth call may encourage opponents behind them to overcall or even raise, building the pot. Particularly in limit games, building the pot in an earlier betting round may induce opponents to call future bets in later betting rounds because of the pot odds they will be receiving.
• To set up a bluff on a later betting round: Sometimes referred to as a long-ball bluff, calling on an earlier betting round can set up a bluff (or semi-bluff) on a later betting round. For instance, a player with a strong initial hand may call instead of raise to see the flop cheaply. That flop may not benefit the player, but the player may still have many 'outs' (cards left to deal that could make a strong hand), or even if the odds are slim they can try to bluff. By raising, this scenario may appear to an opponent like a player who has 'limped in' with a weak initial hand, but after the flop now has a strong made or drawing hand. A recent online term for 'long-ball bluffing' is floating.^[3]

Gap concept[edit]

The gap concept states that a player needs a better hand to play against someone who has already opened (or raised) the betting than he would need to open himself.^[4] The gap concept reflects that players prefer to avoid confrontations with other players who have already indicated strength, and that calling only has one way to win (by having the best hand), whereas opening may also win immediately if your opponent(s) fold.

Sandwich effect[edit]

Related to the gap effect, the sandwich effect states that a player needs a stronger hand to stay in a pot when there are opponents yet to act behind him.^[3] Because the player does not know how many opponents will be involved in the pot or whether he will have to call a re-raise, he does not know what his effective pot odds actually are. Therefore, a stronger hand is desired as compensation for this uncertainty. A squeeze play exploits this principle.

Loose/tight play[edit]

Loose players play relatively more hands and tend to continue with weaker hands; hence they do not often fold. Tight players play relatively fewer hands and tend not to continue with weaker hands; hence they often fold. The following concepts are applicable in loose games (and their inverse in tight games):^[1]

• Bluffs and semi-bluffs are less effective because loose opponents are less likely to fold.
• Requirements for continuing with made hands may be lower because loose players may also be playing lower value hands.
• Drawing to incomplete hands, like flushes, tends to be more valuable as draws will often get favorable pot odds and a stronger hand (rather than merely one pair) is often required to win in multi-way pots.

Important Poker Probabilities Rules

Aggressive/passive play[edit]

Aggressive play refers to betting and raising. Passive play refers to checking and calling. Unless passive play is being used deceptively as mentioned above, aggressive play is generally considered stronger than passive play because of the bluff value of bets and raises and because it offers more opportunities for your opponents to make mistakes.^[1]

Hand reading, tells and leveling[edit]

Hand reading is the process of making educated guesses about the possible cards an opponent may hold, based on the sequence of actions in the pot. The term 'hand reading' is actually a misnomer, as skilled players do not attempt to assign a player to an exact hand. Rather they attempt to narrow the possibilities down to a range of probable hands based on the past actions of their opponent, during both the current hand and previous hands played by this opponent.

Tells are detectable changes in opponents' behavior or demeanor which provide clues about their hands or their intentions. Educated guesses about opponents' cards and intentions can help a player avoid mistakes in his own play, induce mistakes by the opponents, or influence the opponents to take actions that they would not normally take under the circumstances. For example, a tell might suggest that an opponent has missed a draw, so a player seeing it may decide a bluff would be more effective than usual.

Leveling or multiple level thinking is accounting for what the other opponents think about the hands. This information can then be used to the player's advantage. Some players might be able to make educated guesses about opponents' hands; this could be seen as the first level. The second level could be thought of as the combination of the first level and deducing what the opponents think the player's hand may be. Skilled players can adjust their game play to be on a higher level than that of less skilled opponents.

Table image and opponent profiling[edit]

By observing the tendencies and patterns of one's opponents, one can make more educated guesses about others' potential holdings. For example, if a player has been playing extremely tightly (playing very few hands), then when he/she finally enters a pot, one may surmise that he/she has stronger than average cards. One's table image is the perception by one's opponents of one's own pattern of play. A player can leverage their table image by playing out of character, and thereby inducing his/her opponents to misjudge his/her hand and make a mistake.

In live poker, as opposed to internet, stereotypes are often used for initial 'reads'. For instance, people of retirement age are often witnessed to play tight. Players will often project this image on unknown people of retirement age. Young people wearing headphones and hoodies are often witnessed to play more aggressively and mathematically if they played a lot of winning internet poker. These stereotypes can often be good bases to start a profile.

Often, there is a rather small pool of players in a given card playing venue. People will carry their history of playing with them in these environments.

Internet poker players can use large databases of hand histories to get a more precise player profile. Statistical information about opponents is displayed on the tables in the form of a heads up display. The most commonly used software is PokerTracker and Hold'em Manager.

Equity[edit]

Players' equity in a pot is their expected share of the pot, expressed either as a percentage (probability of winning) or expected value (amount of pot * probability of winning). Negative equity, or loss in equity, occurs when contributing to a pot with a probability of winning less than 1 / (number of opponents matching the contribution+1).

Example

Alice contributes $12 to a pot and is matched by two other opponents. Alice's $12 contribution 'bought' the chance to win $36. If Alice's probability of winning is 50%, her equity in the $36 pot is $18 (a gain in equity because her $12 is now 'worth' $18). If her probability of winning is only 10%, Alice loses equity because her $12 is now only 'worth' $3.60 (amount of pot * probability of winning).

Texas hold 'em example

Alice holds J♦8♠. Bob holds K♥7♠. After the flop, the board is 5♥6♥7♦. If both hands are played to a showdown, Alice has a 45% chance to win (which she is unaware of, because she does not know what hand Bob holds), Bob has a 53% chance to win and there is a 2% chance to split the pot. The pot currently has $51. Alice goes all-in for $45 reasoning that she can take the pot immediately if Bob folds or that Bob calls with a worse hand. Bob's simple pot odds for the call are also 32%; since his equity of 53% is greater than the pot odds he has to call, Bob has a positive expected value for the call (if he knew Alice's hole cards).

Short-handed considerations[edit]

When playing short-handed (at a table with 3-6 players), players must loosen up their play (play more hands) for several reasons:^[1]

• There is less likelihood of another player having a strong hand because there are fewer players.
• Each player's share of the forced bets increases because there are fewer players contributing to the forced bets, thus waiting for premium hands becomes more expensive.

This type of situation comes up most often in tournament style play. In a cash game, the adjustments are very similar, but not quite as drastic as the table can ask for what is known as a 'rake break.' A rake break occurs when the floor-man, who represents the casino, agrees to take a smaller portion than usual for the hand. For example, a random casino might normally receive 10% of the pot up to 5 dollars for a 'rake.' In this case the table would only owe 10% up to 3 dollars until there are a sufficient number of players again. In online poker rake breaks are determined automatically.

Structure considerations[edit]

The blinds and antes and limit structure of the game have a significant influence on poker strategy. For example, it is easier to manipulate pot odds in no-limit and pot-limit games than in limit games. In tournaments, as the size of the forced bets relative to the chip stacks grows, pressure is placed on players to play pots to avoid being anted/blinded away.^[5]

Mindset considerations[edit]

In 2014, Bwin conducted a study to see what makes a professional poker player. The brain activity of poker players, of varying degrees, was monitored using EEG headsets and visualised into brain maps.^[6] Leading sports psychologist, James Hazlett, then interpreted the findings:

• More experienced players showed higher levels of focus and concentration throughout the game.
• The amateur players had less control over their emotions, and were prone to allowing negative emotions, such as frustration, distract them.
• Whilst opponents were taking their turn, the expert players opened up another table or watched replays of hands they had played poorly to improve.
• The brain maps showed that the professional players were led more by logic and intuition.

The conclusions of the study suggest that poker players can improve their strategy by considering their mindset. Mental training techniques, commonly used by athletes, could therefore help to improve performance by working on elements such as self-control and concentration.

See also[edit]

Poker plays[edit]

Specific games[edit]

Notes[edit]

1. ^ ^abcdefDavid Sklansky (1987). The Theory of Poker. Two Plus Two Publications. ISBN1-880685-00-0.
2. ^Milovsky, Nicholas. 'The Basics of Game Theory and Associated Games'. Retrieved 11 February 2014.
3. ^ ^abDan Harrington and Bill Robertie (2004). Harrington on Hold'em: Expert Strategy For No-Limit Tournaments; Volume I: Strategic Play. Two Plus Two Publications. ISBN1-880685-33-7.
4. ^David Sklansky (2001). Tournament Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-28-0.
5. ^Dan Harrington and Bill Robertie (2005). Harrington on Hold'em: Expert Strategy For No-Limit Tournaments; Volume II: The Endgame. Two Plus Two Publications. ISBN1-880685-35-3.
6. ^Your Brain on Poker

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. Hard rock casino hollywood florida age to gamble.

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.

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.

Important Poker Probabilities Games

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.

Important Poker Probabilities Calculator

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.

Important Poker Math

By Gerald Hanks

Important Poker Probabilities Cheat

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.