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.

The good news: I can think of several new poker sites that offer something new for battle-weary players. A new game type, new bonus structures, or new software. The bad news: I've seen players burned enough time by honest-to-goodness brand new poker sites (and in online poker terms, that mean it's been around for only 1-2 years) that I don't recommend them. Mike Caro discusses this tell in his 70’s classic Caro’s Book of Poker Tells: The Psychology and Body Language of Poker.The reason why it’s a reliable tell is simple: holding a strong hand, a player is not likely to give a player in front of them a reason not to bet; to the. Live poker tells are easy to pick up on if you know what you’re looking for It was only a year or two ago that live poker tells were being questioned and eventually dubbed ‘overrated’. The online poker generation argued – and to some extent proved – that betting patterns, hand values and ranges are what really matter in poker. Here are some poker tips on how to read poker players and poker tellsFREE online poker training video - http://tinyurl.com/PokerProTraining.

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A detailed look into ten of the most common online poker tells to help you boost your win rate at the tables. In this article, I’d like to discuss various online poker tells, their possible meaning, their general degree of reliability, and how you can use each as a false tell. Just as I would caution you not to put too much emphasis on live.

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

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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.

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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.

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.

How would you compare live poker and online poker?

On the one hand, whether you play poker in a casino or play poker on a computer, it's still the same game. A flush beats a straight in both. Players in both games bet and bluff and deliver and receive bad beats. Many of the skills developed in one format translate readily to the other.

Then again, many players have persuasively argued the games couldn't be more different. It's like comparing chess and checkers, some have suggested. Online poker, a video game, live poker more likened to a sport. One's 'virtual,' the other 'real.'

There was a time in the not too distant past that the contrast between 'live poker players' and 'online poker players' was quite stark. Many pros belonged to one group and essentially ignored the other. You'd hear stories of 'live pros' venturing online and not faring well (with some complaining the game wasn't 'real' poker). Then there would be 'online pros' showing up at live events and struggling with handling cards and chips or game etiquette.

Today there is a lot more overlap, with most top players and many at all levels playing both online and live. Those who do engage in both have to be aware of the differences between how the respective games tend to play.

What are some of the differences between live and online poker? And among these differences, which are the most important ones for players making the jump from one to the other? As you think of an answer, here are several differences to consider.

Bet Sizing

In live cash games you'll often encounter different bet sizing than happens online, primarily when it comes to opening preflop raises. While an online cash game might feature players opening for 2x, 2.5x, or 3x the big blind, in live games it isn't unusual to encounter players opening for 5x or 6x or even more, particularly in the lower-stakes live games (e.g., $1/$2 NL).

Tournaments are a different story, although there, too, you'll occasionally find live players overbetting, particularly inexperienced ones who struggle with keeping track of pot sizes.

Multi-Way vs. Heads-Up Pots

That said, in the live games you'll often encounter looser play, generally speaking, in the form of players doing a lot more calling. One consequence of this trend is more multi-way pots occurring live than online where the preflop betting more typically creates heads-up situations.

It isn't that unusual in a live cash game session to witness a number of limpers preflop and/or several callers of a preflop raise, thereby creating a multi-way situation.

Calling vs. Folding

Meanwhile, if live players are often looser than online players with their preflop calls, postflop things tend to go differently. You'll find that online players are in fact more apt to make big postflop calls with weak- or medium-strength hands than tends to happen live. That means big river bluffs tend to get through more often live than happens online (although of course, everything depends on the player and situation).

One explanation for this tendency is the fact that it is easier for many players simply to click a 'Call' button than to make a tough call live. Not having to endure in person the embarrassment of guessing wrong with such calls make them easier online.

Frequency of Bad Beats

In part because of this tendency to run into more callers online, many players report experiencing 'bad beats' more often online than happens live. This is especially so at the 'micros' and lower limits online, where the small stakes further encourage calls with subpar hands that occasionally do outdraw better ones.

The sense that the bad beats are coming more often online is enhanced, of course, by another big difference between live and online poker, namely...

The Pace of the Game

One of the more obvious surface-level differences between live and online poker is the pace of play. Online poker plays considerably faster than live poker, and some who prefer playing online find the live game too tedious to tolerate. Whereas you might be dealt around 30 hands per hour in a no-limit hold'em cash game, online you'll see 60 hands per hour (or more) at a given table and even more in short-handed games. The ability to multi-table online also means playing a lot more hands per hour than is possible live.

For this reason, the impression of getting more bad beats online can be exaggerated. The fact is, you can seem to experience more of everything online because you're playing many more hands, which in turn affects...

Variance in Online Poker vs. Live Poker

'Variance' is a term often used generically to describe the 'swings' one endures in poker, with the higher 'variance' translating into bigger gains and losses in the short term when compared to your results over longer periods. The faster pace of play online again artificially affects what the 'short term' actually is. You might play a week online and log 10 times the number of hands you'd play if you played live poker for a week, thus giving the impression that your variance has been accelerated greatly.

Even if it is an artificially-created difference, this 'higher' variance when playing online can mean faster, more marked bankroll swings over shorter periods than generally happens live. That means bankroll management has to be approached differently when playing online, where you generally want to maintain a bigger bankroll (in terms of cash game buy-ins or tournament entry fees) than you need when playing live.

Online Tells vs. Live Poker Tells

An obvious difference when playing online is not being able to see your opponents — or for them to be able to see you — which means, of course, the role of 'physical tells' gets omitted from the online game. This also obviously affects table talk, which can be important in live games but becomes a non-factor when playing online (aside from chatbox 'talk'). Experienced live players maintain it is much easier to 'profile' opponents when playing live, especially less experienced ones who tend to give away lots of information very quickly at the table.

That doesn't mean there aren't any 'tells' in online poker. Check out '7 Ways to Get Better Reads When Playing Online Poker' by Nathan Williams for discussion of several examples.

Relative Stakes

One last difference we can add to the list concerns how stakes compare between live and online poker. For various reasons, an online game played at the same limit as a live game will usually feature higher-skilled players, relatively speaking. For example, a live $1/$2 NL cash game generally won't have as many tough opponents around the table as you'll find in a typical $1/$2 NL online game, in part because while there usually aren't any lower-stakes games available live, there are plenty of them online (down to just pennies).

Some have suggested as a rule of thumb a '10-to-1' guideline when comparing live and online stakes — e.g., a $0.50/$1 NL game online would play as 'tough' as a $5/$10 NL game live. Of course, you'll still encounter both good and bad players at all levels, both live and online, so don't take this as a rule without exceptions.

Those are some of the most significant differences between live and online poker. Which would you consider to be the biggest difference out of all of these? Share your thoughts in a comment below.

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