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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.

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

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 isR$90 and the player must call aR$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

nowR$100 and hisR$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.

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.

A pressa para conquistar um corpo mais definido e superar os próprios limites leva muitas pessoas a exagerarem na prática 7️⃣ dos exercícios, sem a devida atenção para evitar riscos.

Em relação aos atletas, essa falta de cuidado é ainda mais grave, 7️⃣ pois pode ocasionar lesões e contusões sérias que vão comprometer sua performance.

Nesse sentido, é importante saber o que é fisiologia 7️⃣ do esporte e como ela pode beneficiar os desportistas.

Os profissionais que trabalham nessa área estudam os efeitos das atividades físicas 7️⃣ nas doenças, para, assim, definir estratégias para redução e reversão da progressão de determinada patologia, evitar contusões, tratar lesões de 7️⃣ modo mais eficaz, entre outros benefícios.

Para saber mais sobre esse assunto e conhecer como surgiu essa metologia, siga a leitura!

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