After the launch of the WSOP (World Series of Poker) in the US in 1970, poker tournaments have become popular in many casinos around the world. It was also during this period that the first books appeared that deal seriously with poker strategy. The popularity of the game has increased greatly in recent years, mainly due to the ability to play online poker against live players. Soon, so-called "poker shows" (eg the European Poker Tour) are introduced in Europe, attracting new players outside the American continent. These shows also come with a desktop camera that scans the players' starting cards, making poker full-fledged spectator entertainment.

Variants of poker : card game There are around 150 variations of the poker game in English literature. Usually, however, poker is divided into 3 basic types:

A variant where a player gets all the cards before the first betting round. These are closed cards, which can be improved later by exchanging one or more of these cards. The most played variant of this type of poker is the classic five-card game Draw Poker. Draw Poker is especially popular with beginners and home games, with Community Card Poker being much more preferred in casinos.

Currently the most popular type of poker, in which players make the best hand of closed cards and community cards that are common to all players. The most popular variations of this game include Texas Hold'em Poker and Omaha Hold'em Poker. There are two major differences between Omaha and Texas Hold'em. At the start of Omaha poker, each player receives 4 cards (only two in Texas Hold'em) and the winning hand consists of exactly two hands in hand and three community cards (in Texas Hold'em any cards). Everything else is identical in both games.

In this variant, each player gets both closed and open cards, from which he tries again to make the best possible hand. In Stud Poker, each round of betting can start with a different player (for example, according to the best cards). As in Texas Hold'em, the winning hand consists of five arbitrary cards. The most popular games of this type of poker include seven-card Stud Poker and five-card Stud Poker.

This poker variant is by far the most widespread and popular worldwide. One of the reasons is that its rules are relatively simple. The game is designed for a maximum of 10 players at one poker table, and is played with deck 52 cards and the chips used to determine the amount of bets are used. In this variant, each player gets to hand two cards and five cards are dealt. At the beginning of the game to be determined dealer (who will deal the cards) and this position moves one space to the left after each game. The game proceeds clockwise, the player on the left hand of the dealer puts the so-called Small into the game blind (Small Blind), the second player to the left of the dealer puts the Big Blind. This is o mandatory bets that must be placed before the cards are dealt. Their amount is given the limit of the table played and during the game they usually increase gradually.

The position at the poker table is often a factor that is often underestimated by many beginners players. At a full table (10 players), we split them into blinds, early, middle and late position. Having a position on a player means that you are entering the game after him and know it his reaction so that you can customize your decision. Blinds The first two positions at the table (Small Blind and Big Blind) where the mandatory bets are paid. The blinds always decide first at the table, so play them often from this position disadvantageously.

Early positions This is the position to the left of the Big Blind - UTG (Under The Gun) and the following two positions. It is also less convenient at the table, as you still have plenty players behind you. It is therefore quite likely that one of them will have a strong combination, and if you are called, you will usually play first, therefore out of position.

Middle position In these positions you already have an overview of the decisions of previous players, so you can afford Play multiple starting hands. Late position The two best positions in the game, called Cut Off and Button (Dealer). You make decisions like last, so you have the most information on how the game at the table goes. It pays to play more starting hands, bluff, etc.

Late position The two best positions in the game, called Cut Off and Button (Dealer). You make decisions like last, so you have the most information on how the game at the table goes. It pays to play more starting hands, bluff, etc.

Winnning combinations in poker ? The winning hands in Texas Hold'em consist of five cards, which are chosen from two of the cards in the hand and five of the community cards on the table. To do this, first select the cards that make up the poker hand (pair, three of a kind, etc.). These cards are then refilled the highest hand and table cards. Thus, a player can build a winning combination of: 28 1. Both cards in hand and three cards on the table 2. One card in hand and four cards on the table 3. No cards in hand and five cards on the table The order and therefore the strength of each combination is determined by the probability with which it is possible to assemble the combination. Overall, there are 2,568,960 different card combinations in poker.

WINNING COMBINATIONS SHIFTED FROM MOST STRENGTH TO LOWEST Royal Flush The highest winning hand in poker, the straight with the ace as the highest card in which they are all cards in the same suit. Only four - spades, hearts, crosses and diamonds can be assembled. Straight Flush Five consecutive cards, all in the same suit, eg 7 7 6 ♦ 5 ♦ 4 ♦ 3 ♦. If two players own a straight, the player with the straight that wins the higher wins card. There are 36 variants of pure straight. Poker (Four Of A Kind) Four cards of the same value, eg J ♣ J ♦ J ♥ J ♠ 3 ♥. In case of equality of combination the four of a higher value wins. If more than one player has four of the same players values, the size of the fifth card, the so-called kicker, decides on the winner. There may be a total of 624 types of this combination. 29 Full house This poker combination consists of three together with a pair, eg 4 ♣ 4 ♦ 4 ♠ 2 ♦ 2 ♥. In the event of a tie, the player with the higher three wins. If they have players the same three, the power of the pair decides. The full house combination has 3,744 possible variants.

Color (Flush) Five cards of the same suit, regardless of their size, eg K ♦ J ♦ 8 ♦ 5 ♦ 3 ♦. In case of conformity the player with the highest card in the suit wins. There are 5,108 possible variants of this combination.

Straight Five consecutive cards, regardless of their suit, eg 6 ♠ 5 ♥ 4 ♦ 3 ♣ 2 ♠. When A straight ended with a higher card wins the equality of two hands. Can be assembled in total 10 200 such combinations.

Note: Ace can be used as the highest and lowest cards. Tzv. a corner sequence, e.g. Straight 3 ♥ 2 ♣ A ♦ K ♥ Q ♠ (aka Around the Corner) in which the ace represents at the same time, the lowest and highest values are usually not considered straight. The same can be said about Skip Straight, jokingly called as Kangaroo Straight, in which he is regularly one value card skipped (eg 4 ♦ 6 ♠ 8 ♠ 10 ♥ Q ♣). 30 Trinity (Trips or Set) The three cards consist of three cards of the same rank, which are complemented by two different cards, eg. Q ♥ Q ♠ Q ♣ 3 ♦ 5 ♥. The strongest trio is the one made up of the highest ranking cards, with the trinity equal the highest option card decides. In poker, it is possible to assemble 54,912 kinds of triples.

Note: Set - a triple consisting of one community card Trips - a trio consisting of two community cards Two Pairs Two pairs consist of two pairs of cards of the same value, eg 3 ♦ 3 ♣ 8 ♠ 8 ♥ A ♥. If the combinations are the same, the pair with the highest value decides, then the second lower pair. If both players have the same pair of cards, the fifth additional card decides the winner. Total 123,552 such combinations can be created.

Pair A combination of two cards of the same rank and three cards without one another context, eg 8 ♦ 8 ♣ 2 ♠ 3 ♦ 5 ♥. A higher pair is stronger than a lower pair if the pair is equal, decides the remaining card in hand. A total of 1 098 240 species of this species may occur combination. 31 High Card The weakest hand containing five cards without any connection, eg K ♥ 8 ♣ 3 ♦ 5 ♣ 2 ♣. Failed to compile any of the aforementioned combinations and therefore only the winner decides highest card, in the case of equality the second highest, etc. In total there are 1 302 540 possible variants.

Sample of poker game Even in poker, the rule is that size matters. E.g. thus the pair of aces is higher than the pair of eights. The same is true for two pairs, threes, quads, etc. The winner is player B. Even if they both have the same winning combination (two pairs), player B has a higher pair. Most often, however, the size of the kicker is judged when the combinations are the same. For example, when the player has the lowest possible winning hand (the highest card), the strength of that highest card decides. The winner is player A. Again they both have the same winning hand (the highest card), but player A has higher kicker.

Fixed Limit A version of poker that specifies the bet you can raise. During In one betting round, a player can raise up to three times. After the last possible players can either fold cards or call the last bet. Bets and raises are determined by the size of the blinds. If the maximum number of bets is reached, it is pot (pot) closed. It is allowed to raise three times again in the following round.

No Limit This is the most free version in terms of bet size. The size of the raises is arbitrary, so each player can bet all his chips at any time. The minimum bet corresponds to the amount of the Big Blind, and if one of the players has raised before you, you can raise again, but at least by the value of the opponent's raise. If a player who wants to call does not have enough chips to make a bet, he will bet his all-in. From that point on, he can only win the part of the pot he covers with his chips. A side pot is created for the other players and they only play for that pot those players who played the chips with it.

Pot Limit Pot Limit is a compromise between Fixed Limit and No Limit. This means that you can bet as many chips as you can in the pot (pot), plus twice the last bet in front of you. So it is not unusual for it to grow and can grow a lot during the next rounds of banks even all-in bets.

Probability and gambling have been an idea since long before the invention of poker.

Poker is a decision-making game that usually determines whether or not you will be successful in this game. So how do you decide whether to play or discard the cards in a given situation? From In the mid-1990s, players of the traditional poker school began to be pushed out of the forefront by young players who were able to capitalize on mathematics in their game. Math is namely a suitable tool for making the right decisions based on the information obtained. So the answer to our question is mathematics. As Chris Ferguson of the 2000 World Series of Poker said: "If you think math is not important, then you don't know that is, we can reduce the chance or happiness factor to an acceptable level and calculate ourselves when it pays to play or rather wait for a better opportunity. One of the basic mathematical methods is Outs, Odds and Expected Value. Let's look at these procedures in detail.

Counting Outs In poker, there is often a situation where we have an incomplete hand that is worse than the opponent, but we still have a chance to beat him. This chance will be greater the more outs we have. So what are outs? These are the cards that complete our commenced hand. In other words, these are the cards that will help us create a better hand than we are holding. The correct calculation of Outs is thus the key to the success or failure of the game, because according to the number of Outs, we often decide whether it pays to stay in the game or fold our cards. When counting outs, we always have to remember that this calculation is not perfect. Because we do not know what cards the opponent holds, so sometimes with cards that seem weak, we can beat the opponent. Of course, the opposite may also happen, for example, when we create a Full House and expect to beat the opponent's three, but he holds Poker. Despite however, it is very useful to keep track of how many cards you are likely to win.

We will show the calculation of Outs on a simple example. As a starting hand we got K ♣ Q ♣ and the flop turned 8 ♣ 3 ♦ 5 ♣. So there is a chance that we can make a flush from the original hand, but we need one more cross card to do this. The number of outs to create a color is in this case the number of remaining cross cards in the deck. There are 13 cross cards in total, 4 of which have already been dealt. The number of Outs is 13 - 4 = 9.

Another similar situation is when a player holds a combination of 2 pairs, which can improve on Full House. 4 cards help him, so the player has 4 outs. For example, if we have a combination of J ♣ Q ♦ and the flop comes Q ♣ 2 ♥ J ♠, then the four cards making up the Outs are two queens and two boys of leftover colors. But counting outs is not always as clear and easy as in the previous examples. Now let's take a look at some examples where this calculation requires much more time and concentration.

After the deal, we got 8 ♦ 5 ♥ and the flop came a combination of 6 ♠ 8 ♥ 7 karet. So we have one pair (which, however, most likely will not guarantee a win) and a chance of straight. There are 8 cards (four nines and four fours) to create a straight. However, we cannot count any of the nines between the outs, because if an opponent holds a ten in his hand, he would have a higher straight and hence would beat our winning hand. So they are our Outs reduced by dangerous nines to number 4.

Cards on the turn Now let's take a look at the situation where we are already facing an opponent's hand. We hold 7 ♦ 6 ♦ and we have one pair on the turn, but the opponent is better off with his A ♠ 10 ♦. What combinations would we be able to beat? Any diamonds will help us to create a Flush, there are still 8 of them. There are paradoxically any of the other three remaining tens to win. There are also 2 left in the package the sevens that make us a triple and don't forget the five that make us a lower straight. These are in deck 4, but we have to subtract one that we have already counted as a diamond card to create a color. Together we have 8 + 3 + 2 + 3 = 8 outů.

Cards on the turn We were given Q ♥ J ♥ and we are all-in against an opponent holding a pair of ladies. On the turn J ♠ 10 ♥ 9 J A ♥ we are in a worse position and we would like to know how many outs will keep us in the game. We will win any card of the color, there are still 9 cards left also J ♣ and J ♦ by creating a triple, altogether 11 cards. Other cards no longer guarantee us a win, but there are still those in which a draw occurs and we will not lose our chips. They are 3 Kings and 3 Eights, because then we will have the same winning hand as the opponent. A total of 17 cards can come on the river to ensure our survival in the game. Some of the English terms in poker terminology that are used to describe certain situations are closely related to the Outs counting.

Gutshot or Inside Straight Draw is such a situation where we get to the straight one internal card remaining. For example, if we hold A ♣ K ♦ in our hand and the flop revealed 5 ♥ J ♦ 10 ♥, we miss any Q to complete Straight. So we have 4 outs.

Open Straight Draw If there is a possibility to create a straight flush combination from both sides, we say he has a player called Open Straight Draw. An example is a player holding 10 ♦ 9 ♠ on the flop J ♠ 8 ♥ 4 ♣. That he has made a straight, missing any lady or seven, so he has 8 Outs.

Flush Draw Flush Draw is the name when a player holds 2 cards of the same suit on the flop turns two cards of the same suit as those in the player's hand. For example, if we hold 8 ♥ 10 ♥ on flop 3 ♥ A ♥ 7 ♦, we miss one heart card to complete Flush. In that in case we have 9 outs.

Backdoor Backdoor refers to the situation on the flop when players are missing 2 cards to complete flush or color combination. They are then labeled as Backdoor Straight Draw, respectively. Backdoor Flush Draw. For example, if a player holds 5 ♠ 4 ♥ on the hand and the flop comes K ♠ 8 ♥ A ♦, Backdoor Straight Draw, because he lacks two to create Straight and three.

The term Hand Odds is an expression of the probability with which we create with us required winning combinations. This is the ratio of unfavorable and favorable results. Calculating how many outs we have to create the combination we want is a useful thing, but we will have a better idea if we can calculate how likely we are we hit one of these outs. It makes no difference if we have 8 Outs on the flop or out this opportunity comes up on the turn. The easiest way to calculate Hand Odds is rule 4 and 2. It is if it does on the flop, the probability is calculated as the number of Outs times four, the turn number Outs times two. So if we have J ♥ 8 ♠ in our hand and A ♦ 7 ♥ 9 ♣ turned on the flop, we hold called Gutshot and we have 4 outs to create a straight. The probability that we can assemble the flop on the river is 4 · 4 = 16% and the turn on the river 4 · 2 = 8%. Hand Odds therefore we express as: 38 100% 16% 6.25 1 5.25 ∶ 1 The hand Odds from the flop on the river is 5.25: 1 and from the turn to the river 11.5: 1. This calculation is relatively simple and easy to remember, but it is also least accurate. Derogation from the correct result can be up to several percent. Note: The number of Outs after the flop is multiplied by four only if you are all-in and do not the next stage of betting on the turn. For the probability that the card we want will come from the flop on turn, multiplies the number of outs by two. The exact calculation for Hand Odds is derived from the classical probability. Probability, we can calculate the probability of a phenomenon by calculating the required card from the flop on the river opposite to the phenomenon “Any card we don't want comes, followed by the other one card we don't want. " More specifically [18]: So if we are all-in on the flop and are not involved in the turn betting phase, we will use the formula: 1 $ 47 `abc 47 ∙ 46 `abc 46% The probability calculation from the flop on the turn is then calculated as: 1 $ 47 `abc 47% We calculate the probability that the card we want from the turn on the river comes with using the formula: 1 $ 46 `abc 46% If we did not count the probability as a complementary phenomenon to the phenomenon “Outs will not come either in one turn ”, we would have to consider 3 situations: come on the turn, come on the river, come on turn and river. Therefore, it is easier to count on the phenomenon when it does not come at all. Example: Consider the situation from the previous example of rule 4 and 2. We have J ♥ 8 ♠ on our hands and na flop came A ♦ 7 ♥ 9 ♣. The number of Outs is 4, so to calculate the probability of a flop on a river, the following applies: 1 $ 47 4 47 ∙ 46 4 46% 1 0.835 0.165 16.5% We calculate the probability of a turn on the river using the third formula: 1 $ 46 4 46% 1 0.913 0.087 8.7% We can see that the exact calculation in this case differs from rule 4 and 2 by 0.5 (resp. 0.7) percent.

If you want to win in poker, the Pot Odds concept is one of the most important ones you should learn. Again, this is a ratio, but Pot Odds compares us to a possible one the amount of winnings over the bet we have to bet to stay in the game. Thus, Pot Odds say nothing about our chances of winning, they only reflect the reward we get for it risk. For example, if we have to call $ 5 to a $ 20 pot, then our Pot Odds are given by a ratio of 20: 5, 4: 1. This ratio says we have to win at least one in five games to stay at zero (we bet $ 5 5 times and win $ 25 once). In general, what the pot Odds are higher, the better it is for us to call and the pot Odds the lower, the better it is to fold. In poker, we often get into situations where our winning combination is not currently best, but has the potential to create a combination strong enough to win sweat. Decision, Whether you call or fold when you face an opponent's bet in such a situation is in poker among the most important. Whether to continue the game or prefer to fold will determine if we compare Pot Odds with the probability of creating a Hand Odds. It is advisable to call a bet if our Hand Odds are lower than Pot Odds the opponent offers us. [20] 41 Example: With the starting hand J ♦ 8 ♦ we got to the turn, where we opened the opportunity to Flush, as shown in the following figure. There is $ 9 in the pot and the opponent has bet $ 2, it pays off for him call a bet?

Solution: We need to compare Hand Odds and Pot Odds to make the right decision. If we have tables, we find that the probability of building a flush from the turn on the river is 19.6%, which is the ratio of Hand Odds 4.1: 1. Pot Odds is calculated as the ratio of the size of the pot (including the opponent's bet) to the amount it is the need to call, ie: 9 $ 2 $ ∶ 2 $ 11 ∶ 2 5.5 ∶ 1 Pot Odds are 5.5: 1, with Hand Odds 4.1: 1. Hand Odds is lower, so it pays to continue the game. But let's take the case that an opponent would bet $ 4. Pot Odds would then be in the 13: 4 ratio = = 3.25: 1 and the bet wouldn't be worth it anymore. Note: We can do the calculation as a percentage, but then it pays to continue the game, if the Pot Odds probability is lower than the winning probability combination. In the previous example, Pot Odds is 5.5: 1 5.5 + 1 = 6.5 => 100 / 6.5 = 15.4%. Hand Odds 4.1: 1 equals a probability of 19.6%. The probability of Pot Odds came out lower, so we made sure the bet really paid off Call the opponent. Professional poker players also use the Pot Odds concept to defend their own good cards. If you have the best hand that wins at the moment, you can to bet a number of chips that simply does not allow opponents to fold. If you currently have 42 the best hand, but threatens to come a card that will allow the opponent to color or straight, then raising it above a certain limit will prevent your opponent from waiting for the missing card.

Implied Odds is already a term for more advanced poker players as it is for mastering it the previous Hand Odds and Pot Odds calculations must be well controlled. Implied Odds are another way we can look at Odds. They can be said to be an extension for Pot Odds and help us decide whether our Straight Draw or Flush Draw is still worth it continuation, or it will be wiser to fold. Unlike Pot Odds, however, they take Implied Odds Consider not only the size of the bet we have to call, but also the total number of chips that we can win when our Draw becomes a straight or a color. If a poker player assumes that he can win a large amount from an opponent chips, so has good Implied Odds. If you expect after passing straight or color from no more chips (eg if all-in), small or even no Implied Odds. It all depends on several aspects that we will discuss further. Factors affecting Implied Odds [16]: 1. Opponent The most interesting for us is an opponent who plays a small number of starting hands hands, but if he hits something on the flop (usually the top pair), he plays very well aggressively and is likely to be willing to go all-in with us. Such the type of player is called Tight-aggressive and gives us a very good Implied Odds. Tight-passive poker player is no longer so Implied Odds interesting. If one of our outs comes to the table, this opponent will be very easily scares and prefers to fold his cards. If he feels stronger, he will be us at best just call. Loose, on the other hand, joins the game very often, playing big a lot of starting hands, so we can't be sure of our Implied Odds. It is likely that these players are in a dangerous-looking situation give up. You can read more about playing poker styles in the Player Typology chapter.

The term Dry Board means there are no cards on the table, or cards of the same suit. In this case, the poker player holding the Open has a Open Straight Draw very good Implied Odds, his opponent will not be able to easily guess the strength of his cards. The term Draw-heavy Board, on the other hand, refers to a situation where they are connected on the table cards or multiple cards in one suit. This board will be feared by opponents so there is little chance that we would win all the chips from them. 3. Stack size In the Implied Odds concept, the size of the stacks plays a large part. The bigger they are player stacks, the more weight Implied Odds gain, and vice versa, the stacks the smaller our Implied Odds fall. When comparing our stack to the stack Of course, we include only the size for the calculation of Implied Odds the smaller of these two stacks. Since we are already familiar with the basic information and factors affecting Implied Odds, we can move on to the calculation and specific examples that give us this calculation more clarify. Implied Odds is again an expression of proportion. This time we measure the size of the sweat + the stack we can potentially win with the size of the bet we face. If us Implied Odds is greater than Hand Odds, it is worth calling, otherwise, we should fold. Example: With a 9 ♣ 8 ♣ starting hand, we have the option of Straight on the flop. Se our opponent has a stack of $ 90, and the opponent bet $ 10 in a $ 10 pot (that is, a bet in sweat size). Is it worthwhile to call his bet?

Expected Value is a term that is more likely to be encountered advanced poker players, the more you improve, the more often you will be at the concept impinge. One of the most important things to decide if you become poker successful, is the ability to maximize your winnings and vice versa to minimize the number of losses. To make a successful decision, we need to know whether the situation is long-term for us in terms of earnings or not. This is exactly what the Expected concept deals with Value. Simply put, this term represents the amount you average on your own by decision you gain or lose. Every action in poker (check, call, bet, raise and fold) can be done expressed by Expected Value. The goal of each player should then be to maximize this numbers to be in the long run in profit. According to [7, p. 84], we calculate the Expected Value by multiplying the possible winnings its probability and then subtract the value of the possible loss multiplied by its value probabilities. We divide Expected Value according to whether the situation is profitable or not (EV) to: • + EV - positive expected value, bringing you money on average • -EV - negative expected value, on average you are bidding for money In almost every literature or scholarly article, the explanation of the calculation is described Expected Value is based on an example of coin tossing. Therefore, we will also show the calculation first at similar model situation. Example 1: With a friend, we bet that if you hit the coin, they'll give you 20 USD. On the other hand, when a virgin falls, our friend gets 10 USD. This bet is good for us and will we profit in this game in the long run? Solution: The probability of an eagle falling is the same as the probability of a virgin falling 50%. Therefore, we calculate the Expected Value as: 20 ∙ 0.5 10 ∙ 0.5 10 5 5 The value of EV is +5, but that doesn't mean we'll win $ 5 each game. By agreement we get 20 USD for a win and lose 10 USD if we lose. In the long run, however we will win $ 5. In other words, if we repeat this game infinitely many times, 46 our average profit will be close to 5 USD, so we will be out of this bet profit in the long run. Note: Do not panic if you are careful about your Expected Value, but you are still they lost several games in a row. It is only bad luck, which in the long run does not play role. Keeping Expected Value is your math and probability, so you will surely get a plus in the long run.

It is good to know what Expected Value means and how to calculate EV correctly a simple example of coin tossing, where there are only two variants and each has a 50 to 50 chance. But how to calculate EV right in the middle of a poker game? This is best explained in the following example. Example 2: We hold A ♦ 9 V in our hand and the board comes with K ♦ 5 ♥ Q ♠ 8 ♦. There's already $ 50 in the pot and the opponent decided to give an all-in of $ 25, as shown in the following picture. We will be ours potential calla to profit in the long term? Giant. 6: Calculation of Expected Value Solution: We can determine if our call is profitable in this situation using Pot Odds, but only by calculating EV we find our average profit or loss if we decide to call. The probability of hitting Flush on the river turn is 19.6% = 0.196. Probability of that The flush we do not create is 80.4% = 0.804. Expected Value is then calculated as: $ 75 ∙ 0.196 $ 25 ∙ 0.804 14.7 20.1 5.4 The result is -5.4 EV, so every time we call in this situation we will lose $ 5.4 in the long run. 47 A good poker strategy always revolves around + EV decisions. The more + EV decisions that is, the more you win the chips / money during your game. Every single game would be so the poker player should have made decisions that maximize Expected Value. Probably we will not always be in a situation where a positive expected value can be achieved. Then we should try to keep the negative EV value as low as possible. Honestly, a poker game often runs very fast and calculates Expected Value usually not as easy as counting Pot Odds. In the game we usually do not have time to find out what action is best for your situation. Expected Value However, it also uses after the game to analyze its own decisions when we can Check out if our game was optimal or better to play it differently the next time we get again. It is especially advantageous if we know the opponent's cards. Then we don't have to rely solely on the probability of building or not building the winning one we require but we can directly compare the probabilities of two specific starting points combinations. Some poker programs, such as PokerStove, can help us with this. Again, we will take a closer look at this example. Example 3: We are in the Cut off position with the starting combination A ♣ Q ♦. The size of our stack is $ 100 and blinds are $ 2 and $ 5. Since we are playing aggressively, we played a raise of $ 15. The opponent on the button has quite a few chips and goes all-in $ 50. He turns the cards and shows us 5 ♦ 5 ♥, to make our decisions easier. It pays off in the long run for his all-in call? Solution: Earlier in PokerStove, we found that at A ♣ Q ♦ vs. 5 ♦ 5 ♥ (Overcards vs. Pair) Before the flop there are 45% odds of winning. 55%. He is in the pot with blinds together $ 57 and Expected Value are calculated as follows: $ 57 ∙ 0.45 $ 50 ∙ 0.5 25.65 25 0,69 EV is +0.69 and we should call the opponent's all-in, as in the long run we will + $ 0.69. It is important to remember that in poker we cannot make big conclusions in just a few games, because there are many bad players who may be currently winning, but in the long run they are at a negative point. These players do not realize the importance of Expected Value and we can say that winning is now just a matter of luck. Good players on the contrary they may have a bad time when they are not doing well and luck does not wish them even when it is mathematics on their side. In the long run, however, they are profitable because they can distinguish profitable decision from that unprofitable.

Understanding the importance of Expected Value is the foundation of any successful poker player, it is that is, without a doubt, one of the most important mathematical concepts to learn. The ability to correctly recognize + EV and -EV maximizes long-term situations winnings and minimizes losses. And that's exactly what poker is about if we have the ambition to be earning player.

In poker there are several game styles to access this game. In this chapter you we will describe the different styles and show how we know whether we are against the conservative or the an aggressive type of opponent. Every player plays in a certain way and it depends on his personality, which of these styles will appeal to him more than the others. But we can say that it does not matter which style you like, you should choose a style that suits you personally best. However, it is important to be able to adapt your playing style to your opponent. It is said that the average poker player should participate in about thirty percent of the games. According to Whether a player is above or below this value, we can basically divide the player types into of two categories - Loose and Tight. A typical feature of Loose style is playing a large number of starting hands, while a Tight player plays only strong hands. So to understand how to “play players” and not just our cards, we need to get to know each other the different types we can meet at the poker table [24]: 1. Weak This note refers to a weak poker player. They are often beginning players who do not yet have enough control over the power of the cards. They are afraid to bet as well in situations where they are clear favorites in the game and are easily subjected to pressure, so they prefer to lay cards on your bet. Consider the situation that this Weak player sitting in the last position and all the players in front of him folded. He despite having relatively good cards, only calls the Big Blind bet. Big Player Blind speaks first on the flop and bet. Weak flop missed, and so the cards throws, even if the opponent's card is low. That did not bet before the flop, left the opponent in the game, and he had it in his own Overhead. 2. Tight This is a conservative type of player who takes part very little in the game only if they hold a strong starting hand. We usually reveal it up to when showing cards when winning. Tight players don't bet unless they're absolutely sure of its position. So if such a player bet before us and we do not 50 very strong combination, we prefer to fold. Most books are recommended beginners learn this style of play.

Loose This type of player is more aggressive, playing virtually any game, from any position. It is therefore much harder to read this player and see if playing regardless of the hand or simply playing playable cards. His goal is to look at the flop, often call any bet, but it never will increase. Loose player plays a lot of games, so he manages to steal a lot of pots and he has a good chance of winning the big pot with the best hands. The downside is that when playing worse starting hands, he will face many a tough decision on the flop and the size of his stack will move both up, down. 4. Super Aggressive The super-aggressive player is very straightforward and plays any two cards and at any time. Its main goal is to get rid of other opponents aggressive betting. It makes this type very exciting to look at, but dangerous to play. It is convenient to sit away from this Super Aggressive player on the left, if we find a strong combination, we can raise and have very likely to call us. If, however, a strong combination we don't have to, we'd better fold. In other words, if it fits such a type players with us at the table, we should join the Tight game. 5. Maniac As the name suggests, this type of player plays as a sense-free. In practice, he is constantly betting exorbitant amounts on below-average cards and relies just for luck. Any tactics against this player is unnecessary and if they do with him you play, you have to hope that you are not playing the game when it will stand happiness on his side.

This subchapter follows the previous ones and the game styles are discussed in more detail here. As already It has been said that the basic division of poker players is on Loose and Tight. This factor is the most manifested in the selection of starting combinations. However, we can further distinguish both of these styles into active and passive style. A typical feature of an active style is a bet or raise, a Tight player on the contrary, he often avoids confrontation, so he checks or just calls. By combining these four styles we get four variants of the game [22]: (a) Tight-aggressive Tight-aggressive players do not play many games, but when they start playing, they play very aggressively. So if the opponent wants to see more cards, it will definitely be him cost a lot of chips. This is a style ideal for beginners, it is safe and relatively profitable. The downside is that against the Tight-aggressive players themselves bluffes well, as he only plays with premium cards, and so on bluff often throws away. (b) Loose-aggressive The style most preferred by more experienced players. Such a player before the flop and on often raises the flop with a wide range of starting hands. His game is thus hardly legible for the opponent. Disadvantages include frequent bluffing, thanks which is the Loose-aggressive stack of the player. Learn to play well Loose-aggressive is quite difficult, but after all the pitfalls have been mastered, it opens the way to the biggest winnings in poker. c) Tight-passive Such a player is not involved in many games and is easy to read. Betting opponents only calls and usually just before the flop. It is very easy against such players bluff, as they play with fear of losing before the game begins. However, if he stays in the hand, he holds a very strong hand in his hand, and as a rival we should discard our cards. d) Loose-passive Loose-passive player can be described as curious. He plays a large number of games and he calls the high raise just to see the flop. If it flop 52 he misses his hand, otherwise he calls almost anything. This is why the nickname "Calling Station" is used for this style. In the short term, this style can be profitable, but in the long run it is Practically excluded to a player playing such a large number of card hands was in profit.

Which of these styles is the best? If we should sort them by profitability, on first place would be Tight-aggressive. Players who already have something behind in poker use but rather Loose-aggressive, because they are more likely to take part in the event, so the game is not boring for them. However, the best poker players can adapt their style according to the situation at the table and their opponents. It is generally said that if you play at a table full of Loose players, it is better to play more Tight and vice versa. It is also good to play aggressively, but to play aggressively you need a lot of experience and above all refined feeling for the game.

Just like the starting hands, they got their names or nicknames, so they got different game combinations styles have their names. Professional poker player Phil Hellmuth came up with an idea to assign individual styles of naming by animals. What is it useful for? Thanks to the association it is much easier to assign an animal to a player than to use long, unattractive characteristics. This a witty and easy-to-remember system divides players into five categories: mouse, jackal, elephant, lion and eagle.

a) Mouse A super-conservative player who raises rarely and mostly does not bluff. So if he raises the mouse, he probably has an unbeatable combination. Advantage The safe game is that the winnings outweigh the losses, but they are not that big. Between The main drawbacks include easy readability.

(b) Jackal He participates in many games, often betting and raising. This is the opposite of the mouse. Between Advantages include Loose style, so if they catch good cards, rivals don't expect it and often wins a big pot. The disadvantage, however, is frequent bluffing and jackal over time loses some time, as more experienced players can use his knowledge Loose style.

c) Elephant An elephant is a player who still calls. He could be compared to Loosepassive style. It is easy to choose starting hands and participates in many games. There's no point in trying to bluff an elephant, but if you have good cards, they will pay you all the bets up to the river. It is therefore an animal from which easily you get money.

d) Lion He plays rather strong starting hands, but occasionally plays with others cards. The lion plays aggressively when he has the upper hand, and folds when he feels defeated. The advantage is a balanced frequency of bluffing, thanks to which it gets money from mice, jackals and elephants. It can be said that a lion will be defeated only by another lion or eagle, but become a lion requires studying and learning from the game of professionals.

e) Eagle The character most players never reach, the eagle is at its peak of the poker world. He has studied poker for many years and is one of the best players. Phil Hellmuth claims that the eagle is one of the top 100 players in the world. If you reach on this status, others will likely watch you on TV as you win games in the world's best competitions.

All-in - bet of all chips Ante - at higher blinds it's a small pot fee (usually 1/10 of the big blind) Bet - bet Big Blind - big mandatory bet; min. the bet you have to pay to participate in the game Bluff - player intentionally different power of his hand Board - community cards Button - best position at the table, Dealer Call - call a bet Cut-off - second best table position, just before Button Draw - when a player is missing one card to create a Flush or Straight Flop - the first three community cards on the table Fold - placing cards, you are not participating in the game Hand - two hand cards Check - game delay; leaving the bet at the same level Kicker - The decisive free card in the event of a tie's strength Outs - The number of cards that improve your hand Overcard - card on hand higher than the highest card on the table Overpair - A pair of hands that is taller than the cards on the table Pot - bank; all the chips that were placed in the game Pre-flop - pre-flop betting, first phase of the game Raise - raise your bet River - fifth, last community card Showdown - the final stage of the game, the cards are shown, the evaluation is in progress Small Blind - small mandatory bet, half of the Big Blind Split - division of the pot; this happens in the same multiplayer winning combination Stack - The number of player chips Turn - fourth community card UTG - Position of the first player, in other words under fire

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