Analysis Of Poker Strategies In Heads-up Poker

Analysis of poker strategies in heads-up pokerunbeatable, unlike the highest hand in classic poker, the “royal flush”, which can be tiedin another suit.To make it possible for more than four players to join in a game the 52-card game madeits first appearance. The 52-card game also made it possible to draw cards and introducemore than one betting round. This introduction was in the 1830s. The flush wasintroduced around this time as well. In this phase the hand ranking was as follows: onepair, two pairs, triplets, flush, full house, fours.3.3 Coming of ageFrom the middle of the 19th century, poker experienced rapid changes and innovations asit became more widespread through the upheavals of the Civil War1. In this phase, the socalled Jack pots were introduced. This meant that when a player had a pair of Jacks orbetter cards he was obliged to open his cards and otherwise he was not allowed to openthem at all. This rule was introduced to drive out wild players, who would bet on anycards they received. The rule was abandoned because it took out the idea of bluffing, andmade poker more like a lottery.In the 1860s the straight made its introduction. The 1864 edition gave the hands as: onepair, two pairs, straight sequence or rotation, triplets, flush, full house, fours. But when astraight was also a flush it outranked the full house. The fours were still the highest hand,even though it was mathematically more likely to ‘hit’ a four than a straight flush. Thereason was that four aces or four kings and an ace could not be tied and a straight flushcould be tied in a different suit.It was not until 1892, when John Keller defended his view that the straight flush shouldbe the highest rank in poker. His most important argument was a moral argument. Hesaid that among gentlemen it was unethical and ungentlemanly to bet on four aces,10

Analysis of poker strategies in heads-up pokerbecause the win was a certainty. A straight flush however, could be tied in a different suitwhich made it morally superior to betting on a certainty.In the 20th century following Draw and Stud, a third major structural division of the pokergame, represented today by Texas Hold’em, was first played. Here the introduction ofone or more communal cards was a fact. The rise of modern tournament play dates fromthe World Series of Poker started in 1970.3.4 Texas Hold’emThe most popular form of poker is Texas Hold’em. This is a poker game for two to tenplayers with fairly simple rules. The object is to make the best 5-card poker hand usingany combination of the 2 cards dealt face down to you and the 5 common cards dealt faceup on the table. Here is the flow of play given by www.everestpoker.com3: The Dealer. Cards are dealt from the position of the Dealer, which rotatesclockwise around the table after each hand. The player designated as Dealer for agiven hand is identified by a round “D” marker on the table. The software willautomatically deal cards on behalf of the Dealer. Blinds. To start the game, the player to the left of the Dealer puts up the smallblind (which is usually half the minimum bet) and the player to his left posts thebig blind (equal to the minimum bet). This gets the pot started and encouragesother players to place bets. They are called “blinds” because these bets are madebefore any card is seen. The Deal. Each player is dealt two cards, called Pocket Cards, which are visibleonly to the player holding them. Betting. After all players have received their two pocket cards, there is a Roundof Betting starting with the player to the left of the player who posted the bigblind. Depending on prior activity in the current hand of play, a player can fold,11

Analysis of poker strategies in heads-up pokercheck, call, bet, raise or re-raise within the bounds of the Game Limits and TableStakes. A round of betting may circle the table several times if there are raises andre-raises. The round ends when all players have either called the last bet or folded. The Flop. Next comes the Flop, where 3 cards are dealt face-up in the commonarea of the table, followed by another round of betting. The Turn. Then comes the Turn, where a 4th common card is dealt face-up nextto the Flop, and a third round of betting occurs. The River. The final common card, called the River, is placed face-up next to theTurn and is followed by the last round of betting. The Showdown. The Showdown occurs after betting concludes. The remainingplayers compare the best five-card poker hands they make using any combinationof their 2 pocket cards and the 5 common cards. The player with the highest handrank takes the pot. Occasionally, two or more players will have hands of equalrank or the best possible hand is comprised using all 5 common cards. In thesecases, the players involved share the pot. Next Hand. After the pot is distributed, the Dealer button moves to the nextplayer on the left (clockwise around the table), and the players to the left of thenew Dealer post blinds so the deal for a new hand can start.3.5 Betting RulesThere are different types of poker when it comes to betting. PartyPoker.com6 gives thefollowing betting options.Limit PokerIn a game of limit poker, the amount you are allowed to bet is limited to a specific size.This limit is in the name of the poker game ( 3/6, 20/40, etc.).12

Analysis of poker strategies in heads-up pokerIn the case of a ‘ 1/2 limit’ game, the minimum sizes of the bets would be: Pre-flop (before the flop): 1 On the flop (when the three first community cards have been dealt): 1 On the turn (when the fourth community card has been dealt): 2 On the river (when the fifth and last community card has been dealt): 2The smallest bet allowed is the big blind. Furthermore, all raises must be done inincrements of the betting amounts.For example, in a 1/2 limit game, the raises will be as follows, limited to four times thefirst bet that was made: Pre-flop: 1, 2, 3 up to 4 On the flop: 1, 2, 3 up to 4 On the turn: 2, 4, 6 up to 8 On the river: 2, 4, 6 up to 8No-Limit PokerIn no-limit poker there is no maximum to the amount a player can bet. The minimum,however, is the big blind. When a player wants to raise another player, he must raise withat least the bet of the other player.When a player wants to call, but does not have enough chips to equal the amount that isbet, he is “all-in”. This means that the player plays for all the chips he has left.Pot-Limit PokerPot-limit is the most popular variant of the poker game in Europe. It is quite similar tono-limit poker but there are certain key differences.13

Analysis of poker strategies in heads-up pokerIn pot-limit poker, players are allowed to bet any amount from the size of the big blind tothe size of the pot. The pot includes the sum of all bets and raises made during the currentround.3.6 Poker EtiquetteIn the biggest tournaments and among the world’s most successful poker players, thebiggest winners almost always have two things in common - good sportsmanship andperfect poker etiquette.Good manners at the table make the game more pleasant for everybody, help you getmore hands per hour and in many cases can actually help add to your winnings.In Las Vegas, there is a saying among old time poker pros: “Don’t tap on the aquarium, itspooks the fish.” More experienced players know better than to insult the lesser skilledplayers, as that is where the money comes from. They also know the negative irownsuperiorskills.14

Analysis of poker strategies in heads-up poker4. Heads-upIn a tournament heads-up is the final phase. Only two players are left and it is a one-onone confrontation. While the game of Poker is the same with heads-up poker and 6-10person play there are also some important differences that need to be taken into account.Especially the rank of the starting hand is different and the probability that another personhas a stronger hand is smaller in a heads-up game.4.1 Rank of Starting Hands for Heads-Up Poker4The ranks of starting hands in heads-up poker are very different from 6-10 poker play.This, of course, is due to the number of possible good hands that your opponents have.When you play one opponent, his hand will have a smaller probability to be good than anopponent that has called when 8 opponents have folded. This opponent called with areason, most likely, because he has a very strong hand.As can be seen in the chart of Top 20 heads-up poker starting hands, pairs are verystrong. Almost any pair is a favourite against a non-paired hand before the flop. A playeris dealt a pocket pair every 17 deals, so the probability of both players holding a pair isapproximately (17 17) 289.Chart of Top 20 Heads-Up Poker Starting Hands1 – A-A2 – K-K3 – Q-Q4 – J-J5 – 10-1015

Analysis of poker strategies in heads-up poker6 – 9-97 – 8-88 – A-K (suited)9 – 7-710 – A-Q (suited)11 – A-J (suited)12 – A-K (not suited)13 – A-10 (suited)14 – A-Q (not suited)15 – A-J (not suited)16 – K-Q (suited)17 – 6-618 – A-9 (suited)19 – A-10 (not suited)20 – K-J (suited)16

Analysis of poker strategies in heads-up poker5. Mathematics in Texas Hold'em PokerPoker is a game of psychology and mathematics. The best players in the world all have astrong handle on both of those aspects. The deck of cards and its possibilities form themathematics that every poker player should be aware of and the other players and theircards. To play poker, intuition can play a big roll, but some awareness of the mathematicsin poker is essential for a good player. Without that awareness, it is difficult to estimatethe best course of action based on what incomplete information you have at any point inthe poker hand up until showdown7.Learning how to properly count the outs and calculate poker odds is a fundamentalrequirement of Texas Hold’em. But first the number of possible starting hands will bediscussed.5.1 Number of Possible Starting HandsIn Texas Hold’em there are 2,652 possible starting hands (52 times 51) because the firsttwo cards dealt can be anything out of the deck. But not all 2,652 are different hands,because the same two cards dealt in two different orders are still the same hand.is still the same hand as.So, that gives 1,326 possible starting hands in Texas Hold’em poker. These 1,326 startinghands are not all different in their value, because there is no hierarchy of suits in poker.17

Analysis of poker strategies in heads-up pokerANDThe hands above are both equal in value as a starting hand. Viewed in this way, there areno more than 169 possible starting hands in Texas Hold’em poker7.The possibility of a hand being suited is very important to the Hold’em player so thatthere are 78 possible suited starting hands (13 times 12 divided by 2) and 78 possiblenon-suited starting hands.ANDThe hands above are different in their value, because a suited hand gives the extraprobability on a flush.To sum it up, the total 169 possibilities break down as7: 13 possible pairs; 78 mismatched cards that are not suited; 78 mismatched cards that are suited.5.2 The importance of odds in PokerPoker odds are a very important concept in poker. It gives the player an idea on how goodor bad his situation is. The following example gives an idea on how odds work8.Let us say you and a friend are flipping a quarter and he gives you 1:1 odds that the nextflip will land on heads. You already know that it will land on heads 50% of the time, and18

Analysis of poker strategies in heads-up pokerit will land on tails the rest of the time. In this case, he is giving you an even bet, becausenobody has a statistical advantage.But what if we said that the friend feels very lucky today and offers you 2:1 odds that thenext coin flip will be heads. Of course you will take this bet, because the chances ofheads or tails coming up are still 1:1, while he is paying you at the 2:1 rate. Your friend ishoping to ride his luck a little longer, but if he gambles with you long enough, he isbound to loose a lot of money with these kinds of odds.The above example is a simplified version of what goes on in Texas Hold’em all thetime. This is summed up in this short principle8:In poker, there are two types of players. The first group consists of players who take badodds in hopes of getting lucky. The second group consists of players who cash in on thegood odds that are left by the first group.5.3 Hand Odds and Poker OddsNext to poker odds there are the hand odds. Hand odds are the chances of making a handin Texas Hold’em poker.To give an example: if a player holds a pair of 2’s and the flop does not contain a 2, theodds of hitting a 2 on the turn is 22:1 and the odds of hitting a 2 on the turn or the river is12:1. How to calculate these odds is described in Chapter 5.4 and 5.5.In Table 1 for some hands the odds are shown.19

Analysis of poker strategies in heads-up pokerOuts OneTwoOne Two Draw TypeCard % Card % Card CardOdds Odds12%4%4623Backdoor Straight or Flush (Requires two cards)24%8%2212Pocket Pair to Set37%13%147One Overcard49%17%105Inside Straight / Two Pair to Full House511%20%84One Pair to Two Pair or Set613%24%6.73.2No Pair to Pair / Two Overcards715%28%5.62.6Set to Full House or Quads817%32%4.72.2Open Straight919%35%4.11.9Flush1022%38%3.61.6Inside Straight & Two Overcards1124%42%3.21.4Open Straight & One Overcard1226%45%2.81.2Flush & Inside Straight / Flush & One 85 Flush & Open Straight / Flush & Two Overcards1634%57%1.90.7517 37%60%1.7 0.66Table 1: Card odds for some draw types8To calculate hand odds, the number of outs is very important. An out is defined as a cardin the deck that helps you make your hand8. If a player holds two spades in his hand andthere are two spades on the flop, there are 9 more spades in the deck (since there are 13cards of each suit). This means that the player has 9 outs to hit his flush. This howeverdoes not mean that this players’ hand is the winning hand.It is, of course, possible that one of the other players has a spade as well. Normally, aplayer does not know what his opponents hold, so he can only calculate odds with theknowledge that is available to him.In Table 2 the number of outs for some hand draws can be seen.20

Analysis of poker strategies in heads-up pokerFlopSpecific Outs#OutsDrawHandPocket Pair to Set[4 4 ] [6 7 T ] 4 , 4 2One Overcard[A 4 ] [6 2 J ] A , A , A 3Inside Straight[6 7 ] [5 9 A ] 8 , 8 , 8 , 8 4Two Pair to Full House[A J ] [5 A J ] A , A , J , J 4One Pair to Two Pair or Set[J Q ] [J 3 4 ] J , J , Q , Q , Q 5No Pair to Pair[3 6 ] [8 J A ] 3 , 3 , 3 , 6 , 6 , 6 6Two Overcards to Over Pair[A K ] [3 2 8 ] A , A , A , K , K , K 6Set to Full House or Quads[5 5 ] [5 Q 2 ] 5 Q , Q , Q , 2 , 2 , 2 7Open Straight[9 T ] [3 8 J ] Any 7, Any Q8Flush[A K ] [3 5 7 ] Any heart (2 to Q )9Inside Straight & TwoOvercards[

Poker is a game of mathematics and psychology. The psychology plays a role in the analyses of opponents’ strategies, bluffing, and hiding your own strategy. Mathematics is important in the calculation of poker odds and pot odds. Good