Texas Holdem Starting Hands Ev

Home Strategy Texas Hold'em Poker. 10 More Hold'em Tips: Understanding Expected Value. The same goes for being the best starter — it has the most positive EV of all starting hands in hold'em.

A pair of aces is the best pre-flop hand in Texas Hold'em Poker

In the poker game of Texas hold 'em, a starting hand consists of two hole cards, which belong solely to the player and remain hidden from the other players. Five community cards are also dealt into play. Betting begins before any of the community cards are exposed, and continues throughout the hand. The player's 'playing hand', which will be compared against that of each competing player, is the best 5-card poker hand available from his two hole cards and the five community cards. Unless otherwise specified, here the term hand applies to the player's two hole cards, or starting hand.

2Limit hand rankings

Essentials[edit]

There are 1326 distinct possible combinations of two hole cards from a standard 52-card deck in hold 'em, but since suits have no relative value in this poker variant, many of these hands are identical in value before the flop. For example, A♥J♥ and A♠J♠ are identical in value, because each is a hand consisting of an ace and a jack of the same suit.

Therefore, there are 169 non-equivalent starting hands in hold 'em, which is the sum total of : 13 pocket pairs, 13 × 12 / 2 = 78 suited hands and 78 unsuited hands (13 + 78 + 78 = 169).

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These 169 hands are not equally likely. Hold 'em hands are sometimes classified as having one of three 'shapes':

Pairs, (or 'pocket pairs'), which consist of two cards of the same rank (e.g. 9♠9♣). One hand in 17 will be a pair, each occurring with individual probability 1/221 (P(pair) = 3/51 = 1/17).

An alternative means of making this calculation

First Step As confirmed above.

There are 2652 possible combination of opening hand.

Second Step

There are 6 different combos of each pair. 9h9c, 9h9s, 9h9d, 9c9s, 9c9d, 9d9s

To calculate the odds of being dealt a pair

2652 (possible opening hands) divided by 12 (the number of any particular pair being dealt. As above)

2652/12 = 221

Suited hands, which contain two cards of the same suit (e.g. A♣6♣). Four hands out of 17 will be suited, and each suited configuration occurs with probability 2/663 (P(suited) = 12/51 = 4/17).

Offsuit hands, which contain two cards of a different suit and rank (e.g. K♠J♥). Twelve out of 17 hands will be nonpair, offsuit hands, each of which occurs with probability 2/221 (P(offsuit non-pair) = 3*(13-1)/51 = 12/17).

It is typical to abbreviate suited hands in hold 'em by affixing an 's' to the hand, as well as to abbreviate non-suited hands with an 'o' (for offsuit). That is,

QQ represents any pair of queens,

KQ represents any king and queen,

AKo represents any ace and king of different suits, and

JTs represents any jack and ten of the same suit.

There are 25 starting hands with a probability of winning at a 10-handed table of greater than 1/7.^[1]

Limit hand rankings[edit]

Texas Holdem Starting Hands Chart

Some notable theorists and players have created systems to rank the value of starting hands in limit Texas hold'em. These rankings do not apply to no limit play.

Sklansky hand groups[edit]

David Sklansky and Mason Malmuth^[2] assigned in 1999 each hand to a group, and proposed all hands in the group could normally be played similarly. Stronger starting hands are identified by a lower number. Hands without a number are the weakest starting hands. As a general rule, books on Texas hold'em present hand strengths starting with the assumption of a nine or ten person table. The table below illustrates the concept:

Chen formula[edit]

The 'Chen Formula' is a way to compute the 'power ratings' of starting hands that was originally developed by Bill Chen.^[3]

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Highest Card: Based on the highest card, assign points as follows:; Ace = 10 points, K = 8 points, Q = 7 points, J = 6 points.; 10 through 2, half of face value (10 = 5 points, 9 = 4.5 points, etc.)

Pairs: For pairs, multiply the points by 2 (AA=20, KK=16, etc.), with a minimum of 5 points for any pair. 55 is given an extra point (i.e., 6).

Suited: Add 2 points for suited cards.

Closeness: Subtract 1 point for 1 gappers (AQ, J9); 2 points for 2 gappers (J8, AJ).; 4 points for 3 gappers (J7, 73).; 5 points for larger gappers, including A2 A3 A4

Add an extra point if connected or 1-gap and your highest card is lower than Q (since you then can make all higher straights)

Phil Hellmuth's: 'Play Poker Like the Pros'[edit]

Phil Hellmuth's 'Play Poker Like the Pros' book published in 2003.

Tier	Hands	Category
1	AA, KK, AKs, QQ, AK	Top 12 Hands
2	JJ, TT, 99
3	88, 77, AQs, AQ
4	66, 55, 44, 33, 22, AJs, ATs, A9s, A8s	Majority Play Hands
5	A7s, A6s, A5s, A4s, A3s, A2s, KQs, KQ	Majority Play Hands
6	QJs, JTs, T9s, 98s, 87s, 76s, 65s	Suited Connectors

Statistics based on real online play[edit]

Statistics based on real play with their associated actual value in real bets.^[4]

Tier	Hands	Expected Value
1	AA, KK, QQ, JJ, AKs	2.32 - 0.78
2	AQs, TT, AK, AJs, KQs, 99	0.59 - 0.38
3	ATs, AQ, KJs, 88, KTs, QJs	0.32 - 0.20
4	A9s, AJ, QTs, KQ, 77, JTs	0.19 - 0.15
5	A8s, K9s, AT, A5s, A7s	0.10 - 0.08
6	KJ, 66, T9s, A4s, Q9s	0.08 - 0.05
7	J9s, QJ, A6s, 55, A3s, K8s, KT	0.04 - 0.01
8	98s, T8s, K7s, A2s	0.00
9	87s, QT, Q8s, 44, A9, J8s, 76s, JT	(-) 0.02 - 0.03

Nicknames for starting hands[edit]

In poker communities, it is common for hole cards to be given nicknames. While most combinations have a nickname, stronger handed nicknames are generally more recognized, the most notable probably being the 'Big Slick' - Ace and King of the same suit, although an Ace-King of any suit combination is less occasionally referred to as an Anna Kournikova, derived from the initials AK and because it 'looks really good but rarely wins.'^[5]^[6] Hands can be named according to their shapes (e.g., paired aces look like 'rockets', paired jacks look like 'fish hooks'); a historic event (e.g., A's and 8's - dead man's hand, representing the hand held by Wild Bill Hickok when he was fatally shot in the back by Jack McCall in 1876); many other reasons like animal names, alliteration and rhyming are also used in nicknames.

Notes[edit]

^No-Limit Texas Hold'em by Angel Largay
^David Sklansky and Mason Malmuth (1999). Hold 'em Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-22-1
^Hold'em Excellence: From Beginner to Winner by Lou Krieger, Chapter 5, pages 39 - 43, Second Edition
^http://www.pokerroom.com/poker/poker-school/ev-stats/total-stats-by-card/
^Aspden, Peter (2007-05-19). 'FT Weekend Magazine - Non-fiction: Stakes and chips Las Vegas and the internet have helped poker become the biggest game in town'. Financial Times. Retrieved 2010-01-10.
^Martain, Tim (2007-07-15). 'A little luck helps out'. Sunday Tasmanian. Retrieved 2010-01-10.

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People play no-limit hold'em for all sorts of reasons — the fun of competition, the entertainment value the game provides, the opportunities for social interaction, and more. Of course, winning money is the central motivation for serious no-limit hold'em players, and it's usually a priority even for amateurs or 'recreational' players as well.

If winning money is important to you and one of the reasons why you play hold'em, understanding expected value is of primary importance.

Understanding Expected Value: Defining EV

There are a couple of ways to think about the concept of 'expected value' or 'EV' for short. One is simply to think of it as the average expectation of gain or loss on any given wager as indicated by the probabilties the wager offers.

Usually those explaining expected value in this way talk about betting on a coin flip, a simple enough example. You've been invited to guess which side the coin will land on, heads or tails, and to bet $1 on your choice against someone else who is also betting $1 you'll get it wrong. If you guess heads and it lands on heads, your opponent gives you $1. If you guess heads and it lands on tails, you have to give the other person $1.

You can win or lose $1 here, but that's not the 'expected value' of the wager. Rather the EV of the bet is found via a formula.

EV = (% Chance of Winning * $ Won) - (% Chance of Losing * $ Lost)

In the case of the coin flip, you have exactly a 50% chance to win $1. You also have exactly a 50% chance to lose $1. Plug those figures into the formula — you can see where this is heading — and you get 50% of $1 (or 50 cents) minus 50% of $1 (50 cents) again and a result of exactly zero:

EV = (0.50 * $1) - (0.50 * $1) = $0.50 - $0.50 = $0.00

A wager like this would be described as one with 'neutral' expected value. That said, when you make that bet the first time, you are either going to end up $1 up or $1 down. In other words, whatever the expected value of a wager happens to be, it does not necessarily have to represent a possible outcome when you make that bet. In fact, often it does not. Rather it represents an average as indicated by the wager's probabilities.

As we said, there are a couple of ways to think about EV. One is to think of it as an average as expressed by that formula. The other is to think of EV as an indicator of the long term value of making the same wager multiple times. We're essentially talking about the same thing here, just describing it slightly differently.

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Instead of betting on a coin flip just one time, say you've been offered the chance to bet $1 on 100 coin flips. Each flip is still a 50-50 proposition, of course, and so in each instance your expected value is going to be neutral or $0.00. However here you will be investing $100 total, and if you are correct exactly 50 times with your guesses you'll win exactly $100 (coming out even). If you are correct more often, you'll win more and profit, and if you are incorrect more than 50 times you'll come away a loser after the coin flips.

But it doesn't matter what the results actually are — it's still a bet with zero or 'neutral' EV, every time you make it. By thinking long term like this and imagining the wager being repeated 100 times, you can understand more readily whether or not you should accept the proposition and make the bet even just one time.

Let's present a wager for which the EV isn't neutral — say, a lottery. You can buy a ticket for $1 and have a chance to win $1,000,000. But your chance of winning is 1 in 2 million. What is the expected value?

Using our formula for calculating EV, we can see the EV here is actually negative:

EV = (0.0000005 * $1,000,000) - (0.9999995 * $1) = $0.50 - $0.9999995 = -$0.4999995

Buy one lottery ticket and lose, and you're out $1. Meanwhile the EV of the wager is almost -$0.50. In order for the EV to be positive, your chance of winning the $1 million prize for your $1 ticket would have to be better than 1 in 1 million. That's not an offer you're going to see in any lottery, of course, which are always going to be negative EV wagers (unless somebody makes a colossal mistake setting up the lottery!).

Understanding Expected Value: Applications to No-Limit Hold'em

Moving over to no-limit hold'em, we are constantly being presented with invitations to make wagers like the coin flip bet or buying a lottery ticket. Being able to calculate the EV of each wager being proposed to you is crucial to being a profitable player, as you have to be able to learn which are positive EV (and take them) and which are negative EV (and avoid them).

The evaluating of EV begins with your starting hand selection. You've heard -offsuit called the worst hand in no-limit hold'em, but in truth that proclamation is all about the expected value of the hand. The same goes for being the best starter — it has the most positive EV of all starting hands in hold'em.

Tracking programs and 'HUDs' used by those playing online poker have helped pinpoint the EV of different starting hands in no-limit hold'em thanks to the high volume of hands being evaluated. They've also helped show the EV of various other aspects of the game, highlighting things like the importance of position in NLHE by showing EV to be negative (for most players) when playing from early positions (e.g., small blind, big blind, under the gun) and EV to be positive (for most) when playing from later positions (the cutoff, the button).

Texas Holdem Hands Chart

Those are examples of where understanding EV helps you learn which starting hands and which positions tend to be more profitable for you. You might win a single hand after limping in from under the gun with , but if you did the same thing 100 or 1,000 times — that is, if you made the same 'wager' by calling the big blind with your suited rags from early position over and over — you'd most likely end up a net loser, with the average amount of money lost over all of those trials an indication of the negative EV of the play.

Understanding EV helps with other specific decisions in no-limit hold'em hands, too, such as the one you face when calling a bet while holding a drawing hand. Say you have and have reached the turn versus an opponent with the board showing . There is $200 in the middle, and your opponent just went all in with his last $100.

Knowing how to calculate pot odds, you can see you're being offered a wager here that requires you to risk $100 in order to try to win $300 — that's 3-to-1 pot odds. Knowing also how to count outs, you know that nine clubs remain among the 46 unseen cards, giving you just under a 20% chance of making a flush on the river. (Let's say you trust the flush will be the winning hand — i.e., that your opponent doesn't have a set that would remove a couple of your outs since they'd make your opponent a full house.)

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Maybe you didn't realize it, but when you compare those 3-to-1 pot odds and your (roughly) 1 in 5 chance of making a flush, you're doing a calculation of the expected value of making the call here. We can recall our EV formula to illustrate this:

EV = (% Chance of Winning * $ Won) - (% Chance of Losing * $ Lost)
EV = (0.20 * $300) - (0.80 * $100) = $60 - $80 = -$20

The call has a negative EV. This one time you'll either win $300 or lose $100, but if you were to make the call 100 or 1,000 or 10,000 times, you can expect to lose on average $20 per call. Fold!

Conclusion

Understanding expected value has the great benefit of helping you think less about the short-term wins and losses that occur with each hand of no-limit hold'em that you play and focus instead on the long-term and your results over a larger sample size of the decisions or 'wagers' you are accepting (or declining).

Best Holdem Starting Hands

The more positive EV bets you accept, the more you will ultimately profit, while taking more negative EV gambles will result in your losing more at the tables. As we said at the beginning, for some players of no-limit hold'em, winning money isn't necessarily the only reason they play. They may like playing more hands (including bad ones), making lots of loose calls from out of position, and never folding a flush draw when they have one.