Player’s Guide

A New Guide to the Starting Hands

in Texas Hold’em Poker.

The key decision any hold’em player makes is whether or not to play the starting 2 card hand they are dealt. And, if so, how to play it.

We present here some valuable new facts.

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Our Model

We have developed these new facts from a new, very comprehensive, computer simulation of our own design.

Simulate? Smiluate!

This document is a Player’s guide. It’s meant to bring the practical implcations of our results to bear. To be helpful to the hold’em player who may or may not care about simulation.

If you’re a poker player who is also a technical person, or if you’re just curious what a sophisticated simulation program looks like inside, then we invite you to ask about getting the complete source code of this program as well as the detailed print outs from a rreasonable run.

For information about how to secure the source code and detailed print outs, see our web page at: http://www.evgr.com/poker, or write to us by e-mail or snail-mail at the address(es) on the cover.

This source code constitute the proofs as to the facts we do summarize here. Usually the best you can get from a poker book is the author’s naked recommendations. No proof, no detailed calculation worksheets and certainly no source code.

Shuffle and Deal

First, imagine a simple computer program that shuffles a regular deck of 52 cards and deals out hands to 10 players, plus 5 community cards face up on the board.

The “shuffle” involves picking these 25 cards at random (without replacement) from the deck of 52

“Dealing” is done simply by assigning beforehand particular sequence numbers to particular parts of a complete round of play. the 7th card picked, for example, is always the 1st card dealt to player 7, and so on.

Randomized shuffling and dealing should be part of any poker simulation. The only thing unusual in what we have done is to have read about, and worried a greal deal over, the quality (and efficiency) of the random number generator algorithm we would use. For more details on that, check out random.zip in the FREEWARE section of our website (http://www.evgr.com/poker).

Hero’s Play

Player 1 is always our hero. Whatever starting hand our hero is dealt becomes the focus hand in that round of play. Focus hands are always played aggressively all the way to the river.

To illustrate this, suppose Player 1 gets dealt a pair of 5’s. During that round all of the other players make four decisions:  (a) to play or fold before the flop, (b) play or fold after the flop,(c) play or fold after the turn and (d) play or fold after the river card is turned up.

At the showdown it may be that everyone but our hero has folded. Fine, then 55’s frequency counter for 0 river foes gets bumped by 1. And 55’s win counter for 0 foes at the river also gets bumped by a fraction, depending at what stage of play the last foe in the round folded.

Depending on the HE Table environment, there will usually be one or more foes contesting the river. If it turns out that our hero has a winning-ranked hand along with one or more foes, then this tie is divided up proprtionately. Let’s say hero ties with 2 foes, then hero’s frequency counter for 2 foes gets bumped by 1 and his win counter for 2 foes gest bumpted by 0.3333.

So, we continue in this way for several million (or billion) rounds of play, keeping track of the frequencies and wins for each condition being examined in the simulation. When the run is done, our program then goes through and calculates, for each condition, the liklihood of winning, or p(win) and saves that information as well.

Foes

Foes are always players 2,3,4,5,6,7,8,9 and up to 10, depending on the particular condition. the foes our hero faces sit at 5 different HE Tables in the same round. Don’t try this in a poker room. It only works on a computer.

HE Tables 1, 2, 3 and 4 always have 10 players.

At HE Table 1 they play as tight as you’ll likely ever find. Every foe assumes that there will only, on average, be 2.5 other players seeing the flop. He/she plays rationally, based on an expert knowledge of “old” facts.[1] In this case he/she would play the hand he/she was dealt only with knowledge that it had favorable odds of winning at a HE Table with 3.5 players (since he/she will always see our hero’s bet).

If the foe was player 8 or 9, however, he/she would have additional information. there would be the cumulative prior action of all preceding players (our hero and other foes) to use as well as an expectation about overall HE Table conditions.

HE Tables 2, 3 and 4 are similar to HE Table 1 except they are progressively “looser” in pre-flop play.

the idea of “looseness” is not vague in this simulation model. It, and how the foes play, consist exactly of the following rules strictly enforced (as only a computer can do).

ü      At HE Table 1 if a player does not have any current information, that is no other player has acted yet, a foe will always assume at least 2.5 small bets have been (or will be) put into the pot, as we just described above. At HE Table 2 the assumption is 3.5. HE Table 3 believes in 4.5 and HE Table 4 foes assume 5.5.

ü      This starting assumption gets modified by actual play. For example, Player 5 always gets to adjust his/her overall assumption about the Table if Players 2, 3 and 4 all are in the pot ahead of him/her.

ü      the foe uses this “assumption” to calculate the odds the theoretical pot is offering for the particular starting hand he/she has just been dealt. This is expert play based on “old” facts.[2]

ü      Armed with (a) the odds of winning at the river against the presumed number of foes for this HE Table, adjusted by the actual number, in case that is greater by the time this foe must make a play/fold decision, and with (b) the odds the presumed pot is offering to continue playing, the foe makes a rational decision whether in fact to play or fold before the flop.

ü      After the flop, the foes at these HE Tables will then play only when they have either a made hand or a 1 card draw to a straight or a flush. At the river, they will play only when they’ve made at least a pair or better. Missed straight and flush draws fold at that point.

At HE Table 5 the players are as loose as possible. they play the classic showdown game where every player goes to the river. Except we provide here for 2 player showdowns (consisting of thero plus Player 2), 3 player showdowns (add Player 3) and so on up to a 10-player showdown (add Players 4 thru 10).

So, HE Table 5 is really 9 different HE Tables, each with a different number of starting players. But instead of numbering them as such we preferred to simply indicate the number of players at the river as being 3, for a 3-player showdown game, 5 for a 5-player game, and so on. That way, we can easily compare them with number of players at the showdown under the more realistic playing conditions of HE Tables 1, 2, 3 and 4.

If you wish, you can imagine in our study that Hero is sitting simultaneously at 5+8=13 different HE Tables, four of them where the foes play their hands quasi-realistically and nine of them where all of the foes play loose and crazy, but at eight of these they are playing short-handed.

Playing Position

Although playing position is generally thought to be the most important factor in selection of starting hands in hold’em, it is not particularly important to the conclusions we’ve drawn here.

We keep track of the fate of starting hands under the control of our hero. All other hands are distributed randomly across position. Our hero is always, in effect, acting “under the gun” but could care less.

If you wish to vary your starting hand selection based on your playing position, which is fundamental to the playing strategies advocated by noted poker authors, then you’ll be using the overall ranking of each hand as a basis for doing so anyway.

That’s it! Or, at least, that’s the beginning of our more detailed story.

Look at it this way. We’ve covered in our model a broad spectrum of HE Table conditions varying from very tight to maximally loose. We’ve also covered the issue of number of players in both possible ways: the number of players at the HE Table in the first place, and the number of good players out of 10 who play rationally and by doing so end up as foes at the river.

This simulation is, we believe, unique

Aggression

Since  our hero always plays aggressively, we need to be able to separate out the wins that occur because of the absolute winning power of the hand from those that occur because the winning hand folded before the showdown, at least for HE Tables 1, 2, 3 and 4. The proportion of p(win) that is left represents the pure power of the hand.

The first step is to find out how much of the total p(win) is due to the winning hand having folded before the showdown. This is shown in Figure ___ as fluctuations above and below the zero plane..

This is easy in the case of HE Table 5, because every foe is playing aggressively as well. Figure __ shows the difference between chance p(win), for each condition in our model, and actual p(win) accumulated across all 169 starting hands. the zero plane is chance, and you will be able to see that regardless of the number of players in the game, in this case, there is no difference between chance and actual p(win)s for HE Table 5.

Any fluctuation above or below the zero plane in the Figure reflects cases where a random hand played aggressively either picks up wins from hands that could have won if they had not folded (above zero), or loses wins because the hand was played too aggressively. That is, our hero should have folded sometimes (below zero).

Somewhere between the HE Table 2 and HE Table 3 overall playing conditions aggression acquires value, at least against a small number of foes.

At some tighter playing conditions aggression with a random starting hand is a losing strategy. At some looser playing conditions aggression with a random hand has positive value.

Since the only difference in the foe’s decision rules between HE Tables is on whether or not to play before the flop, we can see that when everyone at the Table believes there will be an average of about 5 players seeing the flop, or so, selective aggression can become an important factor in play. This increase in overall expectation can be dramatic, especially when only 1 or 2 foes survive to the river.

Figure 1 also shows as the number of foes who play to a showdown increases, when each has an opportunity to fold, the less value there is in aggression with a random starting hand. In other words, the more likely you are to be beat.

Power

So, by subtracting from the measured p(win)s in our simulation run the effect of aggression, we are left with an estimate of the pure playing power of each of the 169 starting hands in Texas hold’em.

We turn now to see how well some of the conventional authorities and writers have done in the past when attempting to derive this estimate of power .. using private methods never fully revealed, even if you buy their book(s).

We sill examine in detail the recommendations about startintg hold’em hands in each of the following poker classics,

ü Hold’em Poker by David Sklansky and Mason Malmuth

ü Winning Low Limit Hold’em by Lee Jones

ü “Super/System’s Power Poker Course in Limit Hold’em” by Bobby “The Owl” Baldwin, in Super/System by Doyle “Texas Dolly” Brunson.

Sklansky Groups

Sklansky was the first poker author to have both ranked all of the starting 2-card hands, and then grouped them with recommendations about how to play each group.

David “Einstein” Sklansky (a nickname attributed to him in Doyle Brunson’s book, Super/System) has been a professional poker player and poker theoretician for decades, and his advice is widely respected.

As for the starting hold’em hands, did he get it right?

The Sweet 16.

Let’s start off with the good ones. The top 16 ranked starting 2-card Hold’em hands are fundamental to solid play. They constitute only about 7% of all hands you will be dealt, however, so it’s improbably that you will get rich by limiting your play to just these.

But it is imperative for good play that you KNOW what they are, and how well they stack up against each other.

Table 1 - Sklansky's Group 1 hands

 AA KK QQ JJ AKs

Sklansky (actually Sklansky and Malmuth, which we will shorten to S&M to save space here) defined 5 members of Group 1, as shown in Table ___above. They also indicate in their book that  the overall rank order of these hands is as shown reading from left to right. AA, that is, is the highest ranking hand of all.

We confirmed, as shown in Figure __, that these are, indeed, the 5 best starting 2-card hands as well as that their actual ranks within the group are exactly as S&M represent.

AA and KK are substantially more powerful than lower ranking hands, however, even than QQ. These two hands are also the only ones with positive power ratings at HE Table 1.

You will recall this was the “tightest” HE Table in our study. Under very tight HE Table conditions these are the only starting hands that should be raised for value. But, as we shall see, if you find yourself at a very tight HE Table you should probably get up and go find better playing conditions anyway.

Table 2  - Sklansky's Group 2 hands

 TT AQs AJs KQs AK

The S&M Group 2 hands are shown above.

Since S&M indicate that their determination of relative rank order within the group is “approximately” as shown, from left to right., we need to point out a minor correction before otherwise endorsing the membeship of Group 2.

The overall power of AK is slightly greater than that of KQs, so we would reverse the order of these two hands within the Group.

We confirm that the membership of Group 2 is the same as that asserted by S&M. Or, rather, we confirm that these hands rank 6, 7, 8, 9 and 10 in overall playing power. However, there is actually a small advantage held by AK over KQs, so our list (Figure ___) shows a correction in the relative rank order within the group, which is just a matter of fine detail.

.Why Raise?

There are 10 hands in these groups, but they are not treated equivalently for purposes of decisions to raise (or not).

Although the S&M rationale for doing so certainly appears to be plausible enough, they do not present any computational rationale or other proof. One must take some of it on faith. As it turns out, however, there have probably been some errors made in these recommendations.

S&M give different reasons for raising (or not), including each of the following.

ü      raise 4  (AA, KK, QQ, AK) in part because “..they lose much of their value in large multi-way pots.”

ü      raise 4 (Aks, Aqs, AJs and KQs) only sometimes in part because “..they do play well in multi-way pots.”

ü      raise 1 (JJ) in a tight game ”..to get out hands like A9.” the idea being that this hand also loses value in multi-way pots, or perhaps that it has less value at a loose HE Table .. which is a similar, but not identical idea.

ü      Never raise1 (TT) for reasons that are not stated.

These are key ideas in current hold’em playing strategy. Since S&M assume certain difficult to prove facts that our model encompasses, however, we can put these assumptions to test.

We measure directly the effect of multi-way action. Also, we vary the degree of looseness of the Table in seeing the flop. So, we can separate out the effects of HE Table conditions and number of foes contesting the pot for each starting hold’em hand.

When we look at these facts for the 10 best starting hands, we get the results shown in Table ___ (below).

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Table 3 - MAD[3] Sensitivity to Playing Conditions

 Rank Hand Table nFoes T x F 1 AA 0.0 0.0 0.0 2 KK 0.1 0.0 0.1 3 QQ 2.3 1.9 2.5 4 JJ 5.7 4.6 6.6 5 AKs 6.1 5.3 7.2 6 TT 7.1 3.7 7.2 7 AQs 5.3 5.4 8.9 8 AJs 9.7 9.0 13.1 9 AK 13.3 20.6 27.9 10 KQs 5.7 4.2 8.4

The mean absolute deviation[4] (MAD) in the rank of a hand among all starting hands is a measure of sensitivity by the hand to playing conditions. Table ___shows MADs for variations in HE Table conditions, variations in number of quasi-realistic foes contesting the pot at the river and in combinations (or interactions) of these two conditions.

Of the 4 hands S&M assume would be most sensitive to multi-way action (AA, KK, QQ, AK) only one (AK) actually is. In fact, it’s mean absolute deviation in rank (among all 169 possible hands) due to varying numbers of foes at the river, at 20.6, makes it one of the most sensitive of hands.

By contrast, the very least sensitive hands to multi-way action are AA, KK and QQ.

Of the 4 hands S&M assume “play well” in multi-way pots (AKs, AQs, AJs and KQs), this conclusion can only be correct if by playing well what is meant is that in each case the hand ranks at about the median of all 169 possible hands in sensitivity to multi-way action.

These hands that are presumed to “play well” in multi-way pots do NOT increase in relative value with increasing multi-way action at all, as many current poker players are inclined to believe.

S&M ignore TT and reserve a special status for JJ in terms of multi-way action. Yet, neither of these hands seem particularly sensitive to multi-way action and it is difficult therefore to take those recommendations too seriously.

Table 4 - Mean Rank Order of Hands

 Number of Players at River Rank 2 3 4 5 6 1 AA 1.0 1.0 1.0 1.0 1.0 2 KK 2.0 2.0 2.0 2.0 2.0 3 QQ 3.0 3.0 3.0 3.0 3.0 4 JJ 14.4 4.8 4.4 4.3 4.0 5 AKs 5.0 5.4 5.4 7.2 26.6 6 TT 26.4 11.0 8.0 6.0 5.8 7 AQs 9.2 8.6 8.6 11.8 33.0 8 AJs 9.2 8.6 8.6 11.8 33.0 9 AK 7.5 7.8 10.0 26.2 40.0 10 KQs 11.2 12.2 18.2 18.0 20.0

Another way to look at these assumptions is to show the mean rank order of each hand for 2, 3, 4, 5 or 6 foes at the river, as shown in Table ___ (above).

S&M ignore TT, but it actually benefits from multi-way action, as does JJ. We would therefore urge you to consider raising these hands for value if the raise is not likely to drive out foes in a loose game

Five of these hands are particularly vulnerable to heavy multi-way action, the kind that increases the liklihood of 6 or more foes playing to a showdown (Aks, AQs, AJs, KQs and AK). With moderately loose showdown action they are neither especially sensitive, one way or the other.

One hand, AK, suffers tremendously with nearly every additional foe who plays to a showdown. This is the only hand in the group that should be raised pre-emptively in an effort to weed out the competition.

With these changes, then, we would recommend a re-write of the pre-flop raising recommendations for Sklansky Group 1 and Group 2 starting hold’em hands.

Table 5 - Sklansky Group 3 Hands

 99 *JTs QJs KJs ATs AQ

There are 6 members of S&M Group 3, as shown in Table __ (above).

One hand, JTs, doesn’t belong in the group. But KTs does. Also, the rank order of each hand in the Grpup is slightly different than Sklansky suggested. These changes have been reflected in Figure __ which is the rank ordered power hands that fall in the 11th, 12th, 13th, 14th, 15th and 16th overall. positions

This discrepancy has the following potential impact on player strategy.

S&M recommend playing only Group 1-3 hands in a tough game from early position. If you follow this recommendation, you should fold JTs from an early position in a tough game, and start playing KTs instead.

So, that’s it for the Sweet 16. Did Sklansky get them right?

In terms of group membership, only 1 hand out of the 16 needed to be replaced, although error of ranking within groups tended to increase. In fact, as we shall see, this error becomes even greater as we move down into the area of Expert playing hands.

In terms of stated rationale for various raising/calling strategies, however, there was considerable error among these very best of hands.

The Expert 24 and the Medium Suited Connector Myth

When we add the next highest ranking 8 cards to the Sweet 16, we reach what we consider to be the smallest playable subset of starting hands.

In doing so, however, we encounter what we have chosen to call the “Medium Suited Connector myth.”  Like most myths, it contains some elements of truth. But the truth has been blown way out of proportion.

Figure 6  - Sklansky Group 4 Hands

 *T9s KQ 88 QTs *98s *J9s AJ *KTs

There are four hands in S&M’s Group 4 that do not belong. In the case of one of these, KTs, it got moved up to Group 3 and was replaced by JTs, which was demoted from Group 3. This was a relatively minor adjustment in hand rankings.

But we are left with 3 suited connectors (T9s, 98s and J9s), the valiues of which keep being rediscovered every year or so, but whose true values have not been put in perspective in practical terms for the regular hold’em poker player.

We need to consider here the overall context, to look at all of the medium suited connecotrs together, to gain some perspective.

Figure ___ shows the rank for each medium (and small) suited connector, starting with T9s and working down through 54s. The mean rank of these hands is shown for each of Tables 1, 2, 3, 4 and 5.

You will note that the classic 10-player showdown results (T5) show a very simple, linear deterioration in the relative rank order of these starting suited connectors as the value of the top card gets smaller. This was discovered sometime around 1972.

A few years later several people discovered that some of the smaller suited connectors (such as 87s and 76s) sometimes played better than their larger cousins (such as T9s). This reversal of the 10-player showdown results was both surprising, and held as a professional holdem players’ trade secret by many. This U-Shaped effect is clearly visible in the HE Table 1 results shown in Figure____.

The problem is that playing in the extremely tight games, such as those we characterize here by HE Table 1, it is difficult to make any money: the pots are small (which is the natural consequence of tight players), and these medium suited connectors, even though they improve dramatically, never rise to the level of being powerhouse starting hands.

In fact, as the games become looser there is a clear trend visible in Table ___ for the showdown linearities to dominate. Even if you think you’re playing under the ideal conditions for medium suited connectors, if one player leaves or a new player joins the game your assumption may suddenly no longer be correct and intertia could easily lead you to end up playing what are just  relatively weak hands.

Another thing that is potentially dangerous is to rely on various “probe” software packages common available today that allow you to pit one hand against another to a showdown, seeing which of them is better.

These would be fine, and the results reliable, so long as there do not exist any underlying non-linearities of the type visible in Figure __ for medium suited connectors. But we DO know that assjmption is incorrect, and it has been known to be incorrect in the poker literatures for decades. We recommend that, unless you already know the answers to the questions you’re seeking and simply want to be precise, you do NOT use isolated one-on-one type simulations at all (the U-Shaped function we’ve already discussed is not the only one in the underlying fabric of Texas hold’em).

Turning back now to the Sklansky Group 4 hands, we need to replace the 4 deviant hands by better ones.(A8s, A9s, JTs and AT). Because the T4 and T5 HE Table conditions still have positive power ratings two of these (J9s and T9s) have a high enough overall power index to just be demoted to Group 5 while the third (98s) slips down to Group 6.

The Starving Play List

We come now to our first overall recommendations regarding limit hold’em play strategies. We call it the “Starving Play List” because it should be appropriate to the most risk-averse, or conservative player.

ü      Pick your 10-player HE Table carefully. Look for players who seem to be having fun, and where at least half of the stay in to see the flop. Table selection is a major determinant of how well your hands will hold up in the long run.

ü      Play only the top 24 hands, as shown in Figure__ thru__. Be sure to note that the figures indicate groups rather than particular hands. That is AdTd means ATs, and  KcQh means any KQ except KQs, etc.

In poker, when every other player knows what your hand is, you suffer tremendous disadvantage. Just playing good cards is not sufficient, nor is raising AA and KK only. You need a carefully planned but hard to read raising strategy. We suggest using what we call a “parallel game” plan.

Suppose you play lower limit games like 3/6, 5/10/, 6/12 and 10/20, but would play other games such as 6/6 or 10/10 if they were spread.

You can decide to play two different limit games at the same time, at the same table, simply by having the following betting strategy:  play hands 1-12 at a \$10/\$10 HE Table, while hands 13-24 you play at the \$5/\$10 HE Table. This is quite simple. You just decide to always raise hands 1-12, and never raise hands 13-24. Otherwise, make appropriate other adjustments in your response to raises by other players before the flop. You can also adjust the fraction of hands you play that you’ll raise, and so on.

The Starving Play List will allow you to play about 3 hands per hour under typical playing conditions. Very conservative, but it will require a great deal of patience.

The Tight Expert’s Play List

If you’d like to play more hands, and are an experienced player, then consider the “Tight Expert’s Play List”, which adds the hands that belong to a corrected Sklansky’Group 5.

The original members of Sklansky’s Group 5, arranged in the order suggested by S&M, are shown below in Table __.

Figure 9 - Sklansky's Group 5 Hands

 77 *87s Q9s *T8s KJ QJ JT *76s *97s *A9s *A8s A7s A6s A5s A4s A3s A2s *65s

There are 18 hands in Sklansky’s Group 5. But 7 of these belong elsewhere. Two (A9s, A8s) deserved promotion to Group 4, as we have already seen.

The five remaining hands are weak suited connectors, and “semi-connectors” (T8s, 97s, 87s, 76s and 65s). We have already discussed the error associated with over-rating the nonlinearities in these hands, especially 87s and 76s.

But these are also among the most sensitive hands to both number of foes and overall tight/loose HE Table playing conditions. 65s, for example, ranks 25th (out of 169) in sensitivity to HE Table conditions, 24th in sensitivity to number of foes at the river and 29th in sensitivity to interactions between these factors.

Indirectly, as a result of their (a) extreme power nonlinearities and (b) extreme sensitivity to HE Table playing conditions, these hands drop out of the top 84 starting hands entirely. In typical limit hold’em casino games at mid and lower limits, these hands should be folded by the advanced player.

The three others (87s, 97s and T8s) are simply demoted. T8s goes to Group 6 while 87s and 97s get moved down to Group 7.

The 7 additions to Group 5 include two (KT and QT) that are obviously closely related to three original members (KJ, QJ and JT) and five higher ranking suited hands (K9s, K8s, Q8s, T9s and J9s) than the small suited connectors they replace. This is because with suited starting hands the rank of the kicker is usually more important than the connected-ness of their values, although with T9s both factors may combine.

If you otherwise follow the S&M guides to poker strategy, some of these changes would impact how you play the game. For example,

“…some hands, such as 87s..play well against many opponents. If there are usually a lot of callers ... these types of hands become playable in early position. However, over playing these hands up front (and most players do just that) can get you into trouble.” (S&M, p.15).

87s is now a Group 7 hand, which S&M do not recommend for play in early position at all. The problem, of course, is that recommending the play of 87s against “many” opponents, without specifying exactly how many or the consequences of not counting accurately, is not clear guidance. S&M do, however, provide themselves an out by the observation that “most players” over play these hands.

We would agree both with (a) not playing Group 7 hands in early position and (b) that anybody who does is over playing them.

You will be dealt one of these starting hands, ranked 1 to 42 globally, about once in every 5 hands. This means you should be involved in about 6 pots per hour. We consider this to be the Tight Expert’s Play List.

The Professional’s Play List

We turn now to Sklansky’s Group 6 hands, as shown in Table __ below.

Table 6 - Sklansky's Group 6 Hands

 66 *AT *55 *86s *KT *QT *54s *K9s J8s

There are 9 members of S&M’s original Group 6. Four of these have already been promoted: AT to Group 4, and three (K9s, KT and QT) up to Group 5. One (55) deserves demotion to Group 7.

A medium 1 gap suited connector (86s) is dropped from the list of playable hands entirely. It has a power profile across HE Table conditions similar to those discussed earlier as Group 5 deviant suited connectors. Also, it’s the 86th ranking hand overall.

We’ve  replaced these 7 changes with the highest available power ratings (T8s, K7s, 98s, A9, K6s, K5s and A8). Some of these are demotions from higher Sklansky Groups as described previously.

These starting hands, ranking from 1 up to 51, constitute 24% of all starting hands. If you follow this Professional’s Play List, you’ll bet in about 1/4th of the pots at your HE Table. But, choose your HE Table with care. Leave tight games or change your strategy.

The Savvy Gambler’s Play List

We turn now to Sklansky’s original Group 7 hands, as shown below in Table ___.

Table 7 - Sklansky's Group 7 Hands

 *44 J9 *43s *75s T9 *33 *98 *64s *22 *K8s *K7s *K6s *K5s K4s K3s K2s Q8s

There are 17 hands in this Group. Unfortunately, 11 of these do not belong here.

The two low pairs, 22 and 33 are not worth playing. Group 8. They have been dropped from all our play lists entirely. Neither are the small suited connectors, 64s, 43s, 75s or the connector 98.. The pair, 44, is demoted down to Group 8.

Suited medium Kx’s have been under valued by S&M, and each of these deserves promotion out of Group 7: K8s up to Group 5, while K7s, K6s and K5s were promoted up to Group 6. S&M had originally placed all Kxs from K2s through K8s into this single Group.

We also recommend a slightly different playing strategy with the corrected Group 7 hands.

S&M recommend Group 7 only when you’re on the Button, with one or more callers in front. In particular, they recommend raising with the small pairs or small suited connectors. But all of these hands have either moved down to Group 8 or taken entirely off the play lists. Each depended on hitting the flop with trips or a flush/straight draw. It turns out, however, there is more value in hoping to hit the flop for a King-high flush draw.

If there is merit in the S&M strategy for Button raises with Group 7 hands in general, then, you should consider each of these hands for the following decision paths: either call unraised pots in late position, raise an unraissed pot from the Button or otherwise fold these Group 7 hands. If you’ve played one then wait for the flop and, if you haven’t made a hand such as a flush draw, trips or two pair, fold.

The Savvy Gambler will have these hands in his/her Play List knowing both that they are good hands with a good flop, that foes generally discount the liklihood you’ll be holding them thus encouraging action when the flop doesn’t look too scarey,  and he/she will have the iron discipline to discard them on those many rounds when the flop goes elsewhere.

The gambling part of this Play List is in the need to pray, or otherwise invoke the Poker Gods, for a suitable flop more than with hands in the other groups.

By adopting the Savvy Gambler’s Play List, without regard to your position, you would on average, participate in about 1/3rd of all pots at your HE Table. The actual number will fall in the range of 1/4rd up to 1/3rd because of raising by other players and your opportunities for late play of these hands. As is true in general, of course, stay away from very tight HE Tables.

The Gambler’s Play List

We turn now to the Group 8 hands which, when added to all of the previous Play Lists, constitute up to 44% of all hands dealt in Texas Hold’em.

Table 8 - Sklansky Group 8 Hands

 *87 *53s *A9 *Q9 *76 *42s *32s *96s *85s J8 *J7s *65 *54 *74s *K9 T8

There are 16 hands in S&M’s original Group 8. Of these, only 2 belong in the group.

Four hands deserved promotion: A9 was moved to Group 6, while K9, Q9, and J7s were moved to Group 7.

Otherwise, all of the remaining changes are demotions out of the Play Lists entirely. Examples are the medium connectors 87, 76, 65 and 54, and the small suited connectors 53s, 42s and 32s. While these hands can sometimes hit ideal flops, and might be played occasionally for surprise value, they are not robust enough overall for us to recommend their play even on the Gambler’s List.

The Jones’ Combinations

Lee Jones, in his book “Winning Low Limit Hold’em,” does not rank all playable hands, so we will have to take a slightly different approach to evaluating his recommendations.

Early Position

Raise with AK, QQ and JJ if “..it will limit the field.” We would strongly urge raising with AK for this purpose, as we have seen. The value of AK deteriorates dramatically as the number of realistic foes increases beyond one at the river. But QQ and JJ actually hold up well, so if you raise these hands it should be for value rather than to limit the field.

“Always re-raise with AA and KK”. Yes, we agree entirely.

Table 9 - Jones Early Position Hands

 AA KK QQ JJ TT AKs KQs QJs *JTs AQs KJs *QTs AJs KTs AK *KQ AQ *AJ

The table above shows 18 hands that Jones recommends for early position play. If we assume that these would be the top 18 ranked hands in the game, then 4 of these do not belong: QTs, JTs, KQ or AJ. In their place should be ATs, AQ, 99 and 88.

But Jones goes on to say that  “..if the game is loose-passive add..” 99, 88, 77, 66, 98s, 87s, QJ, JT, T9, and 98 to the list above.

These should be the 19th thru 28th ranked hands. Unfortunately, we show little correspondence with these recommendations.

So far, of 28 starting hands recommended by Jones we would agree with only about half. This is substantially less than for Sklansky and Malmuth. We leave it as a reader’s exercise to work out the details to compare our rankings with what we have to assume must be Jones’ rankings.

Wrap-Up

We have, during the course of examining in detail the hand rankings of Sklansky and Malmuth, as put forth in their book, “Hold’em Poker For Advanced Players,” updated and revised their rankings and reasons for playing or raising some starting hands. We’ve also presented five overall playing strategies for you to consider, in the form of Play Lists.

Table 10 - The 5 Play List Strategies

 Personality Play Threshold Starving 11.3% Top 24 hands Tight Expert 20.0% Top 42 hands Professional 24.0% Top 51 hands Savvy Gambler 32.9% Top 68 hands Good Gambler 43.9% Top 84 hands

Why not just wait for AA and only play it, folding every other hand that you are dealt?

Because of the need to post blinds in hold’em, you pay for playing at the rate of about 4 ½ small bets (4.5sb) per hour,  If you waited only for AA, you’d be waiting an average of 5-7 hours to play one hand at a cost of 27sb. This is a fairly good net pot to win, just to break even … assuming AA always won, which of course it doesn’t.

Hold’em is structured so that you must play to win.

Each of the recommended Play Lists should suit some hold’em player. But playing any one of them will require patience and discipline.

[1] the “old” facts, well known now for several years among hold’em regulars, are the liklihoods of the “good” starting 2-card hands winning at the river in a 10-player, or 9-player etc., showdown. Despite the fact that this information, alone, is clearly unrealistic it has been in large measure the only factual basis for working out playing strategies commonly available.

[2] See the previous footnote regarding “old” facts

[3] The value in each cell is the mean absolute deviation of the rank of the hand across either (a) the 5 different HE Table conditions (T), (b) across the 9 different numbers of foes at the river (F), or (c) the 45 different combinations of these (TxF’s) which we think of as “interactions” after orthogonal partitioning of variability in the parametric case.

[4] MAD is a robust estimator. In these cases the second moment is nearly infinite, making variance or the standard deviation useless.