Starting hands revisited

Introduction

In this article I would like to take a critical look at the listings and charts of starting hands in Texas Holdem Poker. The goal of the article is not to discourage the use of charts. Rather, the aim is to show you how to use the charts, to sharpen your understanding of the game, to analyze it off the tables and to develop strategies for situations in which the charts do not help you. For this article I use for this purpose the Starting Hands Chart, which was introduced in a previous article.
I will show you mathematical weaknesses in the chart on the one hand, and possible solutions on the other hand how to deal with these weaknesses in the game. Of course you can, and I recommend you to do so, apply the techniques presented to any kind of charts you want to incorporate into your game.

The weakness of charts

One of the typical questions is the vulnerability of the ranges presented in the chart. Let me take a closer look at two examples from the Starting Hands Charts, for typical and frequently occurring situations.

The weakness of the CO Range

I would like to start with an analysis of the CO’s Open Raising Range, specifically with an analysis of whether the button could play profitably against the CO range, if he had this knowledge. For this purpose, I will consider the question of whether the button can profitably approach the CO open raising range with a 100% 3-bet frequency.

Imagine the following situation. MP2 folds and MP3 folds, the CO raised according to the Open Raising Range from the Starting Hands Charts to 3bb, and the button has to decide whether she can profitably 3-bet play any two cards.

If you want to answer this question satisfactorily from the button’s point of view, it is recommended to have a look at the CO Open Raising Range.

This consists of four hand groups:

1. The hands marked in red are folded to a 3-bet.
2. The purple marked hands are called to a 3-bet
3. The orange marked hands will be reraised on a 3-bet as a 4-bet/fold bluff.
4. The light blue hands will be reraised on a 3-bet as a 4-bet with the aim of an all in on further aggression.

Determine the current pot size

Now you are ready for further analysis. To evaluate the vulnerability of the CO range, you first determine the pot size. After the raise of the CO the pot is 4.5bb – the 3bb that the CO raised, and the 1.5bb forced bets from the blinds.
Based on the CO range known from the chart, you have the basics to answer the question whether the BU can profitably 3-bet any two , i.e. whether the CO range is vulnerable in this respect.

Range distribution and expected pot size

The CO raises 310 hands of which he folds 232 to a 3-bet, that is about 75%. The 3-bet would cost the button 9bb which means that the pot would be 13.5bb after a 3-bet.
To make the analysis as simple and efficient as possible, assume that if the CO does not fold directly or the SB or BB enters the game, the BU will not invest any more chips in the pot. If this assumption does not lead to a clear result, you can still decide to cancel the assumption and replace it with concrete calculations of the respective game threads.

Expected value and result

Now you are ready to calculate the expected value of the 3-bet and can answer the question about the profitability of an any two 3-bet.
The expected value (EV) for the BU is the result of 75% fold on a 3-bet in which the BU wins the 13.5 bb in the pot, minus the cost of 9bb for the 3-bet. In the 25% of cases where the CO does not fold, there are no further costs but also no additional profits.

EV = 75% x 13.5bb - 9bb
= 10.125bb - 9bb
= 1.125bb

In conclusion, you can assume an expectation value for the any two 3-bet of about 1.1bb, which means that the question regarding the profitability of this move against the CO range and if the range is accordingly vulnerable can be answered with yes.
What this means and how exactly you can react to it I will show you after the second example.

The weakness of the SB Range

In this example I would like to examine the same questions with you, but this time for the situation that MP2, MP3, CO and the BU folded, the SB raised it to 3bb and now the player in the BB is faced with the question of whether or not he should 3-bet with any two.

As in the first example, you can assume that the SB Open Raising Range is known to the BB.

Determine the current pot size

Since it is about the game SB against BB, there are only 4bb in the pot instead of 4.5bb.

Range distribution and expected pot size

The SB plays 590 hands, of which he plays 444 raise/fold. This means that, similar to the last example, about 75% of the hands are directly folded to a 3-bet. Since the BB has already placed 1bb as a forced bet, the 3-bet in this example costs him only 8 bb. This means the pot has grown to 12 bb after the 3-bet. Similar to the last example, for simplicity’s sake, assume that if the SB does not surrender directly, no more chips are invested in the pot. Now you can calculate the expected value of the 3-bet.

Expected value and result

The expected value in this case is the 75% in which the SB folded and the BB wins the whole pot of 12bb minus the cost of 8bb for the 3-bet. That would be 1bb in this case.

EV = 75% x 12bb - 8bb
= 9bb - 1bb
= 1bb

Similar to the first example, you can answer yes to the question about the profitability of the any two 3-bet and the related vulnerability of the SB range.

Conclusions and actions

Finally, I would like to share with you the conclusions and lessons you can draw from the two examples. These include answers to the questions of whether the charts need to be fundamentally revised or can still be considered a solid foundation for your preflop game and what you can do if you notice that one of your opponents is starting to adjust to the strategy you have chosen.

The question about the lessons learned from the two examples can be answered relatively easily. Never rely on charts or fixed strategies for your game, but be prepared to challenge your strategies and experiences and adjust them accordingly, especially when climbing within the limits.

At this point, however, I would like to answer the question about the principle applicability of the charts with yes and justify this with the two levels of dealing with opponents that adapt to your strategy.

Level 1: do not panic or as shown here do nothing and observe.

• In order for your opponents to adapt to your strategy, they must first actually know it and also be able to exploit it properly. At which limits exactly this is the case cannot be answered with certainty. However, especially at the beginning of your poker career, you should assume that your opponents are neither able to understand your strategy nor have the ability to exploit it.
• In the analysis of the examples, you could observe that both the CO Range and the SB Range appear vulnerable. But for the CO Range it was assumed that the SB and the BB leave the button undisturbed in its effort to attack the CO Range. In reality this might look different, in particular the BU must assume that if he starts to attack the CO with any two, both the SB and the BB will adjust to this behavior. This would soon turn the 3-bet any two approach into a losing proposition for the BU. In fact, the vulnerability of ranges is more problematic in the situation SB vs. BB, because there are no other players who implicitly protect the SB range as in the first example.
• What also speaks for not panicking and to observe is that both examples assume that the BU or BB will not make any further losses in later betting rounds with their weak any two ranges. To what extent this corresponds to reality is open to question.
• But even if you assume that the CO and SB ranges are vulnerable against any two raisers, against stronger opponents, accepting smaller losses against theoretical exploits avoids difficult decisions in the later betting rounds.
• However, if by careful observation you come to the conclusion that one of your opponents is putting too much strain on the vulnerability of your strategy, you have the option to adapt it if necessary.

This brings me to level 2 in dealing with those opponents who adapt to your strategy.

Level 2: Analyze and adapt

• First of all you should appreciate that these opponents against you do not play on autopilot or ABC poker but have observed your game and are now adapting accordingly. That means for you that you should also avoid playing against these opponents on autopilot or ABC poker.
• Tthis can mean that you shift your range distribution from 75% to 66% of the raise/fold hands. For example, by selectively calling the strongest and 4-bet/bluffing the weakest hands from your initial raise/folding range.
• Likewise, it can be a very valid strategy that you come through analysis or testing to the conclusion that a hyper-exploitive counterplay against these opponents is also justified, e.g. by a 100% 4-bet strategy. Be aware, however, that you are entering potentially thin and above all expensive ice and you should be very confident that this particular play against these specific opponents is the right measure.

Last but not least, from a certain level onwards, it is per se essential that you move away from a purely chart based game and gain a good understanding of ranges and playable range distributions. A good starting point for this is discussion with like-minded people in the relevant poker forums.
Finally, I would like to point out that no matter how you adjust your strategy, you have to assume that your opponents will be able to cope with the changed conditions. This means you have to be prepared to get back to level one – namely, not to panic and to observe.

Summary and prospects

In this article you have learned how to use the charts to sharpen your understanding of the game, to analyze off the table and to develop strategies that cover situations where the charts don’t help you. I have shown you mathematical weaknesses in the recommended hand selections in this article using two examples. At the same time, I have also explained why these weaknesses, especially on the lower limits, are not a fundamental problem but should rather motivate you to sharpen your personal understanding of ranges and range distributions even further. Of course you can, and I strongly recommend that you do so, use the techniques shown to further explore the Starting Hand Chart and adapt it to your game and your opponents.