Analyzing NLHE:TAP Concept 3

This is the second installment of my analysis of Sklansky and Miller's No Limit Holdem: Theory and Practice.

Concept No. 3: Most of your actions should include an inherent randomness against perceptive opponents.

"Avoid making virtually any play 100 percent of the time against good players." A few years ago, I was a big believer in this one, but now I just don't buy it. The idea, of course, is that you want to be unpredictable and thus difficult to read. If you never play 62, you are vulnerable if the flop is 662 or 345. Also, if you always raise with AA, your opponent can be sure his QQ are best with a AQ7 flop after you limp in. So, according to this idea, you need to limp at least rarely with AA.

I disagree. As an extremely example, I'm quite confident you should never raise 62o against good opponents when you are five off the button in limit holdem. This holds true for just about any hand worse than about 97o, and sometimes even for hands as good as ATo if your opponents are very tough.

So, why don't you need to worry about flops like 662 or 345 if you never raise with 62o? Three reasons:

1. Even the most perceptive opponents won't be able to figure out exactly what you are raising with anyway. Even if you do raise with 62o sometimes, your opponents are still pretty safe assuming you don't have this hand when 662 flops.

2. There are other, stronger hands that you can play that will make your opponents think twice on flops like this. Instead of playing 62o, play 67s, A6s, and/or 66. These hands do well enough on 662 and 345 flops, and they connect with plenty of other flops as well.

3. Even if you never play 67s, A6s, 66 and always fold when the flop is 662 or 345, this is probably okay! You will still win plenty of other times because the overwhelming majority of flops a card higher than a 6. Even if your opponents know you will always fold when the flop is all under 7, they can't really capitalize on this because those flops rarely show up! This is a very interesting point that I can't remember seeing anywhere else: it's okay for your raising range to include NO hands that connect with certain flops, even if your opponents knew exactly what your range is (which they don't).
**EDIT** 4. This relates to point 2 below. There may be situations where you actually will raise 62o. Who knows, maybe you actually think you opponents are so bad that you think you have +EV in this situation. The point is that your situation encompasses more than just your cards and your position at the table. So, even if your opponents know you never play 62o in the situation they perceive you to be in, you still might have 62o, because you will have perceived the situation at least somewhat differently. Note that this does not mean you should randomize your play like Concept 3 suggests. If you were to play 62o, it would be because the situation seemed to be profitable (+EV).

Another thing Sklansky and Miller say in this concept is "You might sacrifice a little bit of profit in this hand, but by doing so you make all your future hands more profitable." According to game theory, as I understand it, this is just plain bad advice. While it can sometimes be optimal to mix up your game by occasionally playing some hands, these hands need to be profitable in and of themselves... or, at least, not unprofitable.

I also don't really think you need to worry much about randomizing your actions when you have a good hand like AA. If you think raising AA preflop is the best play in a given situation, then it's probably worth doing every time. If you raise with plenty of other hands in similar situations, it's impossible to tell you have AA. You may be worried that you then give up too much information when you limp, since you are essentially announcing "I don't have AA because I always raise AA in this situation!" I have two things to say to this:

1. As in point 3 above, this is probably okay! Just as there are not many flops with three cards under 7, there aren't that many situations where your opponents can exploit you here. For example, even if they know you will always fold to an all-in raise, your opponent cannot exploit this by raising you out, because there are usually several other players for your opponent to worry about.

2. Even if your opponents somehow knew exactly how you play AA in a given situation (and again, they don't), they can never know exactly how you have perceived the situation at hand. For example, I might have noticed a tell that the player to my left is planning to raise, so I might limp in with AA. The player to my right might not have noticed this, and thus he will perceive the situation differently. If he perceives the situation as one in which I would never limp with AA, he would be liable to make a big mistake if everyone folds to him and he tries to bluff me out of the pot. Even more simply, maybe I am in a situation where I always raise with AA, but I misread the situation and call instead. This sort of thing happens all the time.

Some of my conviction on these points comes from studying some game theoretic examples from The Mathematics of Poker by Chen and Ankenman. There actually are situations in poker where you need mix up you play in a given situation (in game theory this is called a "mixed strategy"), but this always happens at the margins of your decisions. For example, if you've somehow determined that you should always raise with K8o on the button but always fold with K6o on the button, there is probably some rate between 0% and 100% at which it is optimal to raise with K7o. Clearly, whether you choose 20% or 80% is not going to make much difference in your results, and you'll be fine at either 0% or 100% as well. Notice, however, that with all other hands, including K8o and K6o, you should not be randomizing your play whatsoever according to game theory. K8 is a raise, K6 is a fold, period. Admittedly, mixed strategies can also be optimal at the extremes, like with AA, but, as I said above, I think you can safely play a fixed strategy, since nobody else really knows what you are thinking, anyway!

This took longer than expected, so I'll save "Concept 4: Sometimes you should bluff to stop a bluff" for next time. Preview: I am not convinced!