HU research - Exploitative, Optimal and Unexploitable Play

In my current research on heads-up play, I have analysed 3 main concepts that people used for push-fold phase of the game, namely,

1. Nash Equilibrium
2. Sage
3. Chubukov hand chart. 

These are all unexploitable strategies where anyone following these push/fold ranges will be guaranteed at least a 0 EV assuming the others are playing perfectly as well. However, as I mentioned in my previous post, something confused me.  Since these 3 concepts are unexploitable, why does it give recommendation that differ from each other. Eg., 97o is a fold according to Chubukov but easy shove with 7bb in Nash?

As I read an article on equilibrium and optimal play just now, I came to this conclusion: The key word lies in Equilibrium


Let's look at this scenario:

I have 6bb left and I have J5o. According to Nash, this is a shove. So I shove with this hand. A few orbits later, I am still left with 6bb and now I got a monster QQ. Remembering that my opponent folded when I shove with J5o, I decided to be a little funny and limp with QQ instead. 

I had made a serious mistake in this hand. I deviated away from the Equilibrium that made shoving J5 an unexploitable shove. In the future, my shove with J5o will become a losing play.

Thus, for equilibrium to function, if I shove J6o with 6bb, I need to shove all my other hands here. Understanding equilibrium will be the key success to winning heads-up game, esp when it is deep stacked. And to think that I played thousands of SnG heads-up without realising this important factor for a long time.

But how about plays that are exploitable? Optimal strategies demands exploitative strategies. Playing unexploitably only serve to ensure that I am only making 0 EV play and making fewer mistakes. It doesnt help me to boost my ROI%.

 Why employ exploitative strategy?

1. First of all, it is because Tom Dwan said so.... lol. He refuted the conclusion from the Noble Prize winner John Nash with regards to Nash Equilibrium (However, Dwan has yet to prove it mathematically). 
2. Unexploitable strategy, though ensuring that it is impossible for anyone to beat me (say, if I follow Nash), but each time I tried to be unexploitable, I am passing up every opportunity to maximise my ROI.
3. When I am already ITM, due to the prize structure, getting first place is very important. Thus, being unexploitable is not really a coherent approach to my eventual target of getting first. 
4. Most of my opponents are not playing "ideally". Hence, following Nash or other equilibrium doesn't help me increase my ROI. 

What is exploitative strategy and what are some of the key things to note?

• Taking advantage of general exploitative tendencies of opponents. This involves
• Knowing the frequencies in which a player keep doing certain action, for eg., 3 bet shoving preflop etc). 
• As well as others...( to be further research on....)

• However, by exploiting others, I am exposing myself to be exploited by others because I am not playing equilibrium ranges!
• Thus, while I am exploiting the typical response of certain styles, I need to be mindful about when my opponent starts to adjust and react to my non-equilibrium tendencies.
•  If I do not adjust, my exploitation of others will become a target that is being counter exploited by others!

(I sort of suddenly realised this fact and being able to put it down in words after playing this game today - below). 

Food for thoughts... ...

• By playing like what I did, relentlessly min raising at BTN, I am opening myself up for exploitation. The villain know this and has also started to attack my tendency by shoving into me. 

• However, I know that the villain is making a huge mistake (a bigger mistake than my min raising frequency), thus I can continue to min raise and expect to get paid off in the future. 

• What should the villain correct counter strategy to exploit my tendency then?