So, I've been recently trying to learn more advanced NL Holdem poker. Specifically, I've been trying to move from playing "Harringon style" and my hand vs a set of hands my opponent may be holding, to "playing range", as in, I suppose, to play what would be "my range" vs an "opponent's range". But, as I was thinking this new mental setup through, this came up.

Each time I am playing, I am only holding 2 hole cards. "My range" is an imagined range consisting of many pairs of hole cards which I could be holding and which I am further projecting to the opponent with my actions.

All those 2-card hands which are contained in my own "my range" could be inferred from a few variables, my actions, but those also include the opponent's range-guessing ability.

What I am stressing here is that that this imagined range I am playing is made up partially by the opponent. I am not really playing against the opponent with that imagined range, if the opponent hasn't also constructed that exact same range for me in his mind. My own imagined range should be mutual, but it isn't definite whether it is.

What I mean is, it is possible that, assuming both of us are thinking about my own range, the range which I have in my mind as "my range" is different to the range which the opponent has assigned to me!

And I may have very little assurance that the range which my opponent has assigned to me as "my range" is close enough to the range which I am projecting as "my range".

If the range I am imagining as "my range" is the same as that which my opponent is assigning to me as "my range", then we have a mutual "my range".

But if my own "my range" is different to my opponent's "my range" then each of us is just playing against themselves.

Applying the same thinking regarding my opponent's range, we can have up to 4 different ranges in total that the 2 of us are playing:
1) My own "my range"
2) My opponent's "my range"
3) My own "opponent range"
4) My oponent's "opponent range"

And, if you find the point of views confusing regarding what is "mine" and "opponent's", let me express these 4 ranges using the terminology of "Hero" and "Villain":
1) Hero's hero range
2) Hero's villain range
3) Villain's Hero range
4) Villain's Villain range

How do you bridge the gap between differences in my own imagined "my range", and the opponent's "my range" - or, put otherwise, the gap between the Hero's hero range and the Villain's hero range?

How do you bridge the gap between differences in my own imagined "opponent range", and the opponent's "opponent" range - or, put otherwise, the gap between the Hero's Villain range and the Villain's Villain range?

To bridge the gap between your range and your opponent's range, it is important to gather as much information as possible about your opponent's tendencies and playing style. This can include observing their bet sizing, the types of hands they show down, and any patterns in their play. By doing so, you can make educated assumptions about the range of hands they are likely to be holding and adjust your own play accordingly.

In addition, it is important to be flexible in your range and not become too attached to a particular set of hands. As the game develops and more information becomes available, you may need to adjust your range to stay ahead of your opponent.

When it comes to bridging the gap between your opponent's range and their opponent's range, it is less important to have a clear understanding of their opponent's range, as this is largely out of your control. Instead, focus on playing your own range to the best of your ability and making educated decisions based on the information you have available.