# Game Theory Poker - Nash equilibrium: Choose between bet or raise and range of hands

I would like to understand how we choose the best action and how we compose the range for it.

I have some notion on zero-sum games and minmax strategies. And I know software that does this for texas holdem: I want to understand how they do it

Example :

-Opponent range 19,61% 260 combos

-My range 16,44% 218combos

now we are on flop in hu situation with Qd 8h 4c;

pot is 100\$and my opponent bet 50\$.

Now calulate the pot odds : 50/ (50 + 100) = 0.33 => 33%

We need 33% of equity to defende (call or raise) part of my range .

The MDF concept (Minimim Defence Frequency) tell us that we must defend (call or raise) 67% of my range (218 combos)

146 combos to defende.

Now this number is theoretical because depends on the opponent's bet frequency(if he bet only with a tris for example... defend 146 combos is the way for loose everymoney :D) (and it also depends on other aspects like a position, stakes and so on.. )

Suppose this number is right, and it is the perfect number of hands to defend:

Now how do I divide my range into a raise-range or call-range?

Which parameter is used? How does game theory create a balance between these two ranges?

I understand that there is a part to range to fold and part to defend but I have difficult to understand how to create in a range of defend a raise and a call range in a balanced way and how to include a bluff.

In article I linked to tell about % of bluff(in theorical way).

The EV calculation is a most important factor to choose a combo to insert in a call-range or raise-range. This is a good article on EV It's possible to calculate the EV of every single combo, ok but i don't understand how i use this data for split range in call-range and raise-range in GTO mode.

how do I establish that a combo is better to raise it instead of calling it?

Thanks a lot..

PS: If you have a good article or good book to study.. linked me