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I would be very interested to learn more about this and why the 1-a/prevent instant profit is not relevant. Do you have any links to info about this?
There is just no reason why it should be. I get this question a lot and it's frustrating because there is 0 reason why preventing instant profit or calling with 1-a frequency should be optimal in any game more complicated than the most simplistic river one (and even then only with numbers not real cards as card removal ruins it).
Maybe one intuitive thing:
Let's say the pot is 100 and OOP cbets 70 on the flop, IP calls and it's 240 in the pot on the turn. Now it goes check-bet 160.
It may seem that IP invested 160 to win 240 but it's not true - they invested 230 to win 170 this means that even if OOP folds a lot here IP still can't make money with nothing. They can make money calling with something which has some equity but it's very difficult to guess where the optimal calling frequency is - it depends on exact ranges and runout and how they match.
"Opponent shouldn't profit automatically" or "we should call 1-a" are basically worthless when thinking about those situations. Optimal play is about finding a strategy which guarantees maximal minimum payoff (that is guarantees the highest possible payoff assuming the opponent exploits us maximally) not about preventing instant profit.
There is no mathematical reason to believe we should prevent instant profit or call with 1-a frequency. Those are shortcuts which work in one street toy games with numbers instead of cards (and even then there are caveats). There are situations in Holdem when we won't allow the opponent to make automatic profit with junk, for example when we have stronger range and are in position but there are so many restrictions for it to apply it's not a useful tool.
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I couldn't find the exact example but on a very similar one it wants to check 65%, then x/r about 7%, and fold 70%.
Again, it would be useful to know what ranges you took for this example. If it was bet-call on the flop and it's the caller betting now it's the most natural thing in the world to fold a lot as explained above.
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I try run a script for know how many % of cbet is optimal , on diferents flops,
I set up like this;
I am not sure what you want to achieve. You can run a tree with 2 (or more) sizes but to do that just fill in the tree config and click "generate script", don't fill this up yourself.
The concept of "optimal cbet size" isn't well defined, you may want to find one of the two:
1)solution for a tree with many cbet sizes (here just build a tree with many available)
2)best c-bet size assuming you can only pick one
2) is not solvable without a lot of trial and error (solve a lot of trees with one size but different one every time and pick one with the highest EV).
This is an old now obsolete tree building interface.
The way to use tree generation window is to first fill tree building form and then click "generate script" in there. The script will appear automatically.