Reuben's mistake in interpreting basic game theory

[punter11235]

Hello all !

Here is a passage from Reuben/Ciaffone book (p.145): (potlimit&nolimit poker) :

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We shall asume the player will always bet exactly what is in the pot. Then by bluffing exactly half as often as the frequency of betting with a winning hand, it will not matter in the long run how the opponent reacts to our bet.


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Well, this sentence is true but it describe strategy which is nowhere close to correct one in this kind of situations. If we use this strategy our opponent simply cant make any mistake, we can always check with made hand or without it and have same result so this is simply bad play.
Proper strategy is to bluff with 2-1 frequency , then we always gain 1/2pot size for every hand this situation occur, no matter what frequency our opponent adopts, he will always lose 1/2of final pot.
Example :
There is 1k in the pot , river make possible flush on the board. Now we bet 1k if :
a)our opponent always fold: he will lose 1k for every 2hands we made our flush (because he will fold to our bluff), so we gain 500$ per made flush
b)our opponent always call: he will lose 2k for our made flushes but catch our bluff for 1k profit, so he will lose same 500$ per made flush.
c)our oppoent adopt 1/2 calling frequency, easy math, he will again lose 500$ per made flush

One can ask why our opponents should choose 1/2calling frequency instead of other one ?. The anwer is :
Because with this strategy they cant lose more than 500$ per made flush if their opponents figure out their calling frequency. Please notice that this is common sense: we should gain sth when we complete our draw. This something is 1/2pot with pot-size value bets, it can be easily calculated how much we expect to gain with diffrent size of value bets at the end but I will not going into this now.
I noticed that the mistake which Reuben made is very common even at this forum. I think that every poker player should make the math by himself and figure out what is correct frequency of bluffing at the end.
Comments ?

Best wishes !

[punter11235]

I misunderstood the passage. Reuben is talking about correct strategy, I should work on my english.
My apologizes for posting this nonsense. (I cant delete it now)