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turn middling flush on paired board w/ boat blocker turn middling flush on paired board w/ boat blocker

09-15-2023 , 09:11 PM
Specific math, not some “play tighter” comment.

When the button open raises pot (3.5bb) he’s risking 3.5bb to win 1.5bb. The effective pot odds are 1.5 : 3.5, so if the button succeeds more than 3.5/(1.5 + 3.5) = 70% of the time, he can profitably open any four cards on the button. The two players in the blinds can’t allow this, so they have to defend a combined defense at least 30% of the time.

Let’s keep this simple and say the defense is shared equally between the small blind and the big blind. Both blinds defend a certain percentage x, so that there’s a 30% chance of at least one of them defending. The chance of one particular player folding is (1-x), so the chance of both folding is (1-x)(1-x). Thus, the chance that at least one of them isn’t folding is 1 – (1-x)(1-x), and we want this to equal 30%.

1 - (1-x)(1-x) =0.30
1 - (1 -2x +x^2) =0.30
1 - 1 + 2x - x^2 =0.30
x^2 - 2x + 0.30 =0

x = 0.16

1 - (1 - 0.16)(1 - 0.16) = 0.30 = 30%

And we want to end up with a total defense percentage of about 16% when hero is in the small blind, or in the big blind after the small blind has folded. The small blind should defend less and the big blind more because of position, but we are going to keep this simple and equal.

There you go MATH. The blinds should defend 16% each. It wasn’t magic or some “just play tighter” comment, it is specific math with specific percentages. Everyone here probably already has a half decent idea of their 3 betting combo which is made up of 3bets for value and 3 bets for bluffs. Throw enough flat combos in between the 3bet value and 3 bet bluffs to end up with enough total combos for 16%. To make it look like this

3bet value hands
Flat hands
3bet bluff hands

CardiffGiant’s phrase was a “shared defense” There you go. I gave CardiffGiant props for talking about this thread in a way not often discussed.
I just gave an example of 3 players in a hand. If you have 4+ players then extrapolate with math, not just some wazz “play tighter” phrase. We play tighter with more players based on math.

Math.
turn middling flush on paired board w/ boat blocker Quote
09-15-2023 , 11:59 PM
yes Wazz, they are the same concept. The maths decribes how much tighter each position should play.
turn middling flush on paired board w/ boat blocker Quote
09-16-2023 , 01:06 AM
Lol
turn middling flush on paired board w/ boat blocker Quote

      
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