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Originally Posted by Carroters
2. Yep balance follows later as 3-bet bluffing ranges are introduced. In chapter 10 we explore polarised 3-bet ranges and this very spot comes up. We need the right bluffs and right frequency of said bluffs to balance this value range if that is we want a polarised and balanced strategy.
I don't think so. According to you there are only two hands which should be 3-bet. They are aces and kings (which is just 12 combinations). But you have a fair number of hands which to call (producing a much larger number of combinations than 12). When this is the case, it's probably a better strategy to hide information and not 3-bet at all. That is you move the aces and kings into the calling range and now your calling range will be better balanced by including a small number of strong hands and you won't have a 3-betting range. If you want to get a better understanding of this, I'll refer you to The
Intelligent Poker Player by Phillip Newall where he addresses hiding information in some depth and why simplified strategies are often better.
On the other hand, if you were against an opener with a wider range and had more 3-betting hands, then you should maintain a 3-betting range and balance it with an appropriate amount of light three betting.
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3. It's okay that this money includes Hero's investment as he gets this back when he wins the pot. If we were to insnsit that Hero gets back purely profit alone we'd be in a realm where the investment goes into a separate pot that cannot yield a return or a "vending machine" as I like to call it. It doesn't matter where the money from the average return comes from. In other words when Hero invests his 3BB is adds on to the pot and is now part of what he stands to win.
No. It appears that your understanding of mathematical expectation isn't quite right.
Let me give an example. If you give me a dollar to hold and then at a later time you take the dollar back, your profit is not $1, it's $0. So if your goal here is to make 30BB you cannot count your initial investment of 3BB since that's not part of your profit.
Now looking at exactly the way it's written you first say:
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but fortunately we can round this frequency up to 1 in 10 since we don't just want to break even ...
I think where the confusion comes in is that 1 in 10 is 9-to-1 odds. And if you want 9-to-1 odds that means you only have to win 27BB on your 3BB investment.
But that's not what your set mining rule states where you say:
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Set Mining Rule: Hero needs to make 10x his investment on average when he flops a set for pure set mining to be profitable.
10x your investment means odds of 10-to-1 which is different from 1 in 10. So:
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We have our target: we need to be winning an average of 30BB from the combination of the existing pot and future money from Villian's stack ...
You're talking 10-to-1 and need to subtract out your initial 3BB investment. If you actually meant 1 in 10 (which is not what is written) then the 30BB (in this example) can include your initial 3BB investment since in reality you're only winning 27BB.
Mason