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Originally Posted by JJTheFish
Im not sure if I am aloud to directly quote from the book. So I will avoid doing it until I know im aloud to?
mm I guess it's a matter of length? Couple sentences is fine, multiple paragraphs probably not.
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On pg 307 volume 1. you use the example of a 3bb bet in your game for example 4. then later on it is stated you can improve the EV by 4bbs/100 by switching to a bet of 5.37bb. Im not sure if you are saying the 3bb is sub optimal and 5.37 is actually optimal. or you are saying 5.37 would be optimal, assuming villain doesn't bluff raise. the latter makes a lot more sense to me, but from the way im reading it, it seams the former is true.
As it says, "If we change the SB's 3 BB bet sizing option to 5.37 BB and re-solve for the equilibrium, the value of the game for the BB increases by about 4 BB per 100 hands." As explained, 5.37 is notable since it's the optimal value for the PvBC-plus-traps spot we saw earlier. Nothing is said about optimality of the sizing in this spot, and of course Villain can bluff raise.
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I read earlier in the book I cant remember where, and maybe I am stating this wrong, (sorry i am just stumbled across this 2plus2 page today) When compering bluffing the river, with a polar range combined with the nuts and threshold bluffing hands with ShownDownValue=0%, i.e say we bet POT with 30% value and 15%bluffs( assume we are all in or cant get bluff raised for simplicity)
If we're perfectly polar as you say, Villain will never want to bluff raise us.
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Compering the same spot with i.e 30% value and 15% bluffs but now our threshold equity for our bluffs has SDV=10% from what I gathered from the book it was saying I should increase my sizing above POT.
You made up the sizing of pot previously, but the equilibrium of the spot above was to bet as large as possible, ie all-in (assuming we have sufficient amount of bluffs in range). If I understand the spot you're describing here, we can't bet larger than all-in, but can continue using all-in though.
Generally speaking though, if our bluffing hands have more showdown value, then the EV of checking is higher, so villain will have to fold more to make our EV of bluffing higher as well, if he wishes to make us indifferent. This stuff is discussed in the context of the [0,1] games in ch 7 and some of the examples as well.
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Although I wasn't fully processing the math, The opposite would seam more intuitive to me. i.e villain needs to call less to make us indifferent to checking back and bluffing our threshold hands and because we are adding hands with equity into our bluffing range, increasing the sizing would just lower calling frequency even more. Im not meaning to across as disputing what you are saying, just having a hard time getting my head around this. If I am reading it wrong great. If I am getting it wrong, if you could try give me a simple example to illustrate, I would appreciate it, that being said when I am finsihed, I will go back at look over the section in question and have another crack at it.