Originally Posted by pksmv
i've start reading your book and its great. Really like your reasoning and how you approach different problems.
BTW, im confused about a concept that you illustrate in the first part of postflop play, i.e when we defend in position given oppo is betting.
The conclusion that you arrived is: the more likely our bluffs are to become the best hands (i.e they some equity) the wider the defending freq must be.
This is only true if your bluffs shouldn't make an immediate profit, which is very frequently NOT going to be the case.
Example: If I min-raise open the button, big blind calls, and the flop is the 9h7c3h. Here, not only do the terms "value bet" and "bluff bet" pretty much suck (most hands are so far from 100% or 0% equity the terms aren't useful), but the button range is so much stronger than the big blinds and we have position that every bet should be +EV. So just because when we bet here with Kc8c and have a lot of equity vs the big blind calling doesn't mean he should call wide. In fact, if the big blind calls here he's going to get crushed.
Originally Posted by pksmv
My problems are:
1) If im reason in the following way it makes sense to me that we have to def more: since oppo bluffing range has some equity he his actually risking less for winning the pot (since he has some fraction of the pot that is the equity of his bluffs), therefore he has to obtain less fold to make an instant profit and therefore we have to defend more.
2) BUT if im reasoning in this other way i get confused: hero out of position OTR and check, oppo bet and the question is how mucj hero must defend? IF oppo's bluff as some equity @ showdown i have to defend less than the classic formula: 1-alpha (where alpha=s/1+s and s is the bet in term of the size of the pot) since:
bluff has no equity:
B: villain bet
F: hero folding freq
S: stack size
For making villain indifferent of bluffing(caller POV):
EV(check) = EV(bet)
S = (S+P)(F)+(S-B)(1-F)
F = B/(B+P)
1-F = calling freq for hero
bluff has some equity E:
EV(check) = EV(bet)
S + E*P = (S+P)(F)+(S-B)(1-F)
F = (EP+P)/(P+B)
Clearly by comparing the two final equation for F we see that in the first case we fold less (so we defend more) while in the second case we fold more (so we defend less).
My confusion arise because the two result from my two reasoninga above are in contradictions. My intuition is that im doing a really dumb thing and im comparing two different objects, that are: in the first example we are considering the equity of improving to a best hands while in the second one im using the show down equity that is different. So my conclusion is that before the river, i.e when oppo bluffs can improve to best hands, we can defend more (if we are the caller) and bluff more (if we are the bettor). While if oppo is bluffing hands that have (significant) show down value we should defend less (fold more). Moreover by doing this, namely to fold more, we given an incentive to oppo to bluff more and so reaching the right hands to bluff.
I would like to have your opinion on all above since i would like to riconciliate the two reasonings. Could you please help me?
Really appreciate you time and thanks in advance.
Ok, so it sounds like you're confused and doing what I just suggested you not do. Do NOT!! try to prevent players from being able to profitably bet any two cards against you when they have a stronger range than you and position.
Just clear your mind for a second, then think of this:
1) The better villains "value bets" and "bluffs" are, the greater their betting frequency should be. If you're OOP, this means your strong hands will make more as check-raises than bets, because villain will bet at such a high frequency.
2) If villains range is way better than yours, then even if you check all your good hands (like you would in the big blind vs button situation) your range still wont' be strong enough to defend aggressively against villains bets. So if the button bets 1/2 PSB here, do NOT!! think you need to defend at least 66.7% of the time.
3) If you find yourself unable to defend your checks AND you have a betting range, then you likely have a problem. For example, it used to be very common for the CO to bet very aggressively against a button cold-caller, but not defend many checks. Clearly, this doesn't make sense. If your checking range is so weak that the button can profitably bet very aggressively, then you need to check more strong hands. This is why you see optimal type bots/solvers show that you should check at a very high frequency when OOP in CO vs BTN or UTG vs CO type spots.
However, this still doesn't mean if you check CO vs BTN and the BTN bets 50% PSB you'll be able to defend aggressively enough to prevent him from being able to profitably bet ATC. That's especially true since checking (as the button) will be +EV with ATC too.
Hope that helps, if not let me know where you're still confused