From upswingpoker blog, a quiz regarding check-raising range OTT as both a defense strategy (against delayed c-bet) and max value strategy. via: https://upswingpoker.com/vs-missed-c-bet-quiz/

Online $2/$5. 6-Handed. Effective Stacks $500.

Hero is in the BB with K♥ 9♥
UTG folds. MP raises to $12.5. 3 folds. Hero calls.

Flop ($27): K♠ 9♦ 4♠
Hero checks. MP checks.

Turn ($27): 5♥
Hero...?

Answer:

...
Additionally, check-raising for value allows you to check-raise as a bluff with hands you would otherwise fold, which expands your overall defense range. If you don't have a value check-raising range, you're going to end up check-folding a lot more often and your opponent will practically print money with his delay c-bets.

-- [end of quote]

It was said in the Answer section that check-raising this turn with nutted combos together with some bluffs "allows us to expand our defense range as we would otherwise have to *check-fold* those bluff combos", which I find not agreeable and want to discuss it.

To me it seems that the stragey *won't* allow expansion of defense range AT ALL. Sure the x/r line can carry bluff comboes, but so is probe/donk betting (with nuts and air together of course), and mathematically, they allow for the same amount of bluff to be carried if the bet & x/r sizing gives same pot odds to our opponent.

Therefore, it appears to me that we don't "otherwise have to *check-fold* those same bluff comboes".

The only difference to me seems that x/r line allows us to trap more bets into the pot thus achiving more value. Not that it can help us bluff more combos.

I understand your argument. After thinking about it, I like the check-raise better because it folds out a lot of 9x hands and perhaps even some 77/88/TT/JJ/QQ. The probe line leads to these hands calling more often, I think, which leads to me going to showdown more often, which is not what I want when I am bluffing.

I think the turn probe can lead to some negative implied odds situations on river where you bluff into the nuts.

Whereas, if my turn check-raise is called, the villain's range is much more defined and my decision to give up is a lot easier. So less money lost with the check-raise line might suggest it is more +EV in this sense. I'm sure those good at the maths can chime in with a more proper response.

The right answer may have to do with your own frequencies, how often you probe and how often opponent lays down to a probe. Because if you do this often and win often, then maybe probing is the right play always.

Personally it's a rare spot, to go check-check. Usually I think villain is so super weak here, because we would expect him to attack this flop ATC.

I just think that having a probing range opens your stack to a lot of exposure that I personally would rather avoid. The check-raise has a higher fold equity % bc your range looks stronger, so if what we are looking for is a turn fold then using the check-raise line is more likely to win, though we do risk both more chips and a possible river.

The check-raise line is good too because after checking twice we show a lot of weakness and almost any villain will jump on this weakness, so v's range is actually super wide after betting// narrower if he instead calls our probe, and leaves us in a bad spot.

Thanks, I like the check-raising too, especially deepstacked facing a villian who often pot-controls flop with even top pair (this does happen when it gets deep).

That said, my main inquiry is *whether x/r allows for more bluff combos than probing* (assuming we play a GTO strategy), in the original upswingpoker Answer, the answer was yes, and it was pointed out as an unique advantage of the x/r option, but I think this is false statement.

Can you elaborate your thoughts on this part?

Ah okay, now I get it.

Hmmm. I'll just give my answer but it may not be the proper one.

re: check-raise line
potentially I do this with my entire range, so I am here only evaluating villain's range and check-raising when I think he is light, so my range doesn't matter at all (to me at least). I am comfortable doing this with 72 or 23 in this spot given the high likelihood of fold (not that 72 or 23 is in my range given preflop play).

re: probe line
I think I personally do not do this with my entire range, as I think the likelihood of being called is greater, so that I pick combos that have equity, especially since I am preparing to also fire a river barrel if called. So draws and hands with some showdown value like middling pairs. 72 and 23 not a good choice in this situation because now I am required to bluff the river to win the pot if he calls.

This is my personal justification (after being forced to think about it) for why. I think the probing is more a "playing your hand" kind of play versus a "playing your opponent" kind of play.

Or just lead turn always since your opponent will never really have a strong hand. Why do a whole counter range construction when you can do the same thing as an offensive move.

Perhaps leading turn is less EV because villain will never bluff, so you only get action when he's sitting on a monster, which is rare, but leads to losing big pots while taking down small pots. I don't know just my feeling on the matter, could be wrong

That's great. Now we can bluff him a ton since we are rarely getting action. Seems +ev to me.

Checking twice avoids unnecessarily splitting your range and trying to balance multiple lines in what might be a spot where we have a limited number of strong hands.

If we probe, we face a real dillemma on what to include in the probe range that doesn't leave our checking range devoid of strong showdown bound hands to avoid being bluffed a lot.

I believe the explanation provided in the op is incomplete. From a cost benefit analysis probing vs x/r would be a less expensive, aggressive way to carry more hands to the river. Mixed with an appropriate check calling range it could be just as effective as a x/x/r range for less cost. You would lose out on bluff money that opponents put in vs a second check though. Also with x/x you have a non-zero chance the turn checks through to the river so perhaps over all possible lines x/x gurantees the least expensive route to the river.

So overall I think I agree with their conclusion but don't fully like the way they phrased their answer.