Check raised on the turn

[rzk]

vma and stellar - you calculate two different things, that's why the answers don't match.

vma's calculation is the cost against his whole range, stellar's calculation is the cost given the knowledge that he c/r'ed.

stellar is also correct in saying that the cost of giving a free card to a 10outer is 0.55 and not 0.8 as i wrote before. i made a stupid mistake thinking that 8/5=1.4.

however, other elements of stellar's analysis are debatable imo.

1. in your analysis for AJ/AK:
- he shouldn't have AK very often based on preflop
- he rarely check-raises AJ against a pf 3-bettor, who's probably more likely to reraise and charge than to fold in this large pot.
- i think you really overestimate how often we get a bet out of AJ on the river. he shouldn't be value-bluffing us because he should know we'll call, and he shouldn't c/c because he should know that we don't have any hands in our range to bluff with.

2. in your analysis for KJ:
- you are right that we lose a lot against this great semi-bluffing hand.
- however, just to keep it perspective, KJ is about 1/13 of his range on the turn
- most importantly though, while incorporating of dealing with the cost of bluffs on the turn, you do not incorporate a similar cost of dealing with bluffs on the river if we check (not necessarily against KJ but against other parts of his range). the point is: in both lines his bluffs always carry a cost.

3. betting into a better hand isn't too bad at all. you usually lose nothing and occasionally lose a chance for your 2 outs if he c/r.

4. a lot of marginal weak hands (44,66,A7,A5s) will call a bet now but you won't get a bet out of them on the river when certain cards fall, OR you will be too scared to bet yourself, OR they will bluff you out on certain cards.

5. in addition to 10 outers, he has some 6-outers in his range (A9,A8s), against which giving a free card is substantially more expensive.

overall, it's very unlikely that the turn bet is really bad. i have a feeling that good players whose videos i've seen routinely b/f in similar spots. examples of a typical free card play in stox's book feature much worse situations (like 3 overcards). but i'm not at all dismissing the possibility that checking is slightly better.