Lefthook

It's interesting you block a decent portion of his bigger combo draws w/ 9d but you also blocks sets too. If we assume villain isn't raising 55, which seems reasonable at this stack depth, then there are only two combos of value villain can raise given our blockers. I wold imagine people over bluff this spot and top two is too high in our range to fold.

So...do we call or jam? This is a tough one to answer. I would guess if we have any fold equity and villain is weighted towards draws that jamming has to be +ev. I don't know how to analyze this spot if we flat though... Can we assume villain barrels all non-board pair turns and determine ev of defending all non-diamond 2,3,K?

Also, it is interesting to consider how we should play board-pairing turns. Exploitatively, we would want to bet on a 5 to fold villain off his equity and check on 8,10 and let villain improve. Especially if we assume zero implied odds.

It seems nasty, and I could be dead wrong, but given you bet this flop I would 3b/jam if I assume he isn't good and his range is draw heavy. It is actually a good spot to have top2 on this board, but it sucks you have 9d and this stack depth is what probably makes you hesitant to continue.

Very good vid, Jeans. Thx for taking the time to illustrate the indifference concept with an example. You also did a good job with your explanations.

I don't even need to mention it, but I will anyway...Sauce your videos and insight are some of the most valuable content on the site. For me personally, I have learned a great deal from your content. I think it's great you turned a relatively uncommon spot into a series as a theory excercise. Plz keep the great content coming. There is a reason almost every video has 50+ likes and 20+ comments. Ignore the trolls plz.

RIO4Life!! (kinda serious)

Alek,
What do you mean by folding AA here nets -1.75, or 3+ bb? I understand your implication that not folding AA has at least as much EV as folding, but not sure how you arrive at -1.75 for a fold.

Thx Ben. Looking forward to part 2!

Well done. Thx

Thx for vid, Zach. Interesting hands.

Have a couple questions:
First hand, you mention wanting to size bigger to rep polarized range. I have heard this mentioned in other videos. I was hoping someone could expand on this and possibly explain the theory behind this concept.
I understand it's theoretically correct to size bigger vs a capped range, does the same reasoning apply?

Also, @ 21:00, as played, if you didn't boat up on turn, I was wondering what your plan was with your hand. Are you betting all rivers except A,8?

Again, your videos are always appreciated.
LH

I think your assumptions will be inherently biased, but not so much as to contradict your conclusion or the makeup of your model, which is most important. I think this is what Sauce is saying in his beastmode manner.

All in all, very valuable content.

Fantastic vid, Phil!
Very impressive work, man.

I have a few questions for anybody who wants to contribute:

• Phil's analysis clearly shows, given his reasonable assumptions, that he is better off calling turn then jamming. But doesn't this also assume that he will play perfect on every river? Phil showed a breakdown of each river to show we have good visibility with our equity distribution, but even still, we will make mistakes that impact our EV. I understand the value from this video is in the method and not necessarily the result, but I feel like this is important for practical application.
  Is it possible to quantify with any accuracy the margin for error Phil is allowed to have that would still justify calling turn?

• Also, is there merit to potting flop for an effective jam given legend's stack? A quick sim from OO using a 6% range (high-card equity), shows we have ~62% with our specfic hand so there is equity to push here. At 3.5 spr after villain cbet, villain call/jam range needs about 44% equity against our range. I approximate villain call range to be: 82+, (AA:97+), (AA:hh), (KK:97+), (KK:hh), (J9+:hh). If this is acceptable, villains calls half the time at 50.58% and Phil nets $6,171. Which seems decently close to ev call($6,806), especially if you account for margin for error.

You're da man!

I actually think this is a great spot to bluff for sb. Facing a bb lead with a wide prf range, and a capped co range given flop and turn action, sb has a perfect stack size to rip.

With your specfic hand, I would puke call/jam. I imagine you would lead turn with at least T5+, K: 68+, 468+, so KT is just too high up in your range to fold if you presume villain to be balanced with decently wide shoving range.

was thinking a bluff-shove would be really sexy with this specific hand, but not sure villain has enough to fold any better. However, I would imagine that if we just get villain to fold random Tx and JJ, we probably have a profitable jam.

I understand those functions, but I was unsure how to account for the potential reduction in cc combinations given the effects of his preflop and flop actions on his range.

In other words, how do I account for his preflop range and flop range to deduce liklihood of having flush on turn in OO?

Wouldn't it not be as simple as putting in a flop continuing range bc villain arrives to flop with reduced combination of hands?

Impressive work, Midori.

When you get the chance, could you show how you got the prob. villain has flush on turn equals 77.5% in OO(under Q4).

after accounting for difference in syntax for PJ and OO, I still had trouble inputting villains entire range and accounting for preflop combos with combos he would shove over our xr.

Thanks a lot. This is great stuff.

Good Work Midori,

It was very helpful and intesting read. I was curious about your syntax for acheiving the avg stack off equity on turn, assuming HvPRE <0.33 on the flop.

Here was my attempt:
select avg(HvPerceivedEquity(v,turn,'AA'))
from game='omahahi', v='9%6h!AA', board='7d5d3c'
where HvPerceivedRangeEquity(v,flop,'AA')<0.33
and HvPerceivedRangeEquity(v,turn,'AA')>0.33

which produced avg equity ~72%

villain has KQ9 on J10x, so 8-A makes a straight.

I think it is fine to defend this pre with fish in pot. Your relative position is good pof, as you get to act last after fish decides.

However, when you lead flop, all this goes out the window. While it is true this is not a board that favors utg opening range, a fish will likely not consider this. So I would prefer a check in this spot otf. Given the action, I would prefer calling utg rr, as a 3bet implies youre representing greater than what you actually have and we dont want to be turning our hand into a bluff...

Thanks Ph33rox. Good stuff

If l-c is preferred, what is our std l-r range look like against a wide bb open? Also, are we limping our whole range as default in sb? If not, this obv weakens our limp range as it takes away AA combinations.

I forgot to input names, but you should be able to follow action given that I am in bb.

Also, the prf range is less the 4b range (1-4%) and fold range (cutoff at 40%)

Hey Zach,

Great analysis. This type of video is what I am looking for in content:

In-depth hand analysis using current software.

For me personally, there is a bit of a learning curve using oo, as I'm relatively new.

Having a guide to help with my own hand review is awesome.

- quick question: @17:30 you discount ev gained when V has set, which he has 25%. You do same when V has flush. This makes sense. Why do you discount those relative ev's again by total % V continues when we have flush ( 25/62, 37/62)?

Then @20:30, why do you discount the total ev when villain continues (3828) again by  the total 62%?

I am probably missing something from the basic definition of ev, but having an explanation would be helpful.

Thank you for your time.

Thx for the response, Sauce. 

I wasn't really arguing for/against anything, just a little confused about how you applied the concept of indifference.

My main point was that in MOP, ex-showdown equity was considered which implies a check is worth 0 EV. This was the baseline for decision making in terms of optimal play. Therefore, when facing a bet, if u call with (1-a) of hands that beat bluff (in one street game) then the game converges to its equilibrium value. 

Later, this point is expanded on when distributions are considered. Calling with (1-a) isn't optimal if villain has range weighted towards value, as he b/e on bluffs but increases expectation with value and bets it with higher frequency.

In your video, you make this same point but use a different method and reasoning. 

In summary, as I understand it, calling with (1-a) of hands that beat bluff is insufficient once the composition of villains distribution is considered (ex-showdown equity). You make this same point without considering ex-showdown equity and, as a result, have IP hands have +EV as a check.

Both ideas reach the same conclusion, but in practice, I was unsure which is better or more correct.

Sorry if this is all jumbled, and again, great video. Really appreciate it.