wobbles

Ben, you mentioned above you were planning some multistreet scenarios which I'm very much looking forward to seeing. One situation I was wondering about is where the multistreet action has narrowed ranges to an extent where our opponent will hold a blocker to our value range a very significant amount. 

When we create our river betting range we add the appropriate number of bluffs to our vbets, however assume our opponent is clairvoyant to our strategy, then he could make too many +EV calls within his range for our bluffs to be neutral EV (his blocker would weight us to bluffs given our true range and he contains it too often due to board texture and action). One option could be to reduce our betsize such that our opponents normal folding region doesn't contain the blocker anymore and thus he can't make too many +EV calls. However, assuming we want to bet large (say our value range is the nuts) then how would we solve this problem? Would we need to reduce our actual bluff frequency so that a larger portion of his range is truly indifferent to calling our river bet? Or do you think that this situation should never arise in optimal play as its unlikely our opponents range should contain such a blocker too frequently/our value range should be wider? This situation has come up a couple times in PLO for me, although rarely. Any thoughts would be much appreciated.

You make good points, one thing to consider though is we will hold trips+ around 20% of the time, and a FD with worse than TP between 25-30% of the time. Most of the FD+TP<< we wont want to c/c, but some TP+draw we can since we still have some SD value vs bluffs and can improve otr. If we c/r too many of the FD+TP<< AND weak TP+draw combos I think we will run into a lot of problems otr. This all ignores whether we want a leading range etc but basically my point is that since we have a ton of semi bluffs and cant raise all of them that would be the reason we may want to structure them the other way.

Zach, alot of the c/r bluff hands you mention have quite alot of SD value and we are most likely value cutting ourselves when called (except the times we boat/trip up OTR which is rare), so I might be hesitant about including too many of those in a c/r bluff range. 

Ben, given a large portion of villains range will contain 6x after the c/r, how do you attempt to create a river bluffing range, given when we hold some candidate hands like 9x and draws ourselves this will weight villains range towards 6x even more (albeit slightly)? If we pick x ratio of bluffing hands to value combos to make opponent indifferent to calling OTR, should we be worried that villain will actually hold the blocker (6x) enough of the time so that he is actually able to make +ev calls with a larger than normal portion of his range. So should we therefore reduce our bluff frequency to make a larger portion of his range truly indifferent to calling our river bet, or would you agree (as Zach pointed out) that since the range that calls the turn is this strong he may have already been exploited by overfolding the previous street. 

Hope that made some sense, cheers.

It should be this: Pot 100, we call 50% vs his 100% bluffing range. He nets (-100,+100) = 0. (We don't net our own money after a bluff works). Or we can use the formula B/(B+P) where B is betsize and P is potsize to find breakeven fold freq (with 0 equity bluff). So 100/(100+100) = 50%

The working you showed below my post is wrong.

Hi Zach, it's my understanding  facing a pot size bet OTR we need to defend 50% of our range to be GTO (not 2/3). The 2/3 would be the value to bluff ratio by the better to make the opponent indifferent to calling for a pot size bet. Calling down with any flush OTR I would assume is GTO, since any river range I construct for OOP that contains more than 50% flushes would almost certainly be overfolding a previous street. 

Given the action I think once villain calls OTT its safe to assume his range consists of Kx, and maybe some QJT. For my calculation I used this turn call range contained within a standardish opening range macro, minus tight 4bet range (Ive tested different opening ranges and results are similar so its not too important). I also used your hand as dead cards. The results I obtained were that OTR villains range contains a boat 45-47% of the time depending on which preflop range was used. I think this argues for a check back. Even if villain calls his entire range we are only just called by more than 50% worse hands. Another thing to note is once he calls flop raise and then turn his range becomes quite strong, so we aren’t going to be bluffing OTR much at all. If you had the read that he would reraise nutted hands prior to the river then I think a case could be made for a vbet.

Thanks a bunch for this thread guys, tons of awesome stuff in here. Just one small thing, I think in the following calc:

46(+$11800)+(.54)(.66)(-$37075)+(.54)(.34)($48875)
=$5428-$13214+$8973
=+$1187, or ~+3bb

is it supposed to be +(.54)(.34)($43675) since phil needs to call $5200 less than effective stacks (its already in the $11800 pot)?

If so the result would be:
=$5428-$13214+$8019
=+$233

Nice vid Odd! In terms of future suggestions for vids something with a GTO focus would be great.

Nice vid Phil, really enjoying this series and looking forward to seeing the rest of the footage. For the hand where Leo checks back AA on the QJ9KQ board, hits nut straight on the turn and is faced with river donk I decided to do some analysis to see whether the numbers in fact support a fold.

I began using a custom 3bet range of 19% of hands (not top 19%), and also tested an 11% and 25% 3bet ranges to see how results differed, including our hand as dead cards.

On the flop I assigned the preflop 3bet range of 19% to villain (assuming he doesn’t have leading range for this board which may be incorrect but simplifies this example), excluding AA (also running sims for exclusion of KK as well)
On the turn after villain checks in creating his range we would need to know whether he has turn leading range or not (how this could affect his turn c/c range) so I created a couple different ranges for illustrative purposes:

Entire continuing range check calls.

From what we have seen from this opponent being comfortable c/c marginals this would probably be;
2PR> translating to 2pair or greater,which occurs 71.37% of the 19% 3bet range minus AA.

Within this turn continue range OTR:
***19% 3bet range; FH = 45.56%, excluding KK pre; FH=36.75%
The following river ranges are obtained from the turn results of each of the respective preflop ranges, however for simplicity’s sake I’ve omitted them and just put river results:
***11% 3bet range; FH = 55.37%, excluding KK pre; FH= 45%
***25% 3bet range; FH = 46.52%, excluding KK pre; FH=38.04%

We require just under 32% equity to make a +EV call so under the above assumptions each circumstance would be a call.

If however, villain chose to check some showdown value OTR (which could be possible as the river will most likely be checked back by Leo) and bet his full houses and non-straight hands his range would look something like this:

FH, (KJ, K9, J9)-ST, T8-2NS> translating to full house, blockers not containing a straight, and bare Q high straight. This is 64.92% of hands that get to the river from the 19 3bet range that calls turn.

OTR:
***19% 3bet range; FH = 70.02%, excluding KK pre; FH = 61.96%
***11% 3bet range; FH = 79.01%, excluding KK pre; FH = 71.34%
***25% 3bet range; FH = 71.08%, excluding KK pre; FH = 63.44%
Each case would be a close fold here, and to demonstrate the effect of preflop ranges in the decision, if villain were folding KK preflop for example, it could be a call.

C/C Range with turn lead range
If we assumed villain leads 100% of straights on the turn then the c/c turn range would be as follows :

2PR>-ST which occurs 36.36% (2 pair or greater excluding straights)

On the river villain if villain leads 100% of range due to absence of straights that could check down;

OTR:
***19% 3bet range; FH = 70.52%, excluding KK pre; FH = 61.31%
*** for an 11% 3bet range FH = 78.74%, excluding KK pre; FH = 69.31%
***and 25% 3bet range FH=69.28%, excluding KK pre; FH = 59.9

If we assumed villain lead nutstraight and c/c rest of continuing range then:
2PR>-NS> occurs 63.4% OTT.

OTR
***19% 3bet range; FH = 50.24%, excluding KK pre; FH = 41.07%
*** for an 11% 3bet range FH = 61.16%, excluding KK pre; FH = 50.68%
***25% 3bet range FH=51.45%, excluding KK pre; FH = 42.67 %


if we also examine the range that checks straight and leads everything else then FH, (KJ, K9, J9)-ST, T8-2NS> occurs 72.42% OTT.

OTR
***19% 3bet range; FH = 69.34%, excluding KK pre; FH = 60.98%
*** for an 11% 3bet range FH = 78.28%, excluding KK pre; FH = 70.16%
***and 25% 3bet range FH=70.67%, excluding KK pre; FH = 62.85%

In summary, depending on villains turn lead tendencies, as well as river donk tendencies (and preflop ranges somewhat as they become tight) the decision could be swayed either way which is why this spot is so close. In reality his actual play is probably lies somewhere in between a couple of the above examples. One thing to note, which we didn’t have the benefit of knowing at this point in the video (since this was a read from the next vid in the series), is villain has river lead range which is unpolarised (potentially on cards he doesn’t expect us to fire enough) so if villain can ever c/c a straight OTT and lead river with it some % this is probably a call based on the above numbers. However this read may not necessarily generalise to this spot in particular.

Hope there was something interesting in all of that and thanks again for this series Phil/Leo!