$500 6max WSOP.com tourney. Posting payouts below--do note that WSOP.com payouts are very top heavy

Table is mostly regs. Didn't recognize BTN but he was fairly active.

1st 11208
2nd 6538
3rd 4557.92
4th 3810.72
5th 3026.16
6th 2652.56

LJ 26.3bb
HJ 23bb
CO 17bb
BTN 23.5bb
SB 14bb
BB (HERO) 30bb

HERO holds A4s

fold, fold, fold, BTN raises to 2.2bb, fold, BB shoves

1. The reshove seems fairly standard to me--wouldn't shove A4o as a side note. First question to other online regs at this stake--seem OK to you? I don't *think* I can ICMizer this since it isn't a push/call spot hence the question.

2. The more interesting question. What is your *exact* shoving range here, given flatting is such a sexy play as well? Bear in mind BTN is disincentivized to call given the ICM. Perhaps {A2s+, A8o+, 22+, KTs+, KJo+, QJs} and maybe a tiny amount of middle suited connectors?

My constant fear in these spots is that I'm shoving too little because defending the BB is such an appealing play.

It maybe standard reshove to active btn in non ICM situations, but when ICM is in play it changes dynamics so much that you have to get out of that +Cev mindset and start playing+$ev instead.

With this in mind, the shove maybe +Cev but not +$ev. You are CL 6max with fairly shallow stacks that are evenish in size. If you lose an allin to another player you are basically crippled and out of the tounry.

This is such an awesome def spot I don't know why we would consider doing anything else here, jam is risky and it forgo the chance to sit back and ladder up if we get called and are crushed. Lets play some postflop poker and let our skill edge come into play

Hi sir thanks for the reply--going to provide a mild counterargument, all in the interest of generating higher level discussion

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So, yeah, I'm aware that *if* I'm called and *if* I lose the allin, I'm in bad shape. However, the same ICM disincentivization that applies to me applies to villain as well, but more dramatically since I can't bust. I'm well ahead of his BTN-when-folded-to opening range. Remember, opening villain is not a fish--he's a reg I see frequently at the 500s and similar stakes who plays decently. He's going to be able to play IP vs. me decently well.

I think there's a lot of--very human--mentality with MTTers whereby people want to sit back and ladder (and don't get me wrong--to some extent this is 100% mathematically correct), but are unwilling or unable to drive the stake of ICM fear into their opponent's hearts.

As a minor note, I believe myself to have a postflop edge vs. this villain, but ~20bb deep...hard to have a huge edge, isn't it?

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As a side note, I was wrong about ICMizer not being able to model this spot--the software, yet again, has impressed me. I've run the spot and posted the results here:



Note that, in the Nash Eq., I reshove 38% (!)...and he can only call 8.4% (!!!). ICM is a powerful force indeed.

So in the end I suppose this post ended up me talking through an idea to myself and coming to a conclusion. Hopefully was an interesting read, and more discussion is certainly welcome. For the record, he just folded to the jam...not particularly interesting, but the hand lingered in my mind after.

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So the most interesting result here is that K2s and Q6s are shoves. In fact, shoving them is even more profitable if villain is calling tighter than {77+, AT+}, and if he's opening wider than 33% to begin with (which could be the case, I feel as though many MTTers are too wide on their BTN in this spot).

How many of you are jamming the K2s or Q6s here? Being honest, I would never even think to. How much money are we torching by not doing so? Obviously if villain makes mistakes and calls us wider than 33%, we stop shoving them, but simply navigate a few pips up and we find hands that are again shoves, but that I can guarantee very few of us would ever think to shove.

Wait, what? That spot is massively +$ev *because* of icm-pressure? I'm not sure if you misread stack-distibutions

Great situation. Being chip leader with this sort of distribution is awesome, since you do still live even when called.

I will take a tiny exception to one of your conclusions. If Q6s is at the bottom of your shoving range, then we are not torching money by failing to jam. It might be something like +$5 or the like, since Q5s is -ev.

AZ I'm gonna run this spot for you in PIO



But I wonder if my opening range for BTN is right in this spot. I feel like if he's good he knows you can shove pretty wide here and that 2.2x sizing also has me thinking he's a bit narrower than a "normal" BTN open. This is a straight 40% range, too narrow, too loose, or just right?



It's an 80gig tree, will take a couple hrs.

^ That's the question isn't it? Potential for an array of adjustments player to player in this spot.

I'd personally open this assuming I assumed BB was competent+



Matterfact add K8o, feeling loosey-goosey. I'm trying to block rejams or flop an invulnerable pair. Also air, I want some offsuit junk I can barrel turn with not some combo draw I cant bet/f.

Initially I never in a million years fathomed shoving as wide as ICMizer calculates that someone can be shoving there. The most interesting part is that the software gives you a range to shove that is Nash, meaning that if op is over folding, you can potentially shove even wider against some opponents.

The majority of my online play was grinding 6-max HTSNG's for years on end so I'm thankfully now well verse on my push fold ranges. However I still need to do some work on 20BB+ push fold spots, with tourny ICM implications.

Thanks for posting the hand. I'm glad your reviewing seemingly trivial spots like this in programs.

Thank you Eggs.

How clever of you to include NAI 3b sizing for me, I'm unbelievably curious as to what it has to say about using them. Will I get roasted here for admitting I don't have any NAI 3b sizings in spots like this? Kind of lazy of me, but I simply haven't put in the work to construct proper ranges for doing so and just play hoping the EV differential between the Simple_Strat and Multisizing_Strat isn't too severe. Always feels bad when I just rip with AA or KK though. I will say past 25bb or so I start to have one.

Anyway, to address the question--first off, I wouldn't read too much into the 2.2x sizing, as it's what he always uses post-antes, all the time. But I think I would reduce the 40% down to 35-36%, as I have a feeling this guy isn't opening the worst combos contained within the 40% range.

Exactly. Now, I will say here that there's a good chance Villain is calling me a bit wider than {77+, AT+} here, which obviously hurts the profitably of me shoving the Nash range. I *think* he calls more like {55/66+, A9s+, ATo+, KQ}, but I obviously can't be positive about that. I say this because I've noticed a common leak at FTs wherein certain regs call reshoves too wide--I've seen a player call off 33 in a spot like this, which is obviously suicidal/very bad.

The funny thing with that leak on their part, though, is that it hurts both of us, and funnels $EV away from us and into the pockets of the other players not in the hand! Isn't tournament poker funny sometimes?

OK I'm just gonna post this here without commentary on the actual strategy. If anyone wants to discuss that and bounce ideas off each other about why it looks the way it does that would be cool. I didn't get a chance to change V's range to be slightly narrower but w/e, this is close. Also I just noticed it's 12.5% antes, I assumed 10% but that wouldn't make a huge difference (if anything it would incentivize us to defend more I believe):

Hero's strategy vs the open



V's response to jam



There are a few things I wanted to comment on though:

1. Does anyone know how ICMIZER actually computes its supposed Nash equilibria? I ask because, if we could solve preflop spots with that program, there would be no need for PIO to have a preflop solver.

The way PIO solves preflop spots is by using flop subsets to try and approximate the full game, and you can get pretty close even with just 40-50 subsets (I used 72 for this tree which I'm told in the PIO thread in the Internet Poker subforum is an extremely good approximation. I have 256gigs of RAM at my disposal so I could've done more but I had other hands queued up that I wanna study).

I just don't see how ICMIZER can come close to this process. This tree I ran took up 80 gigs of RAM and was run since I first posted in this thread. Yet I'm supposed to believe ICMIZER can solve the same tree (or an approximation of it) in mere seconds and without the RAM constraints? I don't buy it.

FWIW I'm also gonna run a tree where hero can only defend, jam, or fold and even that tree is over 50 gigs.

I'm pretty sure PIO implements a counterfactual regret minimization algorithm, and I highly doubt ICMIZER does the same. Any comp sci masters here who can chime in?

I highly doubt ICMIZER is really giving us a true Nash Equilibrium.

I do want to note that a jam-or-fold tree (no option for hero to defend) took mere seconds to run, though the results are much different (PIO actually wants us to go even wider!!). But this is pretty useless when hero has 25bb.

Hero jam or fold


So my only guess is ICMIZER is spitting out some bastardization of a Nash equilibrium jam-or-fold tree solution

2. AZ you have way better results than I do--pretty enviable results actually--so I actually CAN'T flame you but my thoughts on this:

a. and this

b. are:

a.

Yeah you almost surely should have 3b NAI sizings in this spot, and my rationale would be it's part of an equilibrium strategy

b.

Obv we can't have as much an edge w/ 23.5bb eff compared to 100bb eff but I personally think we should try to eek out as much postflop play as possible if we're confident in our game and our ability to exploit holes in our V's game I think that even 23.5bb eff V's are capable of making massive postflop mistakes such that we can exploit heavily, and I think this becomes even more evident when you study NEs and realize that having an option of max{1bb, 10% pot} in your strategy profile can accumulate significant frequency at equilibrium--so it's not like we're doomed to 1-2 streets at this stack depth, far from it. In fact I personally think these shallowish spots are more interesting than deep spots because of how much closer to the edge losing one of these pots brings us.

A clue that ICMizer doesn't give a damn about the full game is that it advocates jamming all Ax and almost all Kx. That would leave BB dead in the water on plenty of flops.

ICmizer probably calculates with this as the basis:
{(blinds + antes + raise)(fold freq) - [bb stack - (blinds + antes + bb stack + btn stack)(bb equity when called)](1-fold freq)}ICM weighting

Then does some balancing to find the max EV for both players.

I like the Pio results, using mainly rag Kx in this spot to 3b/f is quite intuitive and something I've heard advocated by some crushers inc Pads and J Sinclair who doesn't Pio. We have tons of hands that can profitably 3b jam v btn's ambitious range so it seems Pio is preferring to take high cards (that aren't too profitable to not 3b) to the streets.

*preferring to take certain high cards to the streets to protect flats from hands not profitable to jam.

I've been doing some sensitivity analysis on this spot. We'd expect there to be really heavy ICM pressure given the following stack configurations, no? Because it's basically a disaster to not finish at least 3rd with these configurations.



Here's hero's strategy under these circumstances:



And here's V's response:



It seems really odd to me that V's response would be basically identical to the one above, despite hero's strategy being so different.

Does anyone know why?

How much tighter should we be opening BTN in this spot, considering hero can shove 3/4 of the deck against a 40% opening range?

ICMIZER has hero pushing ATC and V only calling with {JJ+, AK}

I think there's two opposing factors at play that, apparently, more or less negate eachother.

Hero pushing so much wider makes V want to call wider since he's doing better vs. our range

But, at the same time, he's far, far more disinclined to bust than before, because of the micro stacks

You made such a good point here. I do think that tournament poker is quite funny in that regard. I think one of the biggest problems for me is using these ranges in ICM spots that I shouldn't. What do I mean by this..

When you are in the middle stages of a tournament I think playing in a play style with a "long term" mentality is where to best apply something like Nash ranges. However because such a large portion of our playing time is in the beginning and middle stages of the tournament, making the shift to final table and more ICM based ranges is hard to notice at times. So I have stacked off thinking "oh this is Nash" (yeah for middle stages, but not for FT's).

Just be cognizant that things do indeed change at the FT or close to it. Most of my mistakes have been in areas like this. It's so easy to get in the habit of not making that mental/strategy switch when your mental muscle memory is geared towards the middle and early stages when it comes to push fold ranges.

GL brother!

Are there limits with Icmizer?

For example, it doesn't consider hero just raising AA/KK here? Or if effective stacks were 28bbs whats best to just call with?

Is everything is just a jam or fold with Icmizer?

What about HRC, can that vary the response of play?