(Semi-OT, long) Random SNG/SNGPT thought

[Shillx]

I was sick and couldn't sleep last night so I began thinking about common SNG situations that we might not be thinking about correctly. Recently a bunch of my shoves have been called and people keep showing me hands that I fully expect them to call with. Varience can be far more of a bitch then bunching (you might have heard the term) but I wanted to see just what kind of effect bunching had in SNGs. It isn't a very important concept in most games but it figures to have a fairly big effect in SNGs. When the blinds are big and most hands get folded around to late position, you have to be worried that the people who are left to act have hands that are quite a bit better then random.

I was thinking about a scenario where you have a 7-handed table, 100/200 blinds and everyone has 2000 chips. You are in the SB and everyone folds around to you where you find 7 [img]/images/graemlins/club.gif[/img] 6 [img]/images/graemlins/club.gif[/img]. The standard play here is to move in but I'm not so sure that it is correct. Let's say you know that the BB will always call a shove with

55+,A5o+,A2s+,K9o+,K7s+,QTo+,Q9s+,JTs (24.7%)

A fairly reasonable range in this spot. SNGPT says that shoving is +$2.57 (+0.3%) with a NoCall% of 74.4 in a $114 SNG. Seems like a fairly clear move in, right? But let's say that everyone that folded in front of us would have pushed if they picked up one of the following hands

33+,ATo+,A2s+,KTo+,K9s+,QJo,Q9s+,JTo,J9s+,T9s (20.2%)

I just did this to make it easier for me but it should prove the point I'm trying to make. After 5 people muck and you see that you have 7 [img]/images/graemlins/club.gif[/img] 6 [img]/images/graemlins/club.gif[/img] you can't assume that AKo is going to be as likely for the BB as 82o. Of the 40 unseen cards, here are the *rough* amount of each that you would expect to find. The numbers are off slightly b/c of inclusion-exclusion but it's close enough.

A: 3.55
K-J: 3.42
T: 3.34
9: 3.19
8, 5-3: 3.11
2: 3.06
7-6: 2.11

So you would expect AKo to be about 30% more likely then 82o in this case. SNGPT assumes the NoCall% to be 74.4 but it is actually about 72%. What is even worse then your decreased FE is that you are a larger dog in this scenario then you are against a random hand. If you get called by AK, you only have about 4.2 cards that will give you a pair while the AK has almost 4.8 pair cards. 76s typically has about 41.6% equity against AKo but it might only have 37.5-38% in this case. I don't know the exact equity becasue I don't know of an equity calculator that does this kinda thing.

Anyway this situation is more like setting the BB call% to 26 and putting your hand in as 63s. The NoCall% is 72.2 and you have 34.9% equity when called for a total EV of -$0.33 (-0.0%). I have a few ideas about how to adjust for this but oftentimes it doesn't matter (either your hand is too good/weak or the BB won't call enough to make it -EV). But when you are sitting to the right of some good players, this can potentially have a big impact. I don't know if there is anyway that you could add this into an SNGPT or SNGW but it certainly would be interesting to see what it does to the optimal push/call %'s. It is pretty easy to guess at what people push in certain positions so it figures to be pretty accurate against solid players.

I know this is kinda from left field but I just wanted to see if it's possible to get something like this in an equity calculator. It just seems people show up with hands more often then they should in these kinds of situations. It also gives more value to shoving hands like A2o over 87s (when SNGPT says the opposite) after a lot of folds since the deck figures to be rich with aces. And if you get called when you hold 87s you are a bigger dog then you might expect.

[checkmate36]

Interesting post Shillx (as usual).

[martinimagic]

Great post. Just out of curiousity have you had personal success with this? I made a committment at the beginning of the year to get better at SNGs and one tool I thought would help was SNG Wizard. It seemed to help some, but (and I would have to sift through my data) I felt like pushes similar to your scenario just were not profitable. Actually, watching some of the better players from 2+2 convinced me the importance of slipping the 10BB was not as important as having some better cards when pushing in this spot. Maybe part of my experience is just what you are getting at... [img]/images/graemlins/tongue.gif[/img]

[ymu]

Very nice post.

I'm guessing you'd need a fairly big change to existing software to calculate EV accounting for this effect, and it would be quite laborious as you would need to input push ranges for each player acting before you - but certainly not impossible.

One possible fudge fix might be to adjust your minimum edge by, say 0.05% for every player (with ~10BB and an understanding of push/fold strategy) who folded before you. Working through some more examples would help to come up with a good fudge factor.

Your point demonstrates that the number of people dealt in DOES matter, even if you're acting late in the hand and it doesn't feel like it should, and would be a really handy way of empirically estimating the adjustment you need to make for this.

[TruFloridaGator]

You're just nasty...in a good way of course. Sick stuff.

I think that we should all incorporate a bit more folding of really bad hands in these type of spots even if it's slightly +EV because of this, especially when we have a healthy 9-12x stack. I see far too many people pushing really bad hands in to regulars in spots like this where it's thin as it is. This type of thinking makes it even worse.

[fluorescenthippo]

this is a really good post unfortunately its hard to incorporate this most of the time. it has been said several times that if everyone folds around to the blinds they are much more likely to have an Ace but of course quantifying it becomes difficult. your first point (you will get called more) was good but i already knew it as i think most people did (even though we all probably dont care to incorporate it). your second point about having less equity with 76s was something that hadn't occurred to me and i doubt has been touched on much by anyone. its good to see some breakthrough posting in STT still! im not sure how any of this can be used but this thread is a start.

[Paul B.]

While this is a sick good thread and would definitely rate amongst the best SNG theory posts ever, it will never be applicable due to imperfect information.

[KoreanBuffet]

Wow that kind of thought would keep me from sleeping for like 3 nights, you are offcially my hero shill, but does anyone think this theory is applicable!?!?!

[dipstikdave]

good stuff. if you could quantify the impact it has it would be interesting to see. expecting a follow up from you soon. [img]/images/graemlins/smile.gif[/img]

[skreemer7]

This came up in a conversation with a couple of my friends recently. When icm calculations are made a player's calling range represents the percentage of the time your push will be called. It seems that instead of using a completely random 50 card deck (without Hero's 2 pocket cards) to find the percentage of the time villain calls, the <u>most likely</u> 50 card deck would be used to find the percentage of the time villain is dealt a hand he calls with. Then the rest of the calculations would be the same. I think......