It is very possible for a valid range to include or exclude individual hands in ways that are "non-obvious" or contrary to how those hands matchup head-to-head. Card removal effects due to opponent ranges are often the reason for this.

Holdemresrouces.net does not calculate actual Nash equilibrium strategies. They are only approximations. And, until we've got quantum computers on our desks, this is going to be true of *any* software that claims to calculate Nash equilibrium strategies for multi-player NLHE poker games. This why I'm so reluctant to use the word "Nash" anywhere within SnG Solver... it can be misleading without putting a whole bunch of asterisks and footnotes after it.

When you turn off "Advanced ICM" in SnG Solver, it calculates a NE *approximation* using a similar method to what holdemresources.net does. The operative word being *similar*. The specific algorithms are certain to differ in a lot of ways... how we construct ranges, initial conditions, weighting operators, how we get strategies to converge, and so on.

And so while I believe that "Advanced ICM=off" and holdemresrouces should generate similar results, they're bound to differ in spots... and you've found such a spot.

Is one wrong and one right? Well, really, they're both wrong. Which one is *more right*? Its pretty hard to say... and trying to figure it out probably a waste of time...

Because...

If you turn Advanced ICM *on*, then you are calculating what is certainly a better NE approximation than anything else. (Still an approximation of course, but as I described a few posts ago, one based on a better mathematical premise).

Honestly, the "Advanced ICM" mode is sorta the whole point of SnG Solver. To not use it means missing out on all the magic. In fact I only included the "off" switch as an academic curiosity... not something to be used for real strategy analysis.

For hands with few players, the beta calculator results on holdemresources are almost perfect NEs though. (Obviously, only within the assumptions: ICM holds, 3 players max in pot, etc).

It is trivial to check if the result is a real NE: For all ranges, all +EV hands need to be played, all -EV hands folded. And any mixed strategy hands need to be 0EV. Although the results are not quite perfect for most hands, the mistakes are usually tiny. (Would just require more iterations, but what is the point?)

Basically, i just disagree w/ the quantum computer statement

Regarding the 23o vs 63o in a *calling* range:
Unlike for pushing ranges, the relevant card removal effects are already correctly considered by stove for calling ranges, if the calling player is last to act. (However, simply looking at stoves equity will cause some slight mistakes due to split pots.)

But does even your beta calculator consider the movement of the blinds on future rounds of play?

I dont necessarily doubt that you can calculate a 3-handed *true* NE for the game you've modeled... but the question is, is that game the same game that we really want the answer to?

That is, the game of poker that is played in the real world has moving blinds and there are equity implications that go along with that. Whether I fold my hand from the BTN vs UTG have very different consequences because (for example) if I'm UTG I'm going to get hit by the BB.

When I talk about creating a real NE for a poker hand... I'm talking about a strategy for the *entire* game of poker as is played... from the immediate hand to the last, moving blinds, increasing blinds, etc. I mean, isnt this the *real* game that we need to try to solve for? Anything else is always an approximation.

This is really the point of SnG Solver... to make the game we're analyzing in our software be closer to the game we're actually playing for real money.

You are correct... I didnt notice that SparkMan said "calling" range... AND

SparkMan, I just went back and double checked this.... are you sure SnG Solver said it includes 32o but not 63o? I cannot reproduce this with the game setup you provided... I get that 32 *suited* is included in the range, but 32o is not.

Right, i was only talking about finding a NE for the simplified game (ie: "Advanced ICM=off").

One of the simplifications would be to assume ICM (or whatever other underlying equity model is plugged in) is correct, which eliminates the need to look into future hands/blind movements. Obviously, this assumption does not hold in reality.

Comparing the results for the simplified game is not necessarily useless though, i think it is actually a good way to find bugs and/or improve confidence in both implementations.

For the full game including blind increases, etc i absolutely agree with you: The best we can do for now is to calculate rough approximations. (Even the Sandholm results did not include blind increases.)

Hey Jason, I downloaded the install file and when it was finished it and I began to run the file it came up with an NSIS error with a big red x saying....

"Installer integrity test failed. Common causes include incomplete download and damaged media. Contact the installers owner to obtain a new copy.

More information at
http://nsis.sf.net/NSIS_Error "

Have you seen this problem?

Does it enable us to customize opponent's hand ranges?

This is first time I've heard of this... sounds like your download failed somehow. Try to download again?

Yes. The tutorial/docs on the webpage are a bit out of date (they're still based on a very early beta). If click on any opponents range, you will bring up an edit window...

Wouldn't be bad if we could see the actual equity for every player. And can you please elaborate more on equilibrium push/call vs +EV push/call?

The next update will have more information in the display that will include the calculated equity for each player.

The "equilibrium" ranges are the approximate Nash equilibrium strategies for each spot. The "+EV" range is the range that includes all of the +EV hands vs the opponents ranges (whether overridden or using the default equilibrium ranges).

Typically, you should use the +EV range as the basis for your actual strategy/analysis. Its the "real answer".

I'm going to put more emphasis on collecting and displaying the +EV range in a future update.

Actually I was asking whether I can manually add or delete certain hands when adjusting opponent's hand ranges, it seems that the program don't allow me to do so.

Oh, I see. No, I'm afraid the ranges can only be specified along a linear scale. This restriction helps the processing to be fast.

Having said that, I just had an idea...

Hey Jason-

I just got the program installed and the first thing I noticed is how drastic of a difference there is with the results from your program and other ICM calcs in certain spots.

Ex.

payout 700,300
3 players all 3k stacks
blinds 150/300

BTN folds, SB all in 3k, Hero in BB w K5s

SB is on 100% range.

Wiz says diff% is + .9%

SNGsolver says + 5.5%

How could this be right?

5.5% is clearly way off, I also can see that for AA it suggest 60% eq difference between fold.

sng_jason - will there be an ability to edit range outside 169 precomputed values? Like manual input?

Thanks.

I agree the value seems a little high, but what may be happening is this:

A) If you fold the SB gets a chip lead and can then pwn you both starting from the next hand where he's UTG.

B) If you call then you get the chip lead and can pwn the others.

Or in other words: the NE solutions (which use ICM equity at eventual leaves) will have very tight calling ranges for the smaller stacks (this phenomenon can already be seen in the holdemresources software) and thus the big stack will be able to get away with shoving much wider in the following hands and thus gain significantly more equity than ICM is predicting: Just one extra steal of the blinds will net you 5% of the chip equity so it's quite possible that the calculation is correct when you account for future play on future hands.

BUT, now we have a different problem:

A) Current SNG software isn't looking ahead and seeing this as being lower EV than it should be.

B) This SNG software is modelling the future based on NE play, when in reality the players are much more likely to call wider than NE would suggest.

So even though the value might be correct for what it's simulating; it may well not be what you want to be using... I'm not really sure whether solution (A) or (B) is better (ie: closer to "true" equity prediction), although I'm guessing (B) is probably better in high limit and/or very reg-infested games.

Juk

EDIT: I may not have explained that very well so it would be good if somebody else could chime in here...

Of course. That SnG Solver gives different results is exactly the point. It doesnt use the standard, highly flawed ICM equations.


I dont understand why this cant be right... why not? The math is the math. SnG Solver says k5s is a clear call against a SB on ATC.

Why is %5.5 *clearly* way off? What are you basing this opinion on? Some other calculator that is based on the standard Harville or Weitzman ICM equations? See my post above for a detailed description of how flawed those models are.

Are you saying 60% is a wrong estimate of the equity gain from calling with AA in that spot? If so, why?

Yes, yes, and yes!

Juk, it sounds like you pretty much get it... you just need to "free your mind" from a few preconceptions.

Yes, unless you're in a really tough game, assuming all the other players are going to be playing close to GTO in future rounds might be a bit extreme... BUT, doing so still gets you *much* better representation of stack equity (go back to my earlier post with the equity comparisons) than the alternative.

Remember that SnG Solver still lets you override opponent strategies for the *current* hand... so you dont lose the ability to model the "first order effects" of a player being too tight/too loose in a spot. Dont get too hung up on the fact that future strategy estimates are not exact when the alternative (*no* future strategy estimates) is *always* wrong.

Also, maybe this isnt clear, the but %EV increase that SnG Solver displays is *relative* EV, not absolute. That is, +60%, means you will have 60% more equity than you started with, not that you will have 60% of the total equity on the table. This might be different than whatever program you're using for comparison.

*Edit*
Yeah, I just confirmed that Wiz's "Diff%" is an absolute difference. So in this spot, the numbers might not be as different as you guys think. So, everyone can relax now.

My next release will have better display of the "numbers" calculated for each spot

I compared the results from advanced mode on and off and what i see is:

In advanced mode

1: BB calls shoves wider, Sb calls a little bit wider
2. Late positions shove tighter
3. UTG shoves wider

Is this observation correct?

This is certainly true in some situations, but its really entirely dependent on the exact spot. There's no specific strategy modifications that happen with the "Advanced ICM" turned on... all of the differences emerge cleanly from the math.

Jason- Thanks for responding. I have a few more Q's

-Are you ever going to allow overcall ranges?

-When we solve a hand, where do we see info such as equity if we fold, equity if we shove, other players equity etc?.(I don't totally understand the %s)

I hope you understand why someone just trying out this program would compare results to WIZ or another calculator. That is all Im familiar with. That being said there are a lot of spots where WIZ fails and in those spots we're used to taking -edges. It is just assuming for the most part when we take -edges. So the first thing I do when using your program is find spots that WIZ fails in(because we should be shoving wider due to blinds coming up) and see what SNG solver spits out.


Also the comment I posted about the +5.5% equity compared to the +.9% in that specific ex.... Thanks for explaining that, If I understand correctly the %s are way different between your program and WIZ. Your program tells you how much more equity you have gained compared to the prize pool, whereas WIZ tells you how much equity compared your current equity. amirite?

i have another question: I tried to analyze a 18man bubble and i get these ranges:



Uploaded with ImageShack.us

The strange thing here is that the Bigstack can not shove ATC. If i model it in sngwiz with your callingranges ATC is highly profitable.

When i now change the Stacksizes like this:



Uploaded with ImageShack.us

The button has still the same shoverange of 92.8%. There must be a mistake, because his Range is capped in your Program to 92.8. It never becomes higher even if he is the dominant chipleader.

I already do have overcall ranges. They're shown in the strategy tree or if you set two opponents pre-flop action to "all-in".


The current version is a little limited when it comes to displaying all the internal numbers (each players equities, breakdowns of fold/push equities, etc...). I'm adding all that kind of stuff to the display now and it will be in an update soon.


Oh absolutely. I expect and welcome the comparisons. I realize that I'm the "new guy" and sngwiz is very established.


I think you have it backward actually. If the prize pool is 1000.0 and your equity goes from 400 to 440, sngwiz will say the equity "Diff%" is 4%, whereas SnG Solver will say you've gained 10%. Wiz's number represents the absolute gain in terms of the total prize pool. Solver's number represents the % gain to your own equity.

I'll be sure make this more clear in a future update (and probably show the sngwiz equivalent too).