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Old 07-14-2020, 07:39 AM   #1
The_nutlow
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Bounty math using HRC vs rules of thumb

Hey all! I am new here but I hope you guys can help me. This is a hand from a 11 dollar bounty builder turbo on Stars I played yesterday. I came across a spot where 2 shortstacked bounties where in play that I covered and was wondering how wide I should be to rejam. I ran the spot in HRC (which I am using for a few weeks now so I might messed something up) and the results where surprising to me. I posted the results below. Given that we are way off the money I just pasted the total regular prizepool for number one, I did not note down the total players left but assumed it from my finishing position which was soon after.





The calculation would suggest that I should rejam with any two. I just can't get my head around that. I also tried to fact check myself, because I think you should never just take answers from an algorithm without thinking (a program is as smart as the person using it). Using the math from https://redchippoker.com/quantifying...-in-knockouts/ I would say that the chipvalue of the 2 bounties is 94 percent of a starting stack (given CO has a 1.5x starting bounty and 80 percent of field is left).

Forgetting the BB behind us for a second and adding this to the existing pot I would need around 22 percent equity for the call to be profitable based on this rule of thumb calculation. Suppose we take a hand out of the bottom of the any two range and compare that to the 2 ranges of the other players given by HRC:



We then end up that we have around 1.5 percent equity less than needed, making this a fold I would say. This is also what my intuition tells me (which is underdeveloped as I am not that experienced yet to be fair). The only reason I can think of apart from the fact that the rule of thumb is a rule of thumb is that the CO covers the UTG player, me having the second best hand would still give me a 1.5x bounty. I would say that is somewhat relevant, I just don't see 52o being a winning play here, but I could be very wrong. A hand like T4s would be a snap jam given both calculations but I don't think I would have jammed that in game.

What are your thoughts on this guys? How much 'faith' should we have in tools like HRC? I ran another bounty spot in both ICMizer and HRC last week and found results that differed quite a bit still. Threads like https://forumserver.twoplustwo.com/1...-spot-1743772/ give me the idea these programs are not (completely) foul proof.

Also, I found an Upswing article (https://upswingpoker.com/knockout-bo...rogressive-ko/) that actually advocates a different chip amount for the bounty in PKO's then the redchip article and a video from Jonathan Little I watched, usually the latter seems closer to HRC so I am led to believe that one is correct but Upswing is not just some site so that confuses me even more.

Sorry for the long post, it just gave me a bunch of questions haha. To wrap it up, in this spot if you have 52o what do you do? And with T4s? Or do we need an even better hand?

Thanks a lot in advance guys!

EDIT: To be clear, villain jams from EP with 12 BB and start bounty, CO rejams with 13 BB and 1.5x bounty and hero is in SB covering both (BB then covers us for 27 BB effective). A starting stack is 5k chips so this effectively around doubles the pot for us given bounties.

Last edited by The_nutlow; 07-14-2020 at 07:48 AM.
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Old 07-14-2020, 10:33 AM   #2
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Re: Bounty math using HRC vs rules of thumb

Your problem is you’ve made this a winner take all tournament with bounties. Try putting the correct payouts in and running it again.
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Old 07-14-2020, 12:20 PM   #3
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Re: Bounty math using HRC vs rules of thumb

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Originally Posted by TwistedEcho View Post
Your problem is you’ve made this a winner take all tournament with bounties. Try putting the correct payouts in and running it again.
Thx for your reply! I checked the notes of KO tournaments for HRC when I started using the software for bounty spots, there it says to make it winner take all for quick early stage calculations, see: https://www.holdemresources.net/blog...ockout-bounty/.

I will fill in the payouts non the less and check if the result is different.

EDIT:
Well you are partly right, it goes from anytwo to 99.1 percent, but the point still stands:


Does this mean we already feel a little ICM with 350 left and 72 paid? The calculation took quite a bit longer, so it might be by introducing ICM HRC just calculates different and that is the reason. The calculation took quite a bit longer although I used the same mode.

52o is still a rejam by HRC but it drops to 20 percent equity given tighter ranges. So by our basic math it is still a fold. Who helps out?

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Old 07-15-2020, 04:08 AM   #4
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Re: Bounty math using HRC vs rules of thumb

As mentioned before, always use the real prize structure if possible. Winner-takes-all will be easier/faster but at the expense of accuracy, only do this if you are lazy or don't know the prize details.

Manual calculation: Side pot

The most important mistake in your manual calculation is that you are forgetting about side pots. There are times when EP wins the main pot while Hero wins the side pot and eliminates CO for the bounty. In your generic equity calculation this scenario is accounted for as 0 equity, as it just assumes everyone is all-in for the same amount.

This specific scenario where EP > Hero > CO is listed as 132 in the equity calculation screenshot you posted and happens a fairly significant 11.45% of the time where you recover some chips and win a bounty.

BB player calling

Note that the BB is forced to fold in the calculation if hero calls, that's because regular HRC calculations only allow 3 active players. You may want to calculate this in Monte Carlo mode and allow 4 active players, so the BB can still call after hero. The BB actually covers Hero and will likely call very loose, this may significantly affect Hero's range here.

Bounty pool

You should also check the calculation details, your regular prize pool is 2035$ and i assume the total bounty pool was 2035$ at the beginning of the tournament as well. Due to the bounties on your active table HRC assumes a remaining bounty pool of 2041$ and that seems too high and you may want to override this. Something like 60 players already busted? So this should be more in the 1850-1900$ area. This won't really make a huge difference here, but it's still good practice to pay attention to it.
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Old 07-15-2020, 12:25 PM   #5
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Re: Bounty math using HRC vs rules of thumb

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Originally Posted by plexiq View Post
As mentioned before, always use the real prize structure if possible. Winner-takes-all will be easier/faster but at the expense of accuracy, only do this if you are lazy or don't know the prize details.

Manual calculation: Side pot

The most important mistake in your manual calculation is that you are forgetting about side pots. There are times when EP wins the main pot while Hero wins the side pot and eliminates CO for the bounty. In your generic equity calculation this scenario is accounted for as 0 equity, as it just assumes everyone is all-in for the same amount.

This specific scenario where EP > Hero > CO is listed as 132 in the equity calculation screenshot you posted and happens a fairly significant 11.45% of the time where you recover some chips and win a bounty.

BB player calling

Note that the BB is forced to fold in the calculation if hero calls, that's because regular HRC calculations only allow 3 active players. You may want to calculate this in Monte Carlo mode and allow 4 active players, so the BB can still call after hero. The BB actually covers Hero and will likely call very loose, this may significantly affect Hero's range here.

Bounty pool

You should also check the calculation details, your regular prize pool is 2035$ and i assume the total bounty pool was 2035$ at the beginning of the tournament as well. Due to the bounties on your active table HRC assumes a remaining bounty pool of 2041$ and that seems too high and you may want to override this. Something like 60 players already busted? So this should be more in the 1850-1900$ area. This won't really make a huge difference here, but it's still good practice to pay attention to it.
Thanks for you reply @plexiq! This is really helpful. I do have some further questions though (after I ran the sims in Monte Carlo).

Manual calculation: You are right, I realized that is of significance but that isn't taken into account in the manual calculation (including that makes it a bit more tedious), but I can see that that might give the couple percent that it is off.

Bounty prizepool: You are right here as well, I assumed it to be correct as the bounty prizepool is slightly bigger than the regular prizepool (it is a 4.8+5+1.2) but this is actually incorrect, even if the busted players all had a stock bounty it is still incorrect, due to the fact that our table is not average I guess. I will pay attention to that in the future, very good point.

BB player calling: This point is very interesting, I did some further calculations on this using Monte Carlo and when you make 4 players active we indeed have quite a more tight range and one I would agree with already more, but it still feels a bit loose, see below:


However, I found 2 things that raised some alarm bells for me, the first is when you use MC but 3 active players (the same situation as the normal mode calculates I would say), you get a different result then when you calculate using the normal mode (see above, for comparison I kept bounty pool the same):


For some hands (that become a fold now) it is like .5 percent or 50cts (in a 11 dollar tourney). Which I would call significant. I don't say that is something we necessarily realize in game, we are no computers, but from a theoretical standpoint I would love to know what causes the difference and which one is "right" so to speak.

This touches on the main point I am struggling with: how 1 to 1 should we apply HRC in our strategy? Disregarding exploitative play (which changes the calculation as well), in some sense the HRC should be the optimal strategy and thus followed to the smallest margin.

I don't think this is entirely correct, usually these algorithms have assumptions (which also explains the different results between the two modes). So we should incorporate that as well in our decision to play or not play a hand using HRC ranges.

Basing myself on the calculation with Monte Carlo and 4 active players, from a practical standpoint I am unsure if we are supposed to risk our tournament life here with like a T8o or 75s which is still in the new calculation. Or that BB should call 13 BB with 92o when we fold. I find it difficult to find an answer on this. I think in bounty spots this is also more of a factor, if we have a purely push fold 15 BB spot with only a regular prizepool I would say this is already less of a factor. Maybe you can help me a bit with that.

EDIT: A small addition to this, I now see that running the same spot in MC mode multiple times also gives results that differ with a similar margin as given before between runs. So I think the calculation did not converge completely/sample size is not enough. Is there a place to change this (because that makes the calculation longer I think it is capped at some point)? In essence this makes my last point even more important, how do we adjust or ranges in game knowing HRC results, because I think we can't say it is 1 to 1. I think we need to take into account the underlying model assumptions.

That is if I didn't enter/used something wrong (again) of course.

Last edited by The_nutlow; 07-15-2020 at 12:32 PM.
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Old 07-15-2020, 12:49 PM   #6
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Re: Bounty math using HRC vs rules of thumb

Monte Carlo mode is actually more accurate because it considers additional card removal effects for folded players, you can find the details here:
https://www.holdemresources.net/blog...nte-carlo-mode

And yes, there is some randomness from sampling in the Monte Carlo results, simply use the "Run Nash Calculation" button in the toolbar to run additional samples until the EVs converge.
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Old 07-16-2020, 06:53 PM   #7
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Re: Bounty math using HRC vs rules of thumb

Quote:
Originally Posted by plexiq View Post
Monte Carlo mode is actually more accurate because it considers additional card removal effects for folded players, you can find the details here:
https://www.holdemresources.net/blog...nte-carlo-mode

And yes, there is some randomness from sampling in the Monte Carlo results, simply use the "Run Nash Calculation" button in the toolbar to run additional samples until the EVs converge.
Thx for the link, that is helpful. I am also just talking more in general, how should we interpret our results from HRC (and other tools/solvers)? Given they are always based on assumptions. Should we sometimes divert from results from these tools based on this knowledge or should we follow it strictly? And if we should take it with a grain of salt/manually change some things, how? It is more a sort of in depth GTO question. As far as I know, NL holdem isn't completely 'solved' yet. Meaning that all solvers, tools and the like have some sort of inaccuracy. As a scientist by training I am kinda interested in that aspect (as you would do the same in an experiment where you use a certain non-perfect algorithm). Maybe someone can shed some light on that.

EDIT: I am completely disregarding exploitative play here for a second, I see that as a perturbation on our GTO strategy, which also changes our calculation anyway (you input other ranges). I am just referring to the 'calculation error' of these programs based on imperfect assumptions.
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Old 07-17-2020, 04:16 AM   #8
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Re: Bounty math using HRC vs rules of thumb

Idk, super general question. Obviously, if you know that the assumptions / abstractions used by a solver cause a certain type of mistake AND you know how to compensate for that mistake then of course, go ahead and compensate for it.

Simply knowing that a solver will provide results that aren't quite perfect for the full game isn't enough to make any adjustments though. Players need to be really careful to not use "solvers aren't perfect" as a catch-all rationalization to deviate towards their personal preferences.

In a nutshell, HRC assumptions:
*) The explicit betting abstraction. So push/fold, or whatever you configure - beware of forced check-downs for non-allin pots if you allow limps/calls.
*) The active player limit, forced folds once that limit is reached.
*) Whatever assumptions come with the selected equity model, e.g. ICM.
*) Card removal for folded ranges is not considered in the default mode, only in Monte Carlo.

Happy to elaborate in more detail if anything is unclear.
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Old 07-17-2020, 10:19 AM   #9
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Re: Bounty math using HRC vs rules of thumb

Quote:
Originally Posted by plexiq View Post
Idk, super general question. Obviously, if you know that the assumptions / abstractions used by a solver cause a certain type of mistake AND you know how to compensate for that mistake then of course, go ahead and compensate for it.

Simply knowing that a solver will provide results that aren't quite perfect for the full game isn't enough to make any adjustments though. Players need to be really careful to not use "solvers aren't perfect" as a catch-all rationalization to deviate towards their personal preferences.

In a nutshell, HRC assumptions:
*) The explicit betting abstraction. So push/fold, or whatever you configure - beware of forced check-downs for non-allin pots if you allow limps/calls.
*) The active player limit, forced folds once that limit is reached.
*) Whatever assumptions come with the selected equity model, e.g. ICM.
*) Card removal for folded ranges is not considered in the default mode, only in Monte Carlo.

Happy to elaborate in more detail if anything is unclear.
To start with the easy question, what do you mean by forced checkdowns? Do you mean that if we allow limps and we have a limped pot pre that HRC assumes no more action post and therefore equity realization is for example a reason to change it? That makes sense given HRC assumes it always comes to a showdown if people stay 'active' (hence not fold) right?

Examples like this are exactly what I am talking about, we shouldn't use tools in a vacuum, I would say. But the point you make is equally true as well, if we start changing HRC ranges without valid arguments because our intuition gets in the way, we created unnecessary biased and wrong results.

In the end I think the right balance is only learned by doing I guess. I will probably post some more hands in the next few weeks when I struggle with something /find it counter intuitive to figure out if I actually used HRC/reasoned correctly.

Some more questions on HRC specific then:
- If we allow advanced betting, hence a player uses the 2x size with part of his range and part of his range he jams of 16 BB for example. How does HRC decide which hands fall in which one? I sometimes find ranges suggesting HRC just doesn't like one sizing and has basically a 0 range for one sizing and in others it just makes some sort of division in range between 2x and all-in. I am curious to know where that division is based on, because I am not always clear on how to interpret these results (should we exclude a sizing because it makes no sense when HRC gives a 0 range etc.?).

- This might be more an ICM question then a HRC question, but I was running some spots with ~70 people left, where ~140 where in the money. I noticed that when calling (and shoving with a shorter stack) we should be quite a bit tighter compared to the ChipEV equivalent spot I ran. At first I thought this was due to the pay-jumps.
To test this I flattened out part of the structure. Instead of having some payjumps I assumed position 11 to 140 get the same pay-out (rescaled to keep the same prizepool) and I left place 1 to 10 the same. Surprisingly we should still call tighter then ChipEV. That surprised me quite a bit, because the situation should be similar to 70 left 10 get paid with the 'elevated min-cash' subtracted for all places right? And are we really considering ICM in a spot where 70 are left and 10 get paid? It is not completely the same as in the latter case we have a huge 10 placed min-cash, but you get my drift. If necessary I will share the runs.
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Old 07-20-2020, 03:25 AM   #10
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Re: Bounty math using HRC vs rules of thumb

Quote:
Originally Posted by The_nutlow View Post
To start with the easy question, what do you mean by forced checkdowns? Do you mean that if we allow limps and we have a limped pot pre that HRC assumes no more action post and therefore equity realization is for example a reason to change it? That makes sense given HRC assumes it always comes to a showdown if people stay 'active' (hence not fold) right?
Correct, yes.

The current HRC is strictly a Preflop calculator and will assume that there is no further betting after the Flop for pots that are not all-in. So if you enable lines that can end in non all-in pots (ie limps / flat calls) then you have to keep equity realization in mind and adjust accordingly.

Quote:
Some more questions on HRC specific then:
- If we allow advanced betting, hence a player uses the 2x size with part of his range and part of his range he jams of 16 BB for example. How does HRC decide which hands fall in which one? I sometimes find ranges suggesting HRC just doesn't like one sizing and has basically a 0 range for one sizing and in others it just makes some sort of division in range between 2x and all-in. I am curious to know where that division is based on, because I am not always clear on how to interpret these results (should we exclude a sizing because it makes no sense when HRC gives a 0 range etc.?).
There are no special assumptions or simplifications in that regard, just the Nash algorithms (Fictitious Play or CFR) doing their thing.

Assuming the ranges converge, hands end up in the action where they are most profitable. In some spots it can be profitable to split a range into several sizings, in others the information you give away by splitting is more significant than the upsides and you will end up with only one sizing played.

If a sizing is played with close to zero frequency then it's usually save to simply drop that sizing entirely. (Lock the range to 0% and re-calculate, the other lines should stay almost unchanged.)

Quote:
- This might be more an ICM question then a HRC question, but I was running some spots with ~70 people left, where ~140 where in the money. I noticed that when calling (and shoving with a shorter stack) we should be quite a bit tighter compared to the ChipEV equivalent spot I ran. At first I thought this was due to the pay-jumps.
To test this I flattened out part of the structure. Instead of having some payjumps I assumed position 11 to 140 get the same pay-out (rescaled to keep the same prizepool) and I left place 1 to 10 the same. Surprisingly we should still call tighter then ChipEV. That surprised me quite a bit, because the situation should be similar to 70 left 10 get paid with the 'elevated min-cash' subtracted for all places right? And are we really considering ICM in a spot where 70 are left and 10 get paid? It is not completely the same as in the latter case we have a huge 10 placed min-cash, but you get my drift. If necessary I will share the runs.
ICM considerations kick in a lot earlier than most players realize. I think that is a left-over mindset from times when ICM tools simply couldn't handle calculations in larger fields.

Lacking an alternative for larger fields, players used to fall back to chipEV and assume it's probably fine. It has only been a few years since ICM tools added initial support for MTT calculations at all and the early implementations weren't all that accurate. (Compare the old HRC MTT model to the current one, that was a huge leap in accuracy: https://www.holdemresources.net/blog...uracy-mtt-icm/)
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Old 07-26-2020, 07:29 AM   #11
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Re: Bounty math using HRC vs rules of thumb

@plexiq Thanks once again for the reply. Sorry for my kind of late responds, had a busy week. I still have a few (follow-up) questions.

Quote:
Originally Posted by plexiq View Post
Correct, yes.


ICM considerations kick in a lot earlier than most players realize. I think that is a left-over mindset from times when ICM tools simply couldn't handle calculations in larger fields.

Lacking an alternative for larger fields, players used to fall back to chipEV and assume it's probably fine. It has only been a few years since ICM tools added initial support for MTT calculations at all and the early implementations weren't all that accurate. (Compare the old HRC MTT model to the current one, that was a huge leap in accuracy: https://www.holdemresources.net/blog...uracy-mtt-icm/)
Large field ICM

I find this very interesting. I played around with HRC a bit, for example a 6seat SNG where place 1 and 2 get paid (non-equal payments). It turns out HRC instantly factors in ICM, and quite significantly I might add. This surprised me, because I felt like literally first hand having ICM considerations makes no sense. On the other hand, there is no law against it and it sorta makes sense that in such a short format surviving is important and you rather not flip. For me the buy-in point just felt like a boundary condition (your ICM stack value when a tourney starts should be the same as the buy-in). For this SNG that is still the case but for large field tournaments with multi-entry, rebuys, add-ons etc. this surely isn't right? Meaning that saying 'you always take an add-on if you get twice the chips for the same dollar amount', would usually be correct but as ICM is a factor we should actually factor this in. This means that the amount you buy-in for (which I stated as a boundary condition) actually isn't, ICM wise you can get a stack that is worth more or less in such a large tourney. In tournament selection this seems quite relevant, you could search for tourneys where you get better 'ICM' value. Although implicit value of having a large stack and being able to bully is a thing too I suppose.

I am completely unsure if I approach this right (and how I would go about calculating EV of add-ons etc.), but this is where my mind takes me from the above insight. I hope you/someone can shed some light on whether this is actually a correct reasoning and how we would go about comparing the different options in a tourney (taking add-on yes/no, 'waiting' for add-on period as you get more chips for same price and rebuy is a 'waste', multi-entry etc.).

EDIT: Not all sites have add-ons that are larger in chips then the initial buy-in. I happen to play on one where that is the case, so that is why I chose that example.

Multitable ICM mode vs Malmuth-Harville
This also brings me to a question on HRC, I normally use MTT ICM mode (as it is default), but should I for single table calculations actually use Malmuth-Harville? Or doesn't that matter?

HRC and sattelites
How accurate is HRC for sattelites? I mean spots where like 11-15 people left when 10 get ticket and such. I usually default to folding everything if I have a good stack and likely make it, if I have a short stack I much rather push then call. If I run these spots in HRC I get sometimes quite 'weird' results. I mean spots where I am not sure if I should fold into the money and risk not making it and having to gamble with a lesser hand later on or push/call.

Lets take an example, I ran a spot where there were 3 people left and 2 got a ticket. I am on the BU with 10bb, SB and BB both have 5bb. I am told to fold all hands including AA. When I am in the BB with 10bb and same stacks, I should call 33 percent of hands against a 5bb SB shove. This sounds super weird to me.

Other example, 7 people get ticket, 9 people left, 7 people with like 10bb and 2 with 2bb. The 10bb stacks are told to shove 30+ percent. I would fold everything, baring [maybe AA and maybe KK/QQ. Or like min-raise strong hands to help bust the shorties, but you get my point of not jamming 30+ percent. The chances the 2bb stacks spin it AND you are one of the unlucky 10bb stacks to bust (if the 2bb spin it up and you get like a 8bb all situation or something, you still have 5/7 to make it). I think this last one is because the calling ranges are 0 for all 10bb stacks, in reality you are not sure people will fold like AK/QQ+ so folding is a hell of a lot better (you see this if you manually change ranges).

The first example still confuses me a lot, the second one makes sense when you think about it. The problem for me is though, if there are like 20 left and 10 get paid, above reasonings are harder and I would like to know if we can default to HRC ranges or we should also fold to preserve stack in hopes of making it. We could manually change all ranges and then hope to find out, but you most likely stack errors then (you run the spot because you don't know it and if you start adjusting ranges although not knowing what is correct you might as well not run it).

I think my question basically boils down to two points:
- How good is HRC for satty math in general? Looking at the first example for instance I don't think that is right
- How do we find the point in a satty tourney where we should start folding all hands/in between situations where we fold everything but AA/KK or QQ+/AK?

I hope you can shed some light on some of these questions once again. Sorry that it became such a long post.
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Old 07-27-2020, 05:48 AM   #12
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Re: Bounty math using HRC vs rules of thumb

I'd rather not get into specific hand examples, I'll just answer more generally.

MTT ICM vs regular Malmuth-Harville (vs FGS)

For single table calculations the MTT ICM model will give you the same results as regular Malmuth-Harville, the only practical difference is that regular ICM skips the MTT stacks setup page. (Under the hood the vanilla ICM option actually uses an exact Malmuth-Harville calculation, while the MTT version uses an approximation of Malmuth-Harville, but in practice you won't be able to notice any differences.)

I'd strongly recommend you use FGS for single table calculations anyway, this is considerably more accurate than plain ICM. That's especially important for some of the examples you posted where you have small stacks and/or high bubble factors. FGS is essentially playing out the tournament game tree several hands deep and plugging in ICM estimates at the last calculated round. Regular ICM calculations only calculate a game tree of the current hand and plug in ICM estimates for the stacks at the end of the current hand.

If you are interested in ICM / FGS accuracy in single table formats and don't mind dry reading, I've done some work on that a while back:
https://www.holdemresources.net/misc...ity_models.pdf

Satellites

HRC doesn't handle satellites in any special way, so this just comes down to how well ICM/FGS is suited for satellites. For single table calculations use FGS as mentioned above for best accuracy, as that will simulate a few hands of play on top of the regular ICM estimates. Check the linked paper to get a rough idea about the accuracy.

Generally speaking, I think ICM does a pretty decent job of estimating the finishing distribution for a given stack and that will be the basis for the HRC MTT satty calculations. Basically you throw the resulting stack sizes of the various lines at ICM and it will let you know the estimated % of any given stack to finish within the top x% (ie, win a seat).

I don't know of any better models to do this and I really doubt players can do any better than ICM by using intuition / manual guesswork or whatever you want to call it. We can do full-tournament solves for small satellites with a few players and see that ICM does pretty well there, but for larger fields we don't really have any hard data.

Add-ons, rebuys, late-registration, etc

You are right, these are all really tricky to model and you'd have to make a ton of assumptions to get anywhere.

For example add-ons with 2x chips, i think it's fairly trivial that it is almost always correct to take these add-ons, except if you already have a gigantic stack. Small stacks profit more from these add-ons than larger stacks, so there's some slight re-distribution of tournament equity. How the option of purchasing that add-on should influence your strategy in the early phase isn't all that clear though, idk.
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Old 08-04-2020, 09:50 AM   #13
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Re: Bounty math using HRC vs rules of thumb

Quote:
Originally Posted by plexiq View Post
I'd rather not get into specific hand examples, I'll just answer more generally.

MTT ICM vs regular Malmuth-Harville (vs FGS)

For single table calculations the MTT ICM model will give you the same results as regular Malmuth-Harville, the only practical difference is that regular ICM skips the MTT stacks setup page. (Under the hood the vanilla ICM option actually uses an exact Malmuth-Harville calculation, while the MTT version uses an approximation of Malmuth-Harville, but in practice you won't be able to notice any differences.)

I'd strongly recommend you use FGS for single table calculations anyway, this is considerably more accurate than plain ICM. That's especially important for some of the examples you posted where you have small stacks and/or high bubble factors. FGS is essentially playing out the tournament game tree several hands deep and plugging in ICM estimates at the last calculated round. Regular ICM calculations only calculate a game tree of the current hand and plug in ICM estimates for the stacks at the end of the current hand.

If you are interested in ICM / FGS accuracy in single table formats and don't mind dry reading, I've done some work on that a while back:
https://www.holdemresources.net/misc...ity_models.pdf

Satellites

HRC doesn't handle satellites in any special way, so this just comes down to how well ICM/FGS is suited for satellites. For single table calculations use FGS as mentioned above for best accuracy, as that will simulate a few hands of play on top of the regular ICM estimates. Check the linked paper to get a rough idea about the accuracy.

Generally speaking, I think ICM does a pretty decent job of estimating the finishing distribution for a given stack and that will be the basis for the HRC MTT satty calculations. Basically you throw the resulting stack sizes of the various lines at ICM and it will let you know the estimated % of any given stack to finish within the top x% (ie, win a seat).

I don't know of any better models to do this and I really doubt players can do any better than ICM by using intuition / manual guesswork or whatever you want to call it. We can do full-tournament solves for small satellites with a few players and see that ICM does pretty well there, but for larger fields we don't really have any hard data.

Add-ons, rebuys, late-registration, etc

You are right, these are all really tricky to model and you'd have to make a ton of assumptions to get anywhere.

For example add-ons with 2x chips, i think it's fairly trivial that it is almost always correct to take these add-ons, except if you already have a gigantic stack. Small stacks profit more from these add-ons than larger stacks, so there's some slight re-distribution of tournament equity. How the option of purchasing that add-on should influence your strategy in the early phase isn't all that clear though, idk.
Thanks for your reply once again @plexiq. I am reading through your thesis, it is an interesting read for sure. I love the balance you tried to strike between academic style and still relevant for poker. If I have some further questions about that I will let you know.

As for the rest:

HRC models
I am still not entirely sure when to use which model in HRC, iea which one is most suited for which situation. I will sum up what I think here, let me know if that is right.

Firstly there is the difference between Monte Carlo vs math/enumerate. When more then 3 players are active MC is clearly the way to go, but if not I am not sure which one is better, even after reading material you supplied earlier. I feel MC is more accurate when sampled correctly due to card bunching and more players taken into account (if you select that). I think usually the reproducibility and faster calculation of normal mode makes that suitable for me.

However, I was wondering about one thing. The limitation of 3 active players, is clear when your option is not in the game tree, but does it also affect ranges directly? I mean suppose we have a bounty spot where ranges are wide, if a possible 4th person is behind you that can overcall after 2 calls and covers you, that affects your shoving range quite a bit i would say. I think that the normal mode would not take that into account and just sets the overcall range of that 4th person to zero. Is that correct? Because then for bounty spots this can be quite relevant and I will take the longer runtime and use MC. In most other ICM spots the 4th overcall range is quite marginal I would say so I think normal math is good enough.

As for ICM/FGS/ChipEV. ChipEV is clear, that is when you disregard ICM. Multitable calculations can't be done with FGS right? So if we are in MTT phase it is clearly ICM mode. For single table you suggest to always use FGS right? Or are there situations where plain ICM is better suited (like bounties or something)?

sattelites
The problem is that in practise lots of people decide to fold 100 percent as they are almost guaranteed a ticket if they have a very large stack, as do I. I think this is quite correct given dynamics after the specific hand you calculate. That is not how HRC calculates, it still finds you should jam as the calling ranges are crazy nitty/0, you still increase your chances because if you fold 100 percent and shorties keep doubling you might end up bubbling still after blinding out (I actually had that yesterday). While the latter is the rational, in practise HRC just calculates your chances of making it are not 100 percent but say 98 percent, when calling ranges are very nitty it is then relevant to push all in for the last 2 percent.

Practically speaking I think however that the odds of you bubbling after blinding out are a lot less then getting called and be in the middle of the pack again and have a lot more risk to not make it. In larger MTT sattelites, game situations after that hand become very important. So in some sense you kinda need FGS I feel, but I am not entirely sure.

That is kinda why I am in doubt how accurately HRC models multitable sattelites. Because as a player you can incorporate these next hand dynamics, HRC (without FGS for MTT) can't. I see the impact is already detrimental comparing plain ICM to FGS for single table sattelites, let alone MTT ones.

This is why I feel diverting from HRC in MTT sattelites is going to make us more money. I am not sure on this though, especially because there are 2 main issues, exploitative play because people don't call/jam correctly GTO wise and the issue of future hands impacting the current one. So I would love some further input if you have it.

add-ons etc
I still find this mega interesting. The first few points are more relevant for me currently but in the future I will do some calculations on this and post them. Because I think this is actually quite a relevant concept. Me jumping in max late reg in events where add-on is 2x chips feels like the best strategy but I would love to back that up in some time.
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Old 08-05-2020, 04:58 AM   #14
plexiq
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Re: Bounty math using HRC vs rules of thumb

Quote:
Originally Posted by The_nutlow View Post
HRC models
I am still not entirely sure when to use which model in HRC, iea which one is most suited for which situation. I will sum up what I think here, let me know if that is right.

Firstly there is the difference between Monte Carlo vs math/enumerate. When more then 3 players are active MC is clearly the way to go, but if not I am not sure which one is better, even after reading material you supplied earlier. I feel MC is more accurate when sampled correctly due to card bunching and more players taken into account (if you select that). I think usually the reproducibility and faster calculation of normal mode makes that suitable for me.

However, I was wondering about one thing. The limitation of 3 active players, is clear when your option is not in the game tree, but does it also affect ranges directly? I mean suppose we have a bounty spot where ranges are wide, if a possible 4th person is behind you that can overcall after 2 calls and covers you, that affects your shoving range quite a bit i would say. I think that the normal mode would not take that into account and just sets the overcall range of that 4th person to zero. Is that correct? Because then for bounty spots this can be quite relevant and I will take the longer runtime and use MC. In most other ICM spots the 4th overcall range is quite marginal I would say so I think normal math is good enough.

As for ICM/FGS/ChipEV. ChipEV is clear, that is when you disregard ICM. Multitable calculations can't be done with FGS right? So if we are in MTT phase it is clearly ICM mode. For single table you suggest to always use FGS right? Or are there situations where plain ICM is better suited (like bounties or something)?
Pretty much spot on.

MC vs Math: Yes, the Math engine always restricts to max 3 active players and that means if Hero is the 3rd to enter the pot then all players behind are forced to fold. This can be quite significant for KO spots.

Downside of MC mode is usability: It's slower, not exactly reproducible, you need to be careful to get sufficient sample sizes for the relevant lines and have to manually run new samples if you need updated EVs after range changes. Generally not very suited for new users as there is more potential for user mistakes.

Equity models: I'd recommend FGS as default for single table calculations, MTT ICM for anything before the final table. Simple ChipEV or ICM for HU.

Quote:
sattelites
The problem is that in practise lots of people decide to fold 100 percent as they are almost guaranteed a ticket if they have a very large stack, as do I. I think this is quite correct given dynamics after the specific hand you calculate. That is not how HRC calculates, it still finds you should jam as the calling ranges are crazy nitty/0, you still increase your chances because if you fold 100 percent and shorties keep doubling you might end up bubbling still after blinding out (I actually had that yesterday). While the latter is the rational, in practise HRC just calculates your chances of making it are not 100 percent but say 98 percent, when calling ranges are very nitty it is then relevant to push all in for the last 2 percent.

Practically speaking I think however that the odds of you bubbling after blinding out are a lot less then getting called and be in the middle of the pack again and have a lot more risk to not make it. In larger MTT sattelites, game situations after that hand become very important. So in some sense you kinda need FGS I feel, but I am not entirely sure.

That is kinda why I am in doubt how accurately HRC models multitable sattelites. Because as a player you can incorporate these next hand dynamics, HRC (without FGS for MTT) can't. I see the impact is already detrimental comparing plain ICM to FGS for single table sattelites, let alone MTT ones.

This is why I feel diverting from HRC in MTT sattelites is going to make us more money. I am not sure on this though, especially because there are 2 main issues, exploitative play because people don't call/jam correctly GTO wise and the issue of future hands impacting the current one. So I would love some further input if you have it.
I think your main point about HRC pushing ranges being too wide isn't really an FGS/ICM issue. Essentially this sounds like players in your game having irrationally loose calling ranges. Even if we had perfect knowledge of the actual tournament equities at optimal play, in high-bubble-factor scenarios that still doesn't protect you from losing EV against mistakes your opponents make.

If you need accurate pushing ranges for your game then you really can't get around manually adjusting the calling ranges to be more in line with the ranges of your actual opponents and then re-calculating the pushes. If you loosen up those satellite calling ranges just slightly then you'll see very nitty pushing ranges, even with the current equity models.

FGS in MTT spots is kind of problematic, depending how it is implemented. If you just leave the stacks on other tables static throughout the FGS calculation then this can easily be worse than not running FGS at all in e.g. bubble spots. Simulating FGS play for all tables would be a good solution, but I don't think that's feasible.

Quote:
add-ons etc
I still find this mega interesting. The first few points are more relevant for me currently but in the future I will do some calculations on this and post them. Because I think this is actually quite a relevant concept. Me jumping in max late reg in events where add-on is 2x chips feels like the best strategy but I would love to back that up in some time.
Assuming equal skill and no re-buys, I think you are correct that buying in as late as possible is the best strategy. You'd probably need a fairly large edge over the field to justify buying in early. Would be interesting to look into this in more detail.
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Old 08-05-2020, 08:01 AM   #15
The_nutlow
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Re: Bounty math using HRC vs rules of thumb

Quote:
Originally Posted by plexiq View Post
Pretty much spot on.

MC vs Math: Yes, the Math engine always restricts to max 3 active players and that means if Hero is the 3rd to enter the pot then all players behind are forced to fold. This can be quite significant for KO spots.

Downside of MC mode is usability: It's slower, not exactly reproducible, you need to be careful to get sufficient sample sizes for the relevant lines and have to manually run new samples if you need updated EVs after range changes. Generally not very suited for new users as there is more potential for user mistakes.

Equity models: I'd recommend FGS as default for single table calculations, MTT ICM for anything before the final table. Simple ChipEV or ICM for HU.
Good to see I finally got that haha. Thx for confirming.


Quote:
Originally Posted by plexiq View Post
I think your main point about HRC pushing ranges being too wide isn't really an FGS/ICM issue. Essentially this sounds like players in your game having irrationally loose calling ranges. Even if we had perfect knowledge of the actual tournament equities at optimal play, in high-bubble-factor scenarios that still doesn't protect you from losing EV against mistakes your opponents make.

If you need accurate pushing ranges for your game then you really can't get around manually adjusting the calling ranges to be more in line with the ranges of your actual opponents and then re-calculating the pushes. If you loosen up those satellite calling ranges just slightly then you'll see very nitty pushing ranges, even with the current equity models.

FGS in MTT spots is kind of problematic, depending how it is implemented. If you just leave the stacks on other tables static throughout the FGS calculation then this can easily be worse than not running FGS at all in e.g. bubble spots. Simulating FGS play for all tables would be a good solution, but I don't think that's feasible.
You are right, I mix 2 things up here. I think I should first play around with changing ranges in these spots (I already noticed that our push ranges is drastically different after we do that).

Apart from that I just meant that going from plain ICM to FGS in single table satellite situations matters a great deal. That is without adjusting any calling ranges. Although we can't calculate that, the same applies in MTT satellite situations. We are able to adjust for this in game though, so I am not sure if following plain ICM (even with adjusted ranges) is the way to go. I will have to do some more studying to find that out.

EDIT: I ran some single table satellite spots using FGS. However, I quickly found that the depth setting of FGS matters quite a lot. I am not sure what the different depth levels mean. Can you tell me that? It might be in your thesis actually, will look at that as well. I also noticed that plain ICM isn't doing that badly in MTT sattelite situations where there are a lot of shortstacks and you are in the BB being able to go trough the blinds but not much more. You still call very nitty (as you should). So I might overassume the need for FGS in MTT situations. Will run some more spots the coming few weeks from hands I play and get back to this.

Quote:
Originally Posted by plexiq View Post
Assuming equal skill and no re-buys, I think you are correct that buying in as late as possible is the best strategy. You'd probably need a fairly large edge over the field to justify buying in early. Would be interesting to look into this in more detail.
Well yeah, which is kinda against popular belief (the run-up a stack and use max rebuys thing). Although that might be for non 2x add-ons.

I remember an interesting spot, I had an Ace in the BB when the SB jammed covering me when I had 10 BB which was around the normal buy-in stack. That was the exact moment before the add-on. If I fold I make the add-on break and are able to get chips much cheaper. If I fold I have 30 BB for 2 buy-ins, If I call and win I have 40 BB for 2 buy-ins. If I call and lose I have 30 BB for 3 buy-ins. I am pretty sure that if you run the math that you can't nearly call ChipEV there, and it might be quite detrimental. That even excludes ICM after the add-on break (your 40 BB stack isn't worth 4/3 of a 30 BB stack, especially in a sattelite format).

It makes for quite interesting situations.

Last edited by The_nutlow; 08-05-2020 at 08:09 AM.
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Old 08-18-2020, 04:19 AM   #16
The_nutlow
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Re: Bounty math using HRC vs rules of thumb

@plexiq The last week I ran some more MTT sattelite spots and I think you're right, HRC does actually quite well. Only spots where there are a couple people left to bust and like 50 get a ticket might not be accurate if like 2-3 players are forced all-in. But that makes complete sense, as HRC doesn't have positional info.

The only question I have left is the depth setting on FGS, I am not entirely clear on that still. What do the different depths mean?

Thx for all the help!
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Old 08-18-2020, 05:50 AM   #17
plexiq
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Re: Bounty math using HRC vs rules of thumb

The FGS depth controls how deep into the game tree the calculation looks, beyond the current hand. Higher depth settings provide better accuracy, but runtime also scales exponentially with the depth. Simply choose the highest depth settings that still result in comfortable runtime on your hardware.

FGS1 (depth 1) means you calculate 1 hand deep, ie the calculation looks into the lines that may play out in the hands immediately following the current one, for all the various stack setups that may result from the current hand.

FGS2 simply looks one hand further than FGS1 (ie, now also looking at all hands that can be reached immediately from any of the FGS1 hands.), etc. You can probably see why increasing depth causes an explosive growth in calculated hand setups.
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Old 08-18-2020, 05:58 AM   #18
The_nutlow
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Re: Bounty math using HRC vs rules of thumb

Oh wow, it is that simple. Just the amount of hands calculated after, got it.

I think that were all my questions. If I have some more I will post them (probably in a new thread) but for now thank you for all the useful comments. You helped me out a ton!
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