05-09-2013 , 08:51 AM
Quote:
Originally Posted by yaqh
Not sure this last part is right. I agree that (in raise/shove games at 40 BB effective) when the SB is opening 2x, the BB is jamming something near 37.5%, and when SB is opening 3x, the BB is also jamming near 37.5%. But in between the SB's 2x and 3x open, the BB's jamming frequency actually goes up. Essentially, he wants to jam more than he does vs the 3x since he has to defend more to keep the SB's bluffs indifferent, and he can jam more than he does vs the 2x since he wins more when SB raise-folds.
Cannot understand why the same does not work at bigger stack sizes (80bb) where SB can open 100% hands with any open size 2x, 2.5x, 3x and BB shove % goes up with SB opening size.
Is it because SB has to back off his opening % when he 3x at 40bb but can still open near 100% when 2x or 2.5x?
05-09-2013 , 09:41 AM
Quote:
Originally Posted by CoronalDischarge
Bet sizing

- Were you solving for bet sizes to any degree, or mostly using intuition and experience when choosing candidate bet sizes to feed to the solver?
The decision trees used to model each river situation did use a bit of of experience and intuition. Mostly, though, I first solved the game with a bunch of options and then pruned the game trees down only keeping the most commonly used sizings. (I sometimes mentioned the unused sizings in the text when it seemed important.) The idea here was to make it easier to communicate the resulting solutions. I didn't think it'd really help anyone if I spent pages describing slight differences in the frequencies with which different combos used different sizings, etc.

Quote:
Originally Posted by CoronalDischarge
- Is it actually possible to ‘solve’ bet sizing in general or in any particular spot, without solving the whole game? Or, hypothetically, if one were in the process of solving the game, would the bet sizes ‘pop out’ somewhere along the line, or is it a case of brute-force solving for every possible set of sizings and then seeing which has the highest EV? Are these questions inscrutable at the moment?
Hm, I don't see how it'd be possible to say much quantitative about equilibrium sizing without solving the game. Basically, the question is, 'Which of my sizing choices has the highest EV at the equilibrium?' and to figure that out, you need to basically need to know how Villain responds to each of your sizings at the equilibrium. In other words, you need to know Villain's GTO strategy at least.

However I tried to focus a lot on sizing in the discussion of the examples in order to build intuition about how different sorts of river starting distributions led to different bet sizings. So hopefully you'll be able to make some guesses at least as to what the equilibrium river sizings might look like just from looking at the distributions.

Quote:
Originally Posted by CoronalDischarge
- You don’t mention geometric growth of pot at all. Is that concept only relevant to games with static hand values? Or would we expect to see sizings trend towards that pattern as ranges across streets get closer to optimal?
Geometric growth of the pot gives us a way to get all-in with bets over multiple streets, and almost all of the discussion in Volume 1 was about single-street situations. (I guess you could say that single-street geometric growth of the pot just means going all-in, but that doesn't need a fancy name.) Multi-street strategies will be the focus of Vol 2.

Quote:
Originally Posted by CoronalDischarge
- There are several places in the text where it appears that the bet sizing ‘Pot’ has special significance. Perhaps that’s coincidence but it kind of chimes with my intuition… 2 to 1 being the lowest whole integer odds, I see it as being a sort of ‘knee of the curve’ point on the risk/reward graph: lower and the rate of loss of value outstrips the rate of risk reduction; higher and it’s the other way round. Does that sound about right, or am I seeing things that aren’t there?
Yea, I think your intuition about the risk-reward tradeoffs makes a lot of sense in general, but a PSB certainly isn't always the right answer. There are often a lot of quite subtle trade-offs and interactions between different parts of the players' ranges that can affect equilibrium bet sizing, as we saw in some of the river examples.

Quote:
Originally Posted by CoronalDischarge
Miscellany

- Would it be possible to get a look at the full results? I’d love to dig deeper into card removal effects and threshold hands, etc.
I don't mind sharing the full solutions, but the thing is they're really a lot of data that I imagine will be hard to make much sense of without some visualization/analysis tools. If you like really long text listings with frequencies for every hand combo in every spot, I can provide those, or if you think an image like the one at the bottom of this post:

http://forumserver.twoplustwo.com/sh...89&postcount=2

would be helpful, I can do that too.

Quote:
Originally Posted by CoronalDischarge
- Similar to the GGOP question, do you think that as ranges become closer to optimal the equity distribution graphs become a) more like a smooth diagonal line and b) less distinguishable between the two players?
I don't see the connection to geometric growth of the pot, but if you mean what I think you do, then yes I think that's a very insightful observation.

I think I pointed out (maybe in discussion of river Ex 6) that any large groupings of hands with equivalent value (i.e. long flat regions on an equity distribution) sort of provide Villain an easy opportunity to put a lot of our hands in a hard spot. So when we solve multistreet situations, that is, when we give players the ability to adjust their river starting distns by playing differently on earlier streets, I suspect they'll often adjust their play so that their river starting distns look more like the symmetric distns case.

I tried to develop this idea a bit more but didn't make much progress towards anything more rigorous or anything more practically-useful. Maybe I'll give it more thought.

Quote:
Originally Posted by CoronalDischarge
- I was a bit surprised that in example 7 the BB wasn’t able to bet his whole range and take the whole pot. The small threat of trips is obviously what makes the difference. Is there a stack size at which the BB could lay claim to the whole pot, given the same ranges? More generally, for any ‘bluff-catcher plus traps’ spots, I imagine there must be an equation into which I could plug stack size, equity of trap hands and frequency of trap hands and that would spit out a yes/no answer to the question, ‘Can the other player capture the whole pot?’ Does that seem reasonable? (Feel free to leave the finding of said equation as an exercise for the reader )
Well, although the BB has a lot of pretty strong hands, most of his range is decidedly non-nutted (the SB does have a chunk of pretty strong hands other than trips) especially given that the stack-to-pot ratio on the river is pretty large. But yea, the BB does pretty well. At beginning of river play, there's 4 BB in the pot and 24 BB behind, so an EV of 28 BB would be capturing the whole pot. And in fact his average EV is about 27.1 BB. Not a bad result for him considering that he's out of position with a lot of money behind and the SB does have some strong hands.

Quote:
Originally Posted by CoronalDischarge
- On a similar note, it was interesting that one of the examples included a non-all-in betting range that contained no nuts. Should there be a straightforward way of finding the min B and/or max S at which it’s ‘ok’ to have no nuts in range, or is that sort of thing contingent on the precise make-up of the equity distributions?
Well we're gonna play our pure nut hands in whatever way gets Villain to put the most money in the pot on average.

The main issue in that spot, IIRC, was that Villain's distribution was such that he didn't hold many hands he could value reraise with (and so he didn't bluff-reraise too much either) even if our betting range was capped. So basically, Villain reraised versus our smaller bet with capped range as much as he could possibly get away with, and it still wasn't enough to motivate our nut hands to prefer making the smaller bet.

I don't think there's any general rule for that which just involves the bet and stack sizes. The particular distributions play a big role.

Quote:
Originally Posted by CoronalDischarge
I think that’s all I’ve got for now. Thank you for taking the time to address this thread, and thank you for the book! I can’t wait for the next one
05-09-2013 , 09:45 AM
Quote:
Originally Posted by Qlka
Cannot understand why the same does not work at bigger stack sizes (80bb) where SB can open 100% hands with any open size 2x, 2.5x, 3x and BB shove % goes up with SB opening size.
Is it because SB has to back off his opening % when he 3x at 40bb but can still open near 100% when 2x or 2.5x?
Sorry, not really sure what you mean?
05-09-2013 , 10:48 AM
Dude thanks for the quick responses; you're a beast at posting as well

Quote:
Originally Posted by yaqh
Anyway, I really do think correctness is very important, so if you do happen to re-locate these spots in the future, please let me know.
Sure thing

Quote:
Originally Posted by yaqh
But if you'll excuse the post hoc rationalization -- very few players, I believe, will make the overbet their standard bet sizing in this spot. That is, some people might overbet sometimes, but I think very few make it the standard sizing they use with most of their river betting range. And there's actually good reason to focus on analyzing decision trees with the standard sizings. If your opponent constrains himself to using one particular sizing on the river, then in effect, the game you're playing is the one where that's his only sizing choice, so that's the one whose solution is most useful to know. Players often, through habit or whatever, effectively constrain their choices of bet sizing before even starting to construct their ranges.

Does that make sense?
Yeah that makes plenty of sense, and ofc the book isn't intended to be a GTO manual but is just as much about maximally exploiting people.

Quote:
Originally Posted by yaqh
Yea, I changed this example after studying it a bit, but it looks like I forgot to update the hand history on p 204 . Thanks for catching this.
OK, so can you recap what the HH is supposed to be up to the river?

Quote:
Originally Posted by yaqh
I'm not quite sure what you mean here. Do you mean that you think (c) should say "B=P, C=4P"?
Yeah that's what I meant.

Quote:
Originally Posted by yaqh
I don't mind sharing the full solutions, but the thing is they're really a lot of data that I imagine will be hard to make much sense of without some visualization/analysis tools. If you like really long text listings with frequencies for every hand combo in every spot, I can provide those, or if you think an image like the one at the bottom of this post:

http://forumserver.twoplustwo.com/sh...89&postcount=2

would be helpful, I can do that too.
Hmm, if it's just a huge wodge of data then the visual representation might be a good alternative. Thing is though even with the chart that you used on p.205 in the book, it wasn't too clear to me which suit combos were being used for some hands, and that was what got me thinking it would be cool to see the full solutions. Ideally I'd like to have the charts and then be able to look up specific hand breakdowns where necessary. How big are we talking for the text files?

Quote:
Originally Posted by yaqh
I don't see the connection to geometric growth of the pot, but if you mean what I think you do, then yes I think that's a very insightful observation.

I think I pointed out (maybe in discussion of river Ex 6) that any large groupings of hands with equivalent value (i.e. long flat regions on an equity distribution) sort of provide Villain an easy opportunity to put a lot of our hands in a hard spot. So when we solve multistreet situations, that is, when we give players the ability to adjust their river starting distns by playing differently on earlier streets, I suspect they'll often adjust their play so that their river starting distns look more like the symmetric distns case.

I tried to develop this idea a bit more but didn't make much progress towards anything more rigorous or anything more practically-useful. Maybe I'll give it more thought.
As far as similarity to GGOP I was just wondering about ways in which relatively simple shapes and patterns might begin to emerge as GTO approaches. I think you said in the book 'a straight line is in some sense the ideal river distribution', or something like that. I love the way you've described it just now, focusing on the eradication of those horizontal stretches the villain can target with indifference, that's awesome.

Thanks again man. Any updates on Vol.2 btw?
05-09-2013 , 10:55 AM
I mean for raise(2x/2.5x/3x)/shove game SB can open 100% hands at equilibrium when 80bb deep. BB will respond by increasing shoving % when SB size goes up since he can win more when SB raise/fold.

Now for the raise/shove game but 40bb stacks BB responds differently. You said that BB reshoves about 37.5% when SB 2x or 3x, but in between BB can reshove a bit more.

Why is that?

Is it beacuse SB can open near 100% hands at equilibrium when he 2.5x, but he cannot when 3x. In result BB shoving % is tradeoff between keeping SB indifferent to bluffing and gaining more value from SB large raise sizes.

Last edited by Qlka; 05-09-2013 at 11:17 AM.
05-11-2013 , 09:14 AM
Quote:
Originally Posted by yaqh
I don't mind sharing the full solutions, but the thing is they're really a lot of data that I imagine will be hard to make much sense of without some visualization/analysis tools. If you like really long text listings with frequencies for every hand combo in every spot, I can provide those, or if you think an image like the one at the bottom of this post:

http://forumserver.twoplustwo.com/sh...89&postcount=2

would be helpful, I can do that too.
+1 for sharing the data. Are Origin/SigmaPlot/Mathematica sufficient for the analysis of the data ?
05-12-2013 , 07:04 PM
Thanks for the long answers, yaqh. I have now finished the book!
I can't stress enough how much I learned reading it, and how it reshaped my way of thinking about the game. You've got a sure buyer of volume 2 in me

Quote:
Since our actual goal is to maximize our EV with each hand, I'm not really sure what raising large enough to make our worst hand unprofitable does for us. Of course, it may be the case that the EV of our better hands goes up at the same time as the EV of our worse hands is going down, but there's no reason that I can see that any particular EV will be maximized at the point where we can just barely get away with opening 100% -- it seems pretty arbitrary.
Yes, it's pretty clear now that you put it that way. I was thinking that as long as we didn't have to fold preflop, we'd like to raise as big as possible in order to have the biggest possible pot to exploit our positional advantage... But if there was a hand that had extremely low equity (like 2222 in PLO), there's no rational reason to base our whole preflop strategy on the sizing needed to make it breakeven.

I have one more question, on the programming side of things :

You say you did most of your calculations and graphs with custom software, so you clearly have some skill in building your own poker programs. I'm currently building a heads-up simulator that pits bots against each other and tries to improve them using genetic programming.

In short stack situations, I feel like the small depth of the betting tree could allow me to find some optimal frequencies and betsizes very quickly. Also, while in some cases genetic programming has a risk of overfitting (ie developping "a robot that plays well against Chessmaster3000" instead of "a robot that plays chess well"), I don't think this pitfall would happen easily in poker, because if you deviate from GTO to exploit a tendancy of the player pool, you immediately become exploitable yourself, and the random mutations of the pool will punish you for it.

Have you experimented yourself with this approach? Do you think there's a technical reason, other than "I'd rather keep printing money myself", which explains the relative dryness of ressources on this subject? (I think your SB minraise/BB shove/SB call charts were never published before, and they're not exceptionnally hard to compute with some patience and CardRunners EV, for instance, so clearly this is a real factor limiting information).

05-12-2013 , 11:36 PM
Quote:
Originally Posted by CoronalDischarge
OK, so can you recap what the HH is supposed to be up to the river?
30 BB effective

Preflop
SB raises to 2BB, BB calls

Flop: (4 BB) 2 T J (2 players)
BB checks, SB bets 1.75 BB, BB calls

Turn: (7.5 BB) 8 (2 players)
BB checks, SB bets 3.25 BB, BB calls

River: (14 BB) T (2 players)
23BB effective behind

Quote:
Originally Posted by CoronalDischarge
As far as similarity to GGOP I was just wondering about ways in which relatively simple shapes and patterns might begin to emerge as GTO approaches. I think you said in the book 'a straight line is in some sense the ideal river distribution', or something like that. I love the way you've described it just now, focusing on the eradication of those horizontal stretches the villain can target with indifference, that's awesome.
Yea, it's an aesthetically-pleasing idea. Even if it's right, though, I'm not sure how to make it practically useful .

Quote:
Originally Posted by CoronalDischarge
Thanks again man. Any updates on Vol.2 btw?
Hopefully out by the end of the year! Working on it a lot these days.
05-12-2013 , 11:43 PM
Quote:
Originally Posted by CoronalDischarge
Quote:
Originally Posted by yaqh
I'm not quite sure what you mean here. Do you mean that you think (c) should say "B=P, C=4P"?
Yeah that's what I meant.
Why do you think that? Perhaps this is a notation issue. C (the raise sizing) is the total amount raised to. It's not the amount above the original bet.
05-12-2013 , 11:44 PM
Quote:
Originally Posted by Qlka
I mean for raise(2x/2.5x/3x)/shove game SB can open 100% hands at equilibrium when 80bb deep. BB will respond by increasing shoving % when SB size goes up since he can win more when SB raise/fold.

Now for the raise/shove game but 40bb stacks BB responds differently. You said that BB reshoves about 37.5% when SB 2x or 3x, but in between BB can reshove a bit more.

Why is that?

Is it beacuse SB can open near 100% hands at equilibrium when he 2.5x, but he cannot when 3x. In result BB shoving % is tradeoff between keeping SB indifferent to bluffing and gaining more value from SB large raise sizes.
For any SB open size, there's going to be some BB 3-betting frequency that makes SB indifferent between open-folding and raise-folding. Call it X. So, X depends on open size. For a minraise, X = 50% and for a 3x, X=37.5%.

Except in very short stacks, there are just two possibilities for the solutions to the shove/fold game:

- BB is 3bet shoving less than X. In this case SB is opening 100% because raise-folding is strictly more profitable than open-folding.
- BB is 3bet shoving at exactly X (up to card removal effects). In this case the SB is sometimes raise-folding and sometimes open-folding with the hands he doesn't want to get all-in.

BB will never be shoving more than X -- if he did, SB would only open-raise with hands that intend to call a shove and open-fold everything else, and (above very short stacks) this would motivate BB to tighten up his 3-betting range.

So yea, there's some stack size where the BB is shoving ~37.5% versus a minraise in the solution to the minr/shove game. I think it turns out to be somewhat deeper than 40BB, but w/e, close enough. At this point, the SB is opening 100% since minraise-folding is strictly better than open-folding.

So at this point, SB is minraising, BB is shoving 37.5%, and X=50%. Now the SB starts to increase his open size. Two things happen. First, the BB increases his shoving frequency, as you said, essentially since he wins more from SB's raise-folds. Second, X decreases. As SB continues to open larger, both of these trends continue until the two numbers meet. BB shoving frequency can't go above X as we said earlier, and X just depends on the SB open size. So after the numbers meet and SB keeps increasing his open sizing, X keeps going down, and it drags BB shoving frequency down with it. And when the SB's open size reaches 3x, X has fallen down to 37.5%, and it's taken the BB's shoving frequency with it.

So that's why, at (something around) 40 BB in the raise/shove game, BB's 3-bet frequency is ~37.5% when SB is opening 2x and 3x but is greater in between. The situation is conceptually the same at 80 BB stacks. BB will 3-bet more and more as SB increases his open size until the point where he's 3-betting enough to keep SB's weak hands indifferent between open-fold and raise-fold, and then he won't 3-bet any more than that.
05-12-2013 , 11:46 PM
^ 5kth post!

Quote:
Originally Posted by CoronalDischarge
Hmm, if it's just a huge wodge of data then the visual representation might be a good alternative. Thing is though even with the chart that you used on p.205 in the book, it wasn't too clear to me which suit combos were being used for some hands, and that was what got me thinking it would be cool to see the full solutions. Ideally I'd like to have the charts and then be able to look up specific hand breakdowns where necessary. How big are we talking for the text files?
Dunno, the solutions aren't usually stored as text files... I'll have to work on exporting them. They won't be too big tho. Just a frequency for every hand at every decision point.

Quote:
Originally Posted by Sektorr
+1 for sharing the data. Are Origin/SigmaPlot/Mathematica sufficient for the analysis of the data ?
Well, it's more of a visualization problem then an analysis one, so I'm not really sure. I'll get this stuff together in a couple days and post it somewhere, though, and we'll see how it goes.
05-12-2013 , 11:48 PM
Quote:
Originally Posted by Ragnarok_1er
Thanks for the long answers, yaqh. I have now finished the book!
I can't stress enough how much I learned reading it, and how it reshaped my way of thinking about the game. You've got a sure buyer of volume 2 in me

Quote:
Originally Posted by Ragnarok_1er
Yes, it's pretty clear now that you put it that way. I was thinking that as long as we didn't have to fold preflop, we'd like to raise as big as possible in order to have the biggest possible pot to exploit our positional advantage... But if there was a hand that had extremely low equity (like 2222 in PLO), there's no rational reason to base our whole preflop strategy on the sizing needed to make it breakeven.

I have one more question, on the programming side of things :

You say you did most of your calculations and graphs with custom software, so you clearly have some skill in building your own poker programs. I'm currently building a heads-up simulator that pits bots against each other and tries to improve them using genetic programming.

In short stack situations, I feel like the small depth of the betting tree could allow me to find some optimal frequencies and betsizes very quickly. Also, while in some cases genetic programming has a risk of overfitting (ie developping "a robot that plays well against Chessmaster3000" instead of "a robot that plays chess well"), I don't think this pitfall would happen easily in poker, because if you deviate from GTO to exploit a tendancy of the player pool, you immediately become exploitable yourself, and the random mutations of the pool will punish you for it.
I haven't done anything like this myself in poker, but I am pretty familiar with heuristic optimization. How are you parameterizing/representing your solutions?

Quote:
Originally Posted by Ragnarok_1er
Have you experimented yourself with this approach? Do you think there's a technical reason, other than "I'd rather keep printing money myself", which explains the relative dryness of ressources on this subject? (I think your SB minraise/BB shove/SB call charts were never published before, and they're not exceptionnally hard to compute with some patience and CardRunners EV, for instance, so clearly this is a real factor limiting information).

I'm not really sure, but I've a couple ideas.

You refer to the raise/shove game solutions -- even though they're pretty simple, I don't think they're the sort of thing you can use profitably in-game without actually knowing what they mean and where they come from. A couple years ago, there was a post that written by a very successful high stakes player that was pretty much standard reading in the HUSNG forum that everyone linked to when a noob asked about the shove/fold charts, and it got the theory completely wrong, on a completely fundamental level. Basically, the poker community's understanding and appreciation for mathematical approaches to the game have been increasing very quickly, and there are a lot of things that seem obvious to people now that didn't a relatively short time ago.

Also a lot of the people outside of academia who work on this stuff in a serious way are botters, and they have pretty strong incentives to not draw attention to themselves. I'm sure they have their own communities or w/e (pokerai.org?), but they don't get much love in the broader poker community or on 2p2.
05-13-2013 , 07:47 AM
Quote:
Originally Posted by yaqh
Why do you think that? Perhaps this is a notation issue. C (the raise sizing) is the total amount raised to. It's not the amount above the original bet.
Hmm, I can't remember now whether there was something specific in the text that made me think that. It could just be that it sort of looks like a typo (to my brain!), given that 5P is a pot-size raise plus the initial bet. Not too important in any case.

Coming back briefly to the GGOP discussion, it is of course possible to apply that sort of sizing schema on the river, if there are multiple bets left. In the book there's that spot where the SPR is ~2 and it turns out that the most commonly used bet size is ~Pot. I found that a bit surprising and, again this might be just me, sort of mathematically inelegant. Which got me thinking that maybe that proved that the ranges being examined were quite far from optimal. I know we're all speculating at this point, but I'd be interested to hear your opinion on the following assertion: sizing lines tend towards GGOP as ranges becoming increasingly GTO, and the extent to which they differ from GGOP is a function of a) range assymetry and (pre-river) b) board dynamism.
05-13-2013 , 08:43 AM
Quote:
Originally Posted by yaqh
I haven't done anything like this myself in poker, but I am pretty familiar with heuristic optimization. How are you parameterizing/representing your solutions?
I'm doing this in Java, and I created a PokerBot class which i'm giving more and more freedom to. Basically at the start they only had 2 parameters : frequency of pushing and frequency of calling. Then they were allowed to min-raise (with very basic postflop play), then to raise to any sizing, then to limp, etc.

I then create 1000 bots pretty randomly that play each other in HUSnGs, and I let the program run for several hours. Every so often the worst bots are kicked out and replaced by new ones, genetically programmed by mixing the behaviors of some of the top robots, with a random mutation.

At the end of all this it returns the parameters of the 20 best performing robots, and so far the results I get are pretty convincing. Of course the more I will go in postflop play, the more complicated this will become because of the depth and width of the betting tree. But we'll see
05-13-2013 , 09:10 AM
Quote:
Originally Posted by CoronalDischarge
Hmm, I can't remember now whether there was something specific in the text that made me think that. It could just be that it sort of looks like a typo (to my brain!), given that 5P is a pot-size raise plus the initial bet. Not too important in any case.

Coming back briefly to the GGOP discussion, it is of course possible to apply that sort of sizing schema on the river, if there are multiple bets left. In the book there's that spot where the SPR is ~2 and it turns out that the most commonly used bet size is ~Pot. I found that a bit surprising and, again this might be just me, sort of mathematically inelegant. Which got me thinking that maybe that proved that the ranges being examined were quite far from optimal. I know we're all speculating at this point, but I'd be interested to hear your opinion on the following assertion: sizing lines tend towards GGOP as ranges becoming increasingly GTO, and the extent to which they differ from GGOP is a function of a) range assymetry and (pre-river) b) board dynamism.
Oh you mean one player could bet and the other raise, etc, with GGOP sizings on the river.

GGOP sizing arises in toy games in polar versus bluff-catcher situations (called clairvoyance games or something in MoP). In these situations, the polar player knows whether he has the best hand, and so he's the only player doing any betting. His opponent just plays check-and-guess. So multiple bets never go in on the river in these games. If it's a river-only situation, the optimal bet sizing is all-in, and if it's a multi-street situation, the optimal sizing is to get all-in with multiple bets using GGOP.

Maybe think about it this way. We can think of any river betting/raising as motivated by a fight for what's in the pot at the beginning of river play, just like initial preflop action is motivated by a fight for the blinds. If there was no money in the pot to try to win, GTO play would be to never put any in, at least not w/o the nuts.

Often, to contest the pot, we might want to bet pretty small. Give ourselves a good risk-reward ratio to try to win the pot and all. OTOH, sometimes the best way to try to contest the pot is to bet as big as possible. Put the guy to a decision for all his chips or whatnot. So there are sort of two approaches to bet sizing here --

- betting in relation to the size of the pot
- betting in relation to the size of the remaining stacks

It makes sense think about the first if we're worried about our risk-reward ratio, and it makes sense to think about the second when we don't need to think about a risk-reward ratio (because we know whether or not we have the best hand) and want to just put as much pressure as possible.

So I think we should think of GGOP sizing as the multi-street equivalent to the overbet all-in on the river. It happens sometimes, but I imagine more standard sizings are more common in real play where players hold complicated (and in particular more symmetric) distributions.
05-13-2013 , 09:26 AM
Quote:
Originally Posted by Ragnarok_1er
I'm doing this in Java, and I created a PokerBot class which i'm giving more and more freedom to. Basically at the start they only had 2 parameters : frequency of pushing and frequency of calling. Then they were allowed to min-raise (with very basic postflop play), then to raise to any sizing, then to limp, etc.

I then create 1000 bots pretty randomly that play each other in HUSnGs, and I let the program run for several hours. Every so often the worst bots are kicked out and replaced by new ones, genetically programmed by mixing the behaviors of some of the top robots, with a random mutation.

At the end of all this it returns the parameters of the 20 best performing robots, and so far the results I get are pretty convincing. Of course the more I will go in postflop play, the more complicated this will become because of the depth and width of the betting tree. But we'll see
Oh ok, so in the first case where the solutions just had a frequency of pushing and one of calling, it seems like a hand ranking is implied. What did you use?

And then, how does this generalize to your more complicated approximate games? I mean, sure, if you're playing shove-or-fold, you're going to shove with some amount of the "best" hands and fold the worst, and your opponent's calling strategy will be similar, but I don't see any obvious analog when we start adding other preflop sizings, postflop play, etc.

Identifying a relatively small set of parameters to describe a poker player which is still rich/flexible enough to express the subtle strategies necessary for high-level play seems like a very challenging problem.
05-14-2013 , 12:37 AM
Quote:
Originally Posted by yaqh
Oh ok, so in the first case where the solutions just had a frequency of pushing and one of calling, it seems like a hand ranking is implied. What did you use?
The "HU all-in equity" ranking of CR EV. I'm not sure how it was made but it worked very well.

Quote:
Originally Posted by yaqh
And then, how does this generalize to your more complicated approximate games? I mean, sure, if you're playing shove-or-fold, you're going to shove with some amount of the "best" hands and fold the worst, and your opponent's calling strategy will be similar, but I don't see any obvious analog when we start adding other preflop sizings, postflop play, etc.

Identifying a relatively small set of parameters to describe a poker player which is still rich/flexible enough to express the subtle strategies necessary for high-level play seems like a very challenging problem.
The way I'm doing it right now isn't very clever, basically for each of the 169 hands, I assing a limp pre frequency, an openshove %, an openfold %, a C-bet % and then one postflop rule taken from a set of rules I created (like "goes all in with 2pair or better" or "goes all in with any gutshot or pair or better"). If both players get to the turn, the hand is then checked until showdown. So far the program is not that time consuming, but I imagine it will be once I tackle the turn or allow some new lines like C-bet/raise/clickback 3bet/shove/fold.

Here's another question I have.

I was thinking about the kind of dynamic that limping preflop generates and I found out this :

Let's say we want to make SB indifferent to limping or openfolding with a very bad hand (32o) at 10BB stacks.
We search for EVlimp = Evfold.
I make the assumption that SB will C-bet 1BB on all flops after a limp, because that's what common in my games.

Spoiler:
EVlimp = 9BB x (prob. of shove pre) + 8BB x (prob. of shove post) + 11BB x (prob. of successful C-bet)
EVlimp = 9(1-c) + 8c(1-f) + 11cf
EVlimp = 9 - 9c + 8c - 8cf + 11cf = 9 - c + 3cf

And EVfold = 9,5BB.
So 9,5 = 9 - c + 3cf
So 0,5 = -c + 3cf
So (0,5+c)/3c = f

And here's what I find :

(I also assumed that SB will always fold if shoved on, which is not technically correct. This could be mostly fixed by adding a call option for SB which it does only with 2pair+, which gives SB something like ~80% equity on average vs BB shoving range.)

So anyway my question is : How would I go about finding out a theoritical equilibrium involving limping? Let's say at 6.8BB, so that minraising isn't possible (because it's the same as shoving but with more options for BB).

The way I'm thinking about it now would be to start with a pushing range all strong and a limping range entirely weak. BB would exploit it by keeping its Nash calling range, and shoving his top 75% when limped on.
Then SB would add some traps (I'm thinking to start with AA because it has blockers anyway and so is rarely called when shoved), which would weaken its pushing range.
So BB would call the pushes a bit wider, and loosen the pressure on the limps which could now hide some strong hands.
Then SB would shove a little bit tighter because he's getting called more often, and we could keep adjusting like that until hitting an equilibrium.

Am I thinking in the right way or getting lost in dumb ideas (in particular, does my reasoning for the choice of trapping hands make sense?)?

As always, thanks for your time, it's an honor and a pleasure to get such detailed answers from a great player like you
05-14-2013 , 08:43 AM
I have trouble understanding card removal effect for raise/shove game. From indifference principle BB will shove exactly 50% hands at ~20bb. I can understand that when SB holds particular holding like AA then he blocks BB's shoving range, so there is less combinations of hands BB will shove - less frequency, for other holdings BBs frequency could be higher. I cannot understand how it affects GTO ranges so BB's shoving range is slightly less than 50%.

Last edited by Qlka; 05-14-2013 at 09:11 AM.
05-18-2013 , 11:41 PM
I just purchased htis book on amazon all give my feedback on it tomorrow after in done reading it tonight. I am usually disappointed in poker books as they just to robotic and don't really go into strategizing against players more the situation of hand. People don't realize how importat the flow of the game is going and the mental part of how the player is thinking in that particular situation. If a really nitty player loses a big pot to a 2 outter on the river they are human beings they might play the same hand very differently the 2nd time around as the results can change a players strategy. This book so far looks like its going in the right direction and more about the player then the situation. So I am excited this will be a good book and all grade it from A to F. I am very firm critic so if i give it C it means its pretty good compared to other poker books i read. I just never been to blown away by poker books because poker is more spontaneous then anything its hard to turn that into a book and then applying that same situation in a book to a real life game. Its always going to have some variance to the situation that is different from the book and it causes people to make mistakes. but anyways gl at the tables i will be reading this all night. Someone said i would be blown away by this we will see.
05-19-2013 , 11:28 AM
Will, does this book replace the Moshman book on HUNLHE, in the sense that anyone who owns your book has no need to purchase the Moshman book, and had you read the Moshman book before you wrote yours?
05-19-2013 , 11:42 AM
Quote:
Originally Posted by Ragnarok_1er
The "HU all-in equity" ranking of CR EV. I'm not sure how it was made but it worked very well.

The way I'm doing it right now isn't very clever, basically for each of the 169 hands, I assing a limp pre frequency, an openshove %, an openfold %, a C-bet % and then one postflop rule taken from a set of rules I created (like "goes all in with 2pair or better" or "goes all in with any gutshot or pair or better"). If both players get to the turn, the hand is then checked until showdown. So far the program is not that time consuming, but I imagine it will be once I tackle the turn or allow some new lines like C-bet/raise/clickback 3bet/shove/fold.
Cool, sounds interesting. If you find the solution to poker, use it for good not evil.

Quote:
Originally Posted by Ragnarok_1er
Here's another question I have.

I was thinking about the kind of dynamic that limping preflop generates and I found out this :

Let's say we want to make SB indifferent to limping or openfolding with a very bad hand (32o) at 10BB stacks.
We search for EVlimp = Evfold.
Why do you think that indifference might hold? Actually I think limping is a large part of the SB's equilibrium preflop play 10bb deep but that he'll still strictly prefer to fold his worst hands like 32o. But that's Volume 2 stuff, so I won't get into it here.

Quote:
Originally Posted by Ragnarok_1er
I make the assumption that SB will C-bet 1BB on all flops after a limp, because that's what common in my games.

Spoiler:
EVlimp = 9BB x (prob. of shove pre) + 8BB x (prob. of shove post) + 11BB x (prob. of successful C-bet)
EVlimp = 9(1-c) + 8c(1-f) + 11cf
EVlimp = 9 - 9c + 8c - 8cf + 11cf = 9 - c + 3cf

And EVfold = 9,5BB.
So 9,5 = 9 - c + 3cf
So 0,5 = -c + 3cf
So (0,5+c)/3c = f

And here's what I find :

(I also assumed that SB will always fold if shoved on, which is not technically correct. This could be mostly fixed by adding a call option for SB which it does only with 2pair+, which gives SB something like ~80% equity on average vs BB shoving range.)

So anyway my question is : How would I go about finding out a theoritical equilibrium involving limping? Let's say at 6.8BB, so that minraising isn't possible (because it's the same as shoving but with more options for BB).

The way I'm thinking about it now would be to start with a pushing range all strong and a limping range entirely weak. BB would exploit it by keeping its Nash calling range, and shoving his top 75% when limped on.
Then SB would add some traps (I'm thinking to start with AA because it has blockers anyway and so is rarely called when shoved), which would weaken its pushing range.
So BB would call the pushes a bit wider, and loosen the pressure on the limps which could now hide some strong hands.
Then SB would shove a little bit tighter because he's getting called more often, and we could keep adjusting like that until hitting an equilibrium.

Am I thinking in the right way or getting lost in dumb ideas (in particular, does my reasoning for the choice of trapping hands make sense?)?
Yea I think those are all good thoughts.

BTW, theoretically, it's not necessarily the case that SB can't have a minraising range at 6.8 BB in the full game. We found that in the preflop-only case, but -- perhaps in the full game, SB minraises a polarized range of pretty strong and pretty weak hands. He can potentially do this in the full game since he has options other than raise or fold that he can use w/ his more intermediate hands. And perhaps vs this new opening range, BB's shoving range tightens up so that SB can actually raise/fold some bluffs. Or something like that. I actually think that assuming SB isn't minraising any at 7ish BB is a fine to start with -- just wanted to mention that isn't something we've proven.

I think your guess at the general form of the solutions seems pretty good, tbh, but of course the difficulty in saying anything too specific arises from the fact that it's hard to estimate the EV of hands once they see a flop, and that's inevitable if you allow limping. It's something I've done a good bit of work on, but that'll have to wait until Vol2...
05-19-2013 , 12:08 PM
Quote:
Originally Posted by Qlka
I have trouble understanding card removal effect for raise/shove game. From indifference principle BB will shove exactly 50% hands at ~20bb. I can understand that when SB holds particular holding like AA then he blocks BB's shoving range, so there is less combinations of hands BB will shove - less frequency, for other holdings BBs frequency could be higher. I cannot understand how it affects GTO ranges so BB's shoving range is slightly less than 50%.
Sure, so at equilibrium at 20BB in the minraise/shove game, the BB is actually shoving about 48.8% of all hands. Something like

22+,A2s+,K2s+,Q3s+,J5s+,T6s+,96s+,85s+,75s+,64s+,5 4s,A2o+,K4o+,Q8o+,J9o+,T8o+,98o

So his jamming range is weighted towards high-card stuff of course, and he's folding his low-card stuff.

The SB's opening range is something like 84% of hands, so the stuff that's being made indifferent to raising or folding (or which actually prefers folding) are like the bottom ~16% of hands -- low card trashy holdings.

Let's take an example of one of these hands and try to see why it actually prefers open-folding to minraise-folding, despite the fact that BB's only jamming like 48.8% of all hands.

Take 32. When SB has 32, there are 1225 combos that BB can have. 633 of those combos fall into the 48.8% jamming range I mentioned above, and 592 do not. So, when SB holds 32o and minraises, he actually gets jammed on more than 50% of the time! So this hand strictly prefers open-folding to minraise-folding -- it's getting jammed on most of the time when it raises despite the fact that the BB's strategy involves jamming less than half of all hands overall.

So basically, what's going on here is that SB's low-card hands that are deciding between open-folding and minraise-folding tend to block a lot more of BB's folding range than his jamming range, so the BB has to actually jam a bit less than 50% of all hands to make them more or less indifferent to minraising.
05-19-2013 , 12:17 PM
Quote:
Originally Posted by ultimatecurse
I just purchased htis book on amazon all give my feedback on it tomorrow after in done reading it tonight. I am usually disappointed in poker books as they just to robotic and don't really go into strategizing against players more the situation of hand. People don't realize how importat the flow of the game is going and the mental part of how the player is thinking in that particular situation. If a really nitty player loses a big pot to a 2 outter on the river they are human beings they might play the same hand very differently the 2nd time around as the results can change a players strategy. This book so far looks like its going in the right direction and more about the player then the situation. So I am excited this will be a good book and all grade it from A to F. I am very firm critic so if i give it C it means its pretty good compared to other poker books i read. I just never been to blown away by poker books because poker is more spontaneous then anything its hard to turn that into a book and then applying that same situation in a book to a real life game. Its always going to have some variance to the situation that is different from the book and it causes people to make mistakes. but anyways gl at the tables i will be reading this all night. Someone said i would be blown away by this we will see.
I'm actually not a huge believer in making a lot of gameflow-motivated plays or engaging in much leveling, at least not unless you know your opponent really well. I think a lot of people leak money doing that sort of thing and would do better if they focused on coming up with solid fundamental reasons to split their ranges, rather than changing them wildly from hand to hand based on things they may well just be imagining.

On a different note, EHUNL might be the kind of book that you want to take some time with rather than trying to read it all in one night. Depends on your background, though, I guess.

Anyway, hope you're blown away, as someone suggested .
05-19-2013 , 12:17 PM
Quote:
Originally Posted by Al Mirpuri
Will, does this book replace the Moshman book on HUNLHE, in the sense that anyone who owns your book has no need to purchase the Moshman book, and had you read the Moshman book before you wrote yours?
No, I haven't read Moshman's HU book. That said, I've heard it's good but quite basic, so I don't think there's actually much overlap between the two at all, and I don't think anyone would call EHUNL a replacement for the Moshman text.

PS: shameless brag:
05-19-2013 , 02:01 PM
Well i read most of it but i didn't even finish reading it. Pretty bad read. The author is to boring. THe first thing to any book being written is it has to have some creativity to it. I think the the moshman book is much better. Even though its more brief sometimes less is more. You will get lost in all the statistics and very minor things like pre flop play and bb situations that a good reg already knows those spots. He writes a history on it. Its pretty ridiculous the detailing he goes into that really doesn't matter. I thought this book would get more into situation and psychological aspect of poker its the opposite. Its a bunch of useless math that doesn't really matter. I am still waiting for a book thats more based on the psychological state of a player based on them winning and losing in certain situations. Because the math no longer matters when a players mental side shifts from a logical to a emotional state. Then the strategy completely changes. An example of this book is what is the optimal shoving range with 35 bbs and he shows a chart of all the hands. That stuff is useless. He can simplify it by saying shove these amount of hands against this type of a player or a player in this mental state. No he writes a whole history about it and has about 5 different charts. and the charts are very boring and very basic. Dont read this book guys i give it an F. And i don't give Fs to often but it was so boring it was the first poker book i have never finished reading.

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