Hey, I got a question. (might not be a very good one but im curious)

Why does GTORangeBuilder solve only for turn and river given preflop and flop conditions? Couldnt the same formulas be used to solve from flop given preflop conditions? The only thing I can think of is the computation of possibilities is too large, so its possible just not practical for your program/server. And if this is possible then the same formulas could be use to solve HUNLHE preflop right? (given a fix bet sizing of cause) And are there any plans to increase the capacity of GTORB to solve the flop?

thx

Hi,

Good question!

Flop solutions are in early alpha and will likely be released by the end of February. The computation required is significant so they take hours to run rather than seconds or minutes, but the exact same algorithm is used.

Regarding solving preflop, you cannot solve preflop in isolation, but rather you must solve the enter game (limited to whatever bet sizing you wish to consider). The exact same algorithm could be used to do this but the computation required is immense. The limiting factor is just computation no major algorithmic change is required.

Researchers at University of Alberta just made major head lines in the last day or two for running that exact type of calculation for limit holdem and it took a 200 super computer cluster months to reach an approximate solution (which is hundreds of thousands of dollars of computation). That said, if you had a few hundred K to spend. there are probably stack sizes / bet sizing limitations you could consider that would reduce HUNLHE to a not too much higher degree of complexity.

-swc

Hey swc,

Awesome program. In regards to flop solution, if both players play a standard 85% 2.5x open game, then anyone deviating from your program's flop solutions would be losing money to other player, correct?

If the above is true, I imagine the HU poker landscape changing quite a bit once your program is released.

Hi, glad you like the program!

GTORangeBuilder currently can't account for strategies that use a bunch of different post flop bet sizes with different portions of their range so its entirely possible (likely even) that there exist complex strategies that use a variety of bet sizes that would come out on top. But if both players play "standard" preflop like you said and then use reasonably standard post flop bet sizing then what you said is accurate.

That said, currently the flop calculations take a long time to run (hours for most 6-max scenarios and even a day or two for something like a minraised pot HU 100BB deep) and there are a lot of different flops so the amount of effort / time / money that is required from someone who really wants to emulate GTO play on a wide variety of flops will be significant.

My guess is that when launched my flop solutions launch they will have a significant impact on HU, particularly in HUSNG and particularly at the higher stakes, but that as usual people who are willing to put in a lot of study time will be the ones to really see big benefits. I don't think its likely that GTORB will kill the games but I do think it will enable players who are willing to put in the study time to play a lot closer to GTO than anyone does currently.

Huh? They've been playing 3-handed lhe since '09.

Yeah totally true of course, not sure why I said that, I think maybe I meant that it was the first year they were doing 3 handed kuhn poker which I think is true but am not sure on, sorry for the error,

My point was mostly that a pure GTO approach in 3 handed is questionable and that 3-handed play is a long ways from figured out. Of course AIs can play whatever they want and have been playing 3 handed for years (snowie plays 6-max of course). However, the fact that they are playing it, doesn't mean they are very good at it, nor does it necessarily mean that a pure GTO approach is necessarily suitable in a field with fish because unlike in 2-handed it can actually lose money playing GTO. I think my point was that the inclusion of as simple a game as Kuhn poker indicates that there is a long ways to go in 3 handed stuff, although of course I wrote that a long time ago so not 100% sure what I was thinking, sorry again for the error.

"They want their AI to be non-exploitative but that is very different from it actually being GTO"

Can you elabrorate on this, please?

I always thought that playing perfectly unexploitable poker was the same as playing perfect GTO.

Playing unexploitable means that no matter what strategy you opponent might use against you, he will not be able to have a positive EV against you (but always <=0).

Isn't that the same as playing GTO, or am I missing something here?

Hi,

So there are two key differences, although they are largely semantics as I think we are mostly just using different terms. That said, terminology can be important so...

1. In my statement above that you quoted I said "non-exploitative" not "unexploitable". "non-exploitative" just means that it doesn't adapt its play based on what its opponent is doing. Strategies that don't change their behavior based on past play are sometimes called static. In repeated games (like poker where you play multiple hands) in general it is always a GTO solution in the repeated game (although often there are non-static GTO solutions) to play the GTO solution to a single round game every single time. Obviously such a GTO strategy is static, but just training a bot to not adapt its play based on its opponents is obviously not sufficient to get you to GTO. A bot that always folds in not-exploitative but not GTO.

2. I think usually when people define "unexploitable" they mean that your opponent would not be able to "exploit you" which is usually defined as, "even if my opponent knew my strategy exactly he could not adjust his play in a way that would increase his EV, compared to how he is currently playing". That is to be exploitable there must be some strategy adjustment your opponent could make to exploit you and increase his EV. Again GTO strategies must be unexploitable, but there are unexploitable strategies that are not GTO. A trivial example would be always folding. This strategy is unexploitable in the sense that no matter what strategy your opponent uses he can not leverage his knowledge of your strategy to increase his EV. However, as you said, GTO requires that you are maximizing you EV at every point, not just avoid exploitation.

A more useful example to consider is a game where you hold the nuts or air and your opponent holds a medium strength bluff catcher (like the clairvoyance game from MoP) and there are 100 chips left to bet. You can bet 50 chips with a "balanced" (according to MoP alpha value) range that is "unexploitable" in the sense that you make our opponent indifferent between calling and folding. If you do so he has no way to exploit you, his EV is the same no matter what he does. So your strategy is unexploitable right?. However, doing that is NOT GTO because betting 50 chips with a balanced range is just a fundamentally weak play. You should be betting the full 100 chips (with a properly balanced alpha range) because that is more effective with your range and will increase your EV. The difference in quality between the strat that bets 50 chips with a balanced range vs 100 chips with a balanced range is not a matter of your opponent exploiting you, him playing perfectly (or always folding, or always calling or whatever he wants to do) has no impact on your EV or on which strategy is superior. The superiority is a matter of EV maximization which is a key element of GTO that is often overlooked because people focus too much on balance. I have a blog post on this here: http://blog.gtorangebuilder.com/2014...ploitable.html

Furthermore, it is worth noting that there are plenty of games (including poker with rake) or a single hand of poker where you are out of position where a strategy like you defined unexploitable (guarantees your opponents EV is < 0) might not exist or where it might exist but not be GTO.

3. If your questions are in regards to snowie rather than GTORB, you can of course use CREV to just measure how close to GTO any strat is on some specific rivers (although I don't think snowie claims to be near GTO and I don't think that it needs to be GTO to be useful). That won't tell you how close to GTO its strategy as a whole is but it will give you an idea of if its really close, not very close, or way off. GTORB automatically calculates and reports its "epsilon equilibrium distance" or "nash distance" with every solution which is the standard game theory measure of quality of an approximate GTO solution. I encourage all GTORB users to verify the reported solution accuracy and so I made videos of how to do so using CREV for river scenarios. You could of course check Snowie against CREV in the same way that you can check gtorb and directly measure its epsilon equilibrium distance, at least on a specific river, if you were so inclined. GTO is a science, is provable and is something you can at least to an extent check yourself so you don't need to take anyone else's word for if something is GTO or not.

Anyways, I made two videos on how to measure epsilon equilibrum distance using CREV that are free on youtube here:

https://www.youtube.com/watch?v=j7xSHC90_Og
https://www.youtube.com/watch?v=-UenhnsjiOY

Then I also have a (not free) CardRunners video on the topic here where I go through measuring the quality of one of the approximate GTO solutions from Janda's book using CREV here, and then show how to shrink the epsilon equilibrium distance by improving the strategy hand by hand based on GTORBs results:

http://www.cardrunners.com/poker-vid...-part-1-asuth/

Sorry this response is so long, but I like to be thorough.

-swc

If I understand correctly, the flop solution solver will calculate the strategy on every turn and river card. Will all the 49 turn strategies be included to people who purchase a flop solution?

Yes, it will show what to do on the flop, every possible turn outcome and for each of those turn outcomes every possible river outcome.

I put up a solution to a trivial toy game near the bottom of this blog post.

http://blog.gtorangebuilder.com/2014...-3-street.html

The scenario/solution itself isn't very interesting (it was designed just to show how to solve a simple flop situation algebraically) but it will give you an example of what a flop solution will look like and you can browse through all the turns and rivers.

Nice, the program certainly becomes so much stronger if it can solve the flop.

It is interesting that you can use the algorithm to solve the entire game given enough computational power. Im not too sure how your algorithm looks like, but I always thought (might be wrong) that you use a more direct formula to figure out which action is best for a particular hand which is very different compare to the team that claim to have solve HU limit poker that is similar to poker snowie which keeps playing against itself until it reaches equilibrium.

Quick GTO question if you dont mind. Does GTO always takes the most +EV line for each hand? If so than capping our range is always part of GTO right? for example if we decide its GTO to check back Q2ss on QT5r then it goes without saying we are checking back all our Tx hands?

thx

GTORB does use a different method (fictious play) than the UoA guys and Snowie (I don't think those two groups do the same thing either but I haven't deeply studied them), and it is a bit more direct in that it directly and exactly computes the EV of each possible action against a given strategy and that strategies exploit-ability at every step as it runs (GTORBs underlying calculations are a bit more like what CREV does). It doesn't do any simulation/randomization and it never "plays itself". However, the GTORB approach is still limited by computation/memory, if processors were 100x faster GTORB would be 100x as fast.

Exact GTO play would take the most +EV line for each hand in isolation where that EV is the EV of the action against an exact GTO opponent. That does not necessarily imply that we would check back all middle pairs if we check back top pair, that will all depend on the hand ranges and our expectation when we play GTO on various turns. For example, if our middle pair hand is much more vulnerable to being drawn out on, or if our top pairs EV when it bets and is called is low because it is often dominated, then middle pair might have a check back EV that is lower relative to its c-bet EV and might become a bet. I'm sure there are ranges/stack sizes where on A63 it is GTO to cbet 76 and check back A2.

Even in simple river situations it is not the case that if you check the top of your range that you should check a slightly weaker non-bluff hand. This can happen for various reasons, but a simple one is blockers. I made an example off the top of my head, with totally unrealistic ranges here:

http://gtorangebuilder.com/#share_sc...8b/root_v=29.1

Basically in this spot QQ/JJ are better value bets than KK because they block the strongest part of the opponent calling range. QQ/JJ are never causing better to fold so they are bet for value, but KK is a check. Again the scenario above is just a model to illustrate a point and is not designed to represent real world ranges in any way. Since it is a simple river spot you can quickly/easily check the solution in CREV if you are skeptical.

Thanks,

-swc

Make sense, I was getting a little confuse with GTO and balance since I thought if its +EV to cbet ATo on QT3r it must be +EV to do so with Q2ss but I guess it doesnt mean its the most +EV thing to do given our entire range and possible taking into account turn and river play. Thanks for the explanation.

I would think that your statement (only) holds for symmetric games, in which each player is given the exact same situation(s). There are some games, for example, the limit betting Nuts-or-Air game, or the No-Limit betting Nuts-Or-Air game w/ finite pot size, where one player can play their end of the (theoretical) equilibrium, and the other player still has positive expectation.

That your opponent is not able to improve their expectation, and your (own) expectation is maximized, against whatever possible adjustment they could make, is very different than your opponent having an expected value of less than (or equal to) zero, no matter what they do.

swc123

Would it be possibly to create a function in GTORB that demands 'no-mixed'-strategies?

Like you have a function that demands OOP-player has to check, would it be possible to create similar, yet very different, function that demands that the different hands in Hero's and Villain's range can only be _one_ action (check/fold/bet/raise) 100% or 0% of the time?

I know we would then probably get a large nash-distance, but such a function could be useful, as it's hard for us humans to exactly check 37% of the time with one hand and bet the other 63% of the time ..

EDIT: and btw thanks for your very in-depth answer earlier, I appreciate it.

Good question, I'd need to think about that. I'm not sure I know an algorithmic way to do that more efficiently than a human looking at the mixed strategy and using intuition to collapse the frequencies to 0 or 1 would do. Its definitely an interesting idea, I'll look into it a bit.

Thanks!

-swc

So this may be a stupid question, but if you believe that GTORangeBuilder gives you a legitimate edge in high stakes poker why sell it? wouldn't you be better off using this edge to $$$ in? If I had invested hundreds or thousands of hours of my time to develop and edge, I definitely would not share it for $500 a year.
Not meaning to insult you, just curious

Good question, for me the answers are largely personal.

I played poker full time after dropping out of grad school (was 2 years into game theory PhD) for about 2 years (mostly NL $400 6max) and I did enjoy it, but around that time I had the idea for TableNinja and got into software and coding, the next few years of my life I dedicated completely to coding and got involved in some non-poker related startups. At that point I discovered that I actually really like coding and the feeling of building something great that a lot of people get value out of more than I like grinding at the tables (although I definitely do miss playing for a living at times).

Furthermore, I live in the US which is a hassle due to legislation and I have a family (I'm 30 and married with a kid so ancient by poker standards) so my current life style were I can work at home doing something I enjoy is just preferable to me compared to trying to be a top high stakes player.

Honestly if I'd had the idea for GTORB 5-7 years ago I probably would have kept it to myself and tried to break into the high stakes games but at this point in my life making great software / great game theory content appeals to me more than being a great poker player.

The other side of things is that like CREV, GTORB is a tool and to really get max value out of it requires a lot of hard work and intense study, I definitely don't think it would make anyone an elite player over night, so its not like by keeping GTORB to myself I could just hit the tables and print money. I think GTORB can make study time a lot more productive and powerful but its a still just a tool and a ton of hard work, discipline, tilt control, game selection, etc are all still required.

I guess finally for full disclosure, the version of GTORB I am developing is always a month or two ahead of what is publicly available (largely just because I don't release anything publicly without a ton of testing) so I always have a slightly more powerful version of the software available to myself.

Also a much less indepth answer to that is at the bottom of the FAQ: http://gtorangebuilder.com/#faq

Hi swc123,

I have a question concerning the functionality of GTORangeBuilder Flop. It is possible to create a tree with more than one bet sizing (for example I want to bet 30%, 50% and 100% of the pot on the flop). Are there the restrictions of how many such variable bet sizings I can make (I know that the complexity of solving the flop is enormous and if I make the tree really big by adding many bet sizings for bets and raises, the complexity will be gigantic)?

In addition, I am curious about what time GTORB Flop will be released to the public. I know that many people asked you this question and if I am not mistaken you planned to release it in mid or late February. I am just really looking forward for GTORB Flop

Hi,

So I did take a step towards releasing flop calculations today by releasing a strategy pack with 7 flop solutions + video commentary / mathematical analysis by me. There is a preview video for it here: https://www.youtube.com/watch?v=z78AfmXR65Q.

Then the pack is available at http://gtorangebuilder.com/#gto-dojo

Then there is also a demo flop solution (requires a turn license) available with an accompanying free (no license required) youtube video here:

Video: https://www.youtube.com/watch?v=z78AfmXR65Q
Solution: http://gtorangebuilder.com/#share_sc...9555/root_v=31

In terms of when it will be possible for people to run their own flop calcs, like they can currently do turn and river calcs, I'm still considering how I want to allow for that. That is how many people I want to open it up to, who gets access and how much it will cost, what level of limitations on scenario complexity there will be etc. As the previous poster pointed out there are some incentives to me to keep it to myself (or to limit it to a small group) so I'm weighing my options a bit. I'll definitely make a more detailed announcement about it by the end of February.

At the moment the scenarios I've run with 3 bet sizes like what you are describing tend to end up enough less accurate (because the tree is so complex and I've been capping the computation time at a fixed number of hours) that they aren't as useful and the EV difference between using 3 bet sizes and 1 good one has tended to be small enough that it is not measurable within the large margin of error of the 3-bet size solution. I think that just to keep my own costs down (both on storage and computation) I'll put some max number of decision nodes on the game tree in conjunction with range size, probably somewhere in the 500K-2 million decision nodes range for bigger ranges, which would definitely rule out a 33%/50%/100% tree. That said its entirely possible that 6 months from now the flop performance will be a lot better and more will be possible.

Hope this helps,

-swc

Thanks for your reply, swc123.

It looks super interesting and I really like all videos and blog post.

Hard to justify the price for myself though when I can't even play online right now.

Hah yeah, if you can't play definitely going to be hard for the software to pay for itself

Glad you like the blog, though, I'm going to try and continue to make it a priority to keep releasing some quality free content.

As promised (actually a day or two late ) here is an update announcement about or plans for flop calculations.

http://blog.gtorangebuilder.com/2015...ibrary-is.html

TLDR: The plan is to focus on providing carefully constructed high quality solutions that people can ask questions about in conjunction with continuing to produce video analysis packs. All turn license holders will get access as part of their turn license.

Isnt this getting cheaper after time?
alternatives ? free similare software?

Good question!

When we release our flop library (which will be free for all Turn license holders and should be out in about a week) we will be eliminating the turn license and just having a generic GTORB license that grants access to the full flop solution library, free unlimited turn and river calcs, and probably some other goodies including some exploitative calculations I'm hoping to build in in the longer term. It won't be cheaper but you will get a fair amount more content at a similar price.

We may at the same time decide to make the river calculations free indefinitely.