Full post-flop solver release March 07, 2015 00:32

Today we are releasing the most powerful analytic tool to ever enter the poker market: post-flop Nash equilibrium solver for Holdem.

This is not an equity calculator, decision tree software nor some kind of shady AI thing. This is something much simpler and way more powerful. PioSOLVER solves post-flop games - it's that simple. It tells you how good the solution is (for how much it's possible to exploit it by perfect adversary). It provides exact EV of every play, every hand, exact frequency of every play and exact range the play is made with. All this is provided in the form of fully browsable tree which you can save for later reference. Nothing is hidden or implied - every detail is there and we made efforts to present it in accessible and instructive way. PioSOLVER is magical game theory optimal box people were waiting for. It provides insight into the game which was impossible to get before.

All poker theory, cleverly sounding concepts, pages of written advice and hours of coaching videos are going to be revisited from now on. PioSOLVER doesn't make assumptions. It doesn't fall for tempting rhetoric. It just solves games and exposes any human prejudice. It doesn't recommend bluffing a lot or bluffing a little it tells you which bluffs are part of optimal play and which aren't. It doesn't tell you that such and such hand have nice implied odds or plays nicely post-flop - PioSOLVER doesn't use vague language like that. It tells you exactly how much every hand makes and exactly how to play it. It communicates in cold specific numbers.

To see an example we are going to solve a 3bet pot with typical HU ranges assuming preflop raise to 25 (2.5bb), 3bet to 90 and a call. The starting pot is 180 and starting stacks are 100bb preflop (so 910 now). The flop is going to be Ks Th 4c. For the record, this solution is 0.123 from Nash equilibrium which means that our perfect adversary, one knowing our exact strategy and exploiting every small detail of it would win 0.012bb/hand vs us. We would pay 0.15bb/hand in rake playing on typical online site to put this number in perspective. Let's look at the flop c-betting strategy:

 Inormation visible on this view:

  • Optimal c-betting frequency is 59.43%.
  • There are 138.5 combos c-betting and 94.6 combos checking.
  • 87s with a backdoor flush is a a 97.1%-97.7% (depending on a combo) c-bet; without a backdoor the c-bet is made only 12.1% of the time.
  • Available actions are bet 100 and a check.
  • Strategy for all other combinations is shown. To see the details you just hover your mouse over a square containing the combo of interest and details are displayed  in right bottom corner (on the picture the mouse is over 87s)

This is a "Strategy" view. Let's go into c-bet 100 branch and explore other available information:

Here we see Strategy+EV view for in position player against a c-bet. Visible information:

  • In position player (Villain) should fold 37.15% of his range which constitutes 153.9 combos. The call is made with 62.81% of hands and a raise is almost never made (not a  suprise for experience HU players but it's nice to see this confirmed)
  • A3s with a backdoor is a marginal call yielding 1.116/1.235/1.312 gain over fold (respectively for possible combos). A3 of diamonds is a fold. Calling would be -13.021 (or 1.3bb) mistake
  • In the main view the strategies are shown for every hand. In the "Zoom view" (controlled by hovering a mouse over main view on the left) the information about strategy and EV of a play is combined. As you can see there is EV of play for every combination and every action. Raising with A3s is a big mistake regardless of suit combination.

Let's now click "Villain EV" button and see how much every hand makes:

Here we see EV for every hand with nice color gradient. Hands in the red are close to 0 (some are slightly below zero because the solution didn't converge yet to folding 100% and just folds 99.9% or similar making -ev play in 0.001 of cases this has marginal effect on overall quality of the solution). Other than that we can see:

  • Total EV for in position player once the cbet is made is 57.86 - hardly surprising with a flop which hits 3bet range that well.
  • 64s (a hand we focus on this screen) is worth about 65 with a backdoor flush and 36.993 without it. Having a backdoor flush is worth almost 3bb here.
  • Other hands have their EV displayed in the main view (one on the left) to see the details for specific information we just hover the mouse over specific squares (as we did on 64s in this image)

Let's explore further by choosing a call, 3c turn. We will see how Villain defends against a second barrel:

 Here we can see the range view in action. Overall Villain's range at this point consists of 257.3 combos, raisiing range has 20.3 combos, calling range 168.5 and folding range 68.4. We can also see how to see range for specific actions. So we may notice that:

  • Raising value range is mainly KQ/KJ and to lesser extent AA. We can see that optimal play is to raise for value/protection here with those hands but slowplay stronger ones most of the time (like AK or KK/KT)
  • Semi-bluff raises are AQ (by going to Strategy and EV we can can see that bluff and a call are very close with AQ combos, both worth about 1.7bb depending on combination)
  • Folding range is interesting as well. We can see that underpairs (99 and lower) fold now and that A3 folds as well.
  • Another interesting thing is that A5 is better hand than A3 (because it can make a straight). Optimal play often value potential over immediate value. By going to Strategy + EV view we can see that Ad5d for example is worth 0.8bb and it's more than As5s/Ah5h - why it's more is an interesting quesiton and one of the biggest realizations GTO solutions provide. I will go through it in another post.

Ad5d is better than As5s and Ah5h against a 2nd barrel:



Finally we are going to explore 2nd barrel - call line. The river is Ad. Hero checks, should Villain value bet an ace here? Try to think if say A5 is a bet or a check here, then:


 The answer: A5 is a  clear bet. Betting is about 3.4bb better than checking. Of course we could explore further why that is and what exactly calling range of OOP player on the river is. I will stop here though as it should already by clear what kind of things are possible to see with PioSOLVER. The whole tree takes 1.735GB and you can easily replicate it with either PioSOVLER basic or PioSOLVER pro.

I invite you to visit our product pages for PioSOLVER basic and PioSOLVER pro. If you would like to read more try resources page. If you are still not sure we make completely free turn and river solver available: PioSOLVER free. If you have any questions email as at piosolver@piosolver.com  or post in our support thread on twoplustwo. 

This is an early release. This means several things:

  • Our first clients will be very first people on the planet to get insight into how optimal play in Holdem looks like
  • We tested PioSOLVER for hundred of hours and several computers but we couldn't predict every possible computer setup nor every possible problem. We will be working with our first users to get all those fixed and to improve the sticking points in the interface. You may count on a priority support during the initial period. We are ready to provide direct 1-on-1 support if problems can't be sorted by email or forum posts (our support thread is on twoplustwo forum). It's our priority to make PioSOLVER experience as smooth as possible for our first adopters.
  • During the initial period your voice as to choices in the interface and further solver functionality counts more. The development is not stopping today. We are on the quest to make an ultimate poker tool and we will gather feedback and wishes to get to this point. There are a lot more things which could be done to show the results in better way or to solve bigger games. Which direction we choose to go to depends to big extent on what our users' reaction is.