Comparison of Simple Preflop Holdem solutions calculated with different settings! Examples of GTOSims solutions formats!
In this article we will consider and compare the strategies calculated in the Simple Preflop Holdem solver using different calculation parameters, thereby justifying the choice of parameters used for calculations that are sold in our store of preflop gto solutions GTOSims. All examples can be downloaded and browsed in the free version of Simple Preflop Holdem. We will also demonstrate in what formats the user receives the solution purchased in GTOSims and how to open them. This article focuses on the calculation parameters for solutions that are listed on the GTOSims.com website under the authorship of SimplePoker.
General information about test calculations
As an example, on which the tests were performed, a 6-max tree was used, where the stacks of all players are 100bb and the opening strategy for the CO position in the ChipEV model was calculated (game for chips / no rake). For the two earlier positions in the game tree only the fold option is used and the starting ranges for the early positions are set as a folding range so that the cards removal effect is correctly taken into account in the simulation.
Inside the CO fold branch, all other players also have the only action option - fold. The fold EV of CO does not depend on the further play (the EV of the fold can change depending on the further play only in ICM calculations), so this technique was used to simplify the calculation.
Inside the CO open raise branch, the game tree is fully built.
Starting with the version of Simple Preflop Holdem v2.0, the solver has a new bucketing (simplifying postflop calculation by grouping similar hands), which has become revolutionary for calculating preflop equilibrium multiplayer strategies, taking into account any action, which made SPH unique and the best gto solver in its class. The new bucketing made it possible to perform calculations faster, with fewer resources required, and also more accurate due to the fact that bucketing was created based on a combination of all kinds of hands and boards, as well as using the most successful divergence parameters from the latest scientific research and experiments.
Preflop strategies that were calculated for GTOSims used bucketing 10,000 / 10,000 / 10,000 (flop / turn / river), since our calculation experience shows that a larger number of buckets practically does not affect the strategy. More detailed buckets does not make solution more accurate, at the same time such computations can require very large resources (RAM and computation time), which, in combination with complex trees, leads to unreasonably expensive calculations.
For the test we performed two calculations:
- with buckets 10,000 / 10,000 / 10,000 - the same bucketing that was used for GTOSims store solutions
- with buckets 10,000 / 100,000 / 100,000 - the maximum number of buckets available in Simple Preflop Holdem (in theory, it is possible to generate larger set of buckets, but in our opinion this does not make sense)
Calculation parameters in both cases:
To demonstrate the identity of the solved equilibriums, we attach screenshots of strategies at different "depths" of the game tree:
CO strategy (Fold / OR). There are minimal differences, in particular, mixed strategies for several hands differ, but the actions EV of mixed strategies differ by less than 0.001BB - these differences do not affect the further strategy in any way
CO Raise 2.00 -> BTN Strategy
CO Raise 2.00 -> BTN Fold -> SB Strategy
CO Raise 2.00 -> BTN Fold -> SB Raise 10.00 -> BB Strategy
CO Raise 2.00 -> BTN Fold -> SB Raise 10.00 -> BB Raise 100.00 -> CO Strategy
CO Raise 2.00 -> BTN Fold -> SB Raise 10.00 -> BB Raise 100.00 -> CO Call -> SB Strategy
As we can see, the solutions are as similar as possible at all levels, so the use of 10,000 / 10,000 / 10,000 buckets is reasonable, and the solutions using them are accurate.
You can study other branches in this calculation in detail by downloading both files:
You can open examples in the free version of Simple Preflop Holdem (download link); to open a file go to the File -> Open menu or using "drag and drop".
When calculating the equilibrium for the selected street, the strategy for further streets is also calculated taking into account the given game branches of the tree and all kinds of runounts (the tree is calculated fully starting from the given street). If we talk in particular about preflop calculations in Simple Preflop Holdem, then the postflop tree is also calculated, but the postflop strategy is not saved due to abstractions (bucketing) - the detailed postflop strategy will be inaccurate, but at the aggregated level it allows you to get an accurate preflop solution.
Experimentally, we found that in order to obtain high-quality preflop strategies, it is enough to use literally two postflop sizings in order to correctly take into account the equity realization. Additional sizings practically do not affect the strategy, while significantly complicating the calculation (in terms of the required RAM and the duration of the calculation).
In this section, we have compared two solutions:
- using the standard simplified postflop tree similar to the one we used for GTOSims calculations
- a more detailed option: with donk bets and large number of bets on all postflop streets
Both files were solved on 5,000 / 5,000 / 5,000 buckets, since when using large bucketing for the detailed version, a lot of resources are required for calculation, even for such a simple preflop tree (> 350 GB RAM).
As in the case of bucketing, we will show you the results of calculations at different levels:
CO strategy (Fold / OR)
CO Raise 2.00 -> BTN Strategy
CO Raise 2.00 -> BTN Raise 7.00 -> SB Strategy
CO Raise 2.00 -> BTN Raise 7.00 -> SB Fold -> BB Strategy
CO Raise 2.00 -> BTN Raise 7.00 -> SB Fold -> BB Raise 100.00 -> CO Strategy
The results are identical. For independent research of the obtained strategies, you can download both files:
- download preflop solution with simplified postflop tree
- download preflop solution with detailed postflop tree
GTOSims solutions formats
When purchasing a preflop solution authored by SimplePoker on the GTOSims website, you will receive a strategy solved on 10,000 / 10,000 / 10,000 postflop buckets and with a simplified postflop (the information is relevant for all solutions at the time of publication of the article), sufficient for a preflop sim to be very accurate (additional complications of calculations do not lead to higher accuracy, according to our experience and experiments).
You will receive an archive, inside which the solution will be presented in three formats:
- Simple Preflop Holdem File (.bin)
- A set of charts in the PioSolver format (PioCharts). This format is open, so you can also interact with it programmatically
- In the format of charts screenshots (.PNG), structured by folders corresponding to the game tree
We also recorded a short video instruction on how to work with such archive and how to open its content:
We hope this article will be useful to you! If you are interested in writing a similar material that we will publish for other users, please write to us by email: firstname.lastname@example.org
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