Why not to use pre-built solutions and non-user defined game trees to review lines
A brief look at an emerging way of quickly performing “line checks” and why this form of study can be detrimental
By Brandon Wilson
This article will make the claim that using third-party or otherwise non-user-defined solves to check user-played lines is misguided insofar as the solves are not either (a) reasonably simple enough to have been reasonably executable in-game or (b) directly reflective of the actual strategy the user was employing in-game. How precisely to determine the highest EV-yielding mix of options for either player in a given Nash equilibrium is beyond the scope of this article and not relevant to its claim.
Was my play “GTO”?
Equilibrium solver outputs are only game theory optimal, or GTO, in the context of the parameters of the game theoretical simulation in which they exist. That is, an action taken in one simulation may be the most “optimal” insofar as the parameters have allowed, but a different action might be taken altogether in an adjacent sim with different (and perhaps higher EV-yielding) parameters. As such, utilizing a third-party-solved game tree, or pre-built line-checking software, to determine post-game whether a play were “GTO” is suboptimal.
Consider the following example. To quantitatively evaluate a hand, a user purchases a sim database or an otherwise third-party solved tree for a given spot. We’ll call it a single-raised pot between the button and big blind at 20 effective big blinds. Let us assume this game tree has solved for two flop bet sizes for the in position (IP) player: 25% and 75% (although many pre-solves contain even more, especially at deeper stack depths).
On the A-T-3 two-tone board, the user explores the node in which he faced a 25% pot bet out of position (OOP). In-game, the user would have needed to proceed under the assumption that his human opponent were playing this 2-size split in order to lend validity to the results of the solution he’s studying. Otherwise, the continuing range played in game will likely differ significantly in comparison that of the solver playing clairvoyantly against a 2-way split. Moreover, in later nodes, if this solution employs additional range splits the player was not attempting in-game, the disconnect between the strategies grows, and the effectiveness of the line review, as it were, degenerates.
A common result of this approach is to end up exploring incredibly low frequency nodes. In a game such as No Limit Hold-’Em, this is destructive, because studying as if a combination appears in a range at, say, a 0.05%, when in reality the players holds it closer to 50%, results in critical errors and easily misapplied conclusions.
Thus, the best abstraction for study will contend with the most likely strategy(s) of most human opponents. In other words, studying models too far removed from reality is not good study. And as blanket “GTO” tools continue to sell to a wide array of poker players of varying skill, this poses an obvious problem: users checking lines under parameters far removed from what they played.
A better way to check lines and study poker
Two immediately clear solutions to this problem exist.
First, players can learn to use equilibrium solvers to build their own game trees with real strategies they are playing and expect from their opponents. This approach is no more “GTO,” as it were, than the aforementioned pre-solves. It would, however, result in ranges that map onto their games more practically and strategies the user can more accurately implement as she practices by consistently building more skillful game trees.
Secondly, the pre-solve market can better serve its customers by offering more simplified solved game trees so that the discrepancies between the frequencies in their outputs and the ones faced in real life aren’t so wide due to drastic range splitting that is not often replicated in-game.