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Old 06-30-2020, 12:34 PM   #1
Join Date: Feb 2019
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Optimal Game Tree Construction

Is it better to make strategy profiles parsimonious or to include many, many sizings?

The advantage of parsimonious game trees would be they save RAM, and the strategy splits are a bit more "natural" if multiple sizings are viable. Plus if you study a hand where someone takes a sizing that's wildly different from the modeled sizings you can always just add in the chosen sizings as needed. Like if you use bet sizings of (20%, 50%, 100%, 150%) by default and someone bets 37.5% on the flop and then 75% on the turn you can just add those in. The downside would be that by default you have a lower chance of actually capturing an optimal size--there's lots of spots where 37.5% dominates 20%, for example.

The advantage of really big trees is they're really big and "cover your bases" better for that reason. But the downside is with really big, granular trees the strategy splits in theory may not be as natural as the ones you encounter in game. So although there may be spots where 37.5% is sheerly better than 20%, if you always use a strategy profile with (20%, 37.5%, 50%, 75%, 100%, 150%) you're more likely to capture that in your trees but in practice many people are not good enough and the dEVs may be trivially small, anyway, such that the strategy gets split more in theory than it does in practice--and this can definitely have effects on strategies further down the tree. Of course, you can always node lock the strategy to be split however you want.

Is the a consesus "best-practices" for tree building?
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Old 07-05-2020, 12:26 AM   #2
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Re: Optimal Game Tree Construction

It all comes down to maximizing computational efficiency. This is individual to your specific hardware and solver.

There are clearly diminishing returns to making your strategy more complex. Every extra betting option makes the game tree exponentially larger and harder to solve, while only adding microscopic amounts of EV. You want to find a game tree that can be comfortably solved within a reasonable amount of time with your hardware.

Try this: Solve a very very complex tree with many bet sizes and mark down the EV and time to finish. Now reduce one player to use a single bet/raise size, resolve, and note the EV loss. In most cases the difference between a complex strategy and a simple strategy is negligible.

As a rule of thumb, always try to make sure that the solver can comfortably get stacks in by the river.

There's a saying in poker: "A simple strategy executed well will outperform a complex strategy executed poorly".
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