Hello all!
I'm not a poker player, rather a neuroscientist, who while nursing a burnout last year became obsessed with combinatorics. (The brain is also a pretty complex entity.) In my journey, I stumbled across poker as a prime real-world example, but couldn't find an exhaustive model of post-flop combinatorics, with which to play around. (If one exists and I just couldn't find it, please do let me know!) So, I enumerated the entire post-flop sample space, evaluated suit symmetry throughout the dataset, and created a reduced look-up-table-based model. From an initial ≈56.2 billion possible combinations, there are actually only 607,300 unique ways a post-flop hand can evolve (and correspondingly the number of statistically unique boards at the river), which can be efficiently simulated for multiple players on a desktop computer.
Now I'm trying assess the utility of such a model by announcing it in various channels, and ChatGPT tells me that this forum is one of the most widely used by poker fans of all kinds. So, I openly ask for any feedback from anyone who has interest in the combinatorial statistics of the game or the simulation thereof (i.e., to approximate equity).
Although this is to me a surprising extent of statistical redundancy, I acknowledge the fact that the ultimate statistical scope of the game (i.e., including decision trees) extends orders of magnitude beyond the combinatorics themselves. Analogically, “I've just discovered that the universe is 100,000-fold smaller than previously thought. But it's still enormous, so it makes no practical difference to our lives.” I also am aware that there are already numerous post-flop tools available, including the Power-Equilab software provided for free on this website, which achieve equivalent results. (Modern algorithms and Monte Carlo simulators are fast enough to accurately approximate probabilities of multi-player situations on the fly).
Therefore, I’m struggling to see any utility of such a model in any context. One contribution it could provide is a pre-calculated statistical analysis of the post-flop game for multiple players, obviating the need for on-demand compute power, but I struggle to see the practical value of even this. I’m anyhow preparing to release the model on GitHub, along with a stand-alone visualisation tool to explore the statistics of any board, but as this is quite a heavy time investment (and I actually have a job), I’d like to hear your thoughts on the matter already in order to settle my internal conflict. What utility, if any, could you see in such a model?
Otherwise, my only analogical counterargument is, “Yes, a 100,000-fold smaller universe makes no practical difference to our lives. But it’s still something we’d want to know,” (says the scientist in me.)
Cheers, and best of luck in your games!
Mike
PS. Please also post any technical questions you may have about the model for me. I'd be happy to (try to) answer them and will post again once it's available to download. But be advised that writing up the description and implementation of the model, as well as organising the data for maximum interpretability, is taking me quite some time. -_-
