Comment by TZubiri

For games that are as complex as pokemon, it's usually necessary to restrict analysis to some subset. In this case team typing was used.

I personally like restricting to generation 1, as it is very cannonical, very static, and one of the simplest.

Furthermore I like the 1v1 format, which instead of a team, it's just 1 pokemon vs the other. Otherwise you have to resort to heuristics.

But even with a 1v1 and generation 1 restriction it still isn't solved!

Even a single matchup it's very complex to arrive to a theoretical mathematical problem, and still quite burdensome to write a montecarlo simulation.

For example:

Tauros vs gengar (Not an uncommon matchup in competitive gen 1)

Hypnosis has a 60% accuracy, tauros can sleep for 1 to 6 turns with equal probability. Tauros can 2HKO with Earthquake, but can also crit. Gengar can 4HKO, with each crit counting as a double hit (both crits having roughly 20% chance).

The question of who has the advantage is to my knowledge unsolved (also consider that in 1v1 the answer is different, as in teams you only have 1 sleep, so Gengar wastes it). It's also different from the problem of choosing the actual correct move, not only do you need to find the best first move, but in the game decision tree, you need a decision for each node. For example, if Tauros has 60% HP and Gengar has 100%HP, is it still better to go for hypnosis, or better to go for damage and hope for 1 out of 2 crits. This is all made more complex by the fact that both mons have a speed tie, so it's yet another probability event of who will attack first.

https://www.smogon.com/forums/threads/gengar-vs-tauros-1v1-w...

For a simple gen 1 with hidden teams, I think there's a bigger game tree than chess, and even Poker. The fact that it's non-stochastic with hidden information makes it very similar to poker analysis wise, I bet Counter Factual Regret Minimization approaches would work as well.