I think that a game that revolves around effectively using / beating a specific Pokemon is usually deep. If it's not what we want in a metagame, that's fine, but I don't think that a game that revolves around a specific Pokemon is competitively shallow because of revolving around that Pokemon. I don't see what's not deep about what you described.
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I will say that I see why Mewtwo is too powerful in RBY. But I just don't see how RBY Ubers is not a game with plenty of competitive depth, although that may be because I simply don't understand or don't appear to understand the notion of competitive depth.
I don't know what you see as deep. Why do you think rby ubers is deep?
I'm going to say that for a game to be considered deep it must be possible to significantly improve at the game even after many years of scrutiny and metagame development by elite players. Obviously, that's far from an ideal definition, given that it integrates a massive time period.
Thinking on what makes a game
feel deep, it's that there are a lot of options available, but also your choices and other events (opp choices, hax) can have significant direct and indirect implications for future decisions in the match, creating advantages and disadvantages. When we battle we create sub-goals that work towards our goal of winning. e.g. to put my Lapras in a favourable position I need to KO their Chansey and paralyse their Starmie (that's one sub-goal comprised of two more specific sub-goals).
A meta where gameplay is shallow might see lots of inconsequential events, or events that have limited impact, only affecting one sub-goal (e.g. if getting 30% chip damage on something meant you were 30% closer to X threat sweeping and
nothing else). I'm going to suggest that RBY 6U's problem is that there are too many of these events. By contrast, some events can define the entire match, impacting every other possible sub-goal. For instance, throwing out early paralysis and catching a Chansey. This is an event that has huge ramifications for pretty much every pokemon on your team- Egg can't easily land sleep, Lax can now switch in easily on Chansey and damage the opposing team, your own Chansey now gets stalled out by the opposing Chansey and so on. It greatly impacts your sub-goals, in turn forcing you to apply your understanding of the game to re-evaluate your position and objectives. A deep game has lots of events that matter, having broad and/or highly impactful consequences
So there are at least two components to depth already outlined (there's probably more if you look at written pieces on game design, but combing through search engine results is enough to make we want to gouge my eyes). Actually, now that I think on the stuff on sub-goals, simply having lots of them is important, so that's three.
- The player has lots of significant, substantially different options available in order to achieve victory
- Over the course of a match the player will generate a significant number of sub-goals in order to get the win
- Gameplay naturally generates lots of events whose consequences are highly impactful and/or broad in their impact on player sub-goals
There's bound to be more to it, but that at least is progressing towards something more useful