The genius of Pokémon games

The Pokémon games celebrate their 20-year anniversary this year. There are currently six "generations" of these games; each generation consists one or two complementary pairs of games (each pair is essentially the same game, but with some catchable pokémon being different, and some details in the storyline changed), and a third individual game in some cases. If we count each complementary pair of games as essentially the same game, there are 16 distinct games in total (27 if we count all games individually). This is, of course, only counting the core games, not the side games nor spinoffs (which usually are of a completely different genre and use completely different game mechanics.)
Curiously, each of the core games uses essentially the exact same basic game mechanic. From the very first games of generation 1 to the latest games of generation 6.

Describing the common aspects of the game mechanics of all the games would be too long, but to pick up the most essentials, it's basically a turn-based JRPG with a party of at most 6 pokémon, each with at most 4 moves, them being able to learn new moves as they level up, or using special items. Pokémon belong to different "classes" with a rock-paper-scissors system of strengths and weaknesses against other such "classes". Wild pokémon can be defeated for exp, or caught and added to the player's roster. The core story consists of the protagonist starting with one starter pokémon and advancing from city to city, challenging gym leaders, and ultimately reaching the Pokémon League where they will fight the "Elite Four", as the ultimate challenge and "soft end" of the game (although in most of the games the gameplay will continue after that with additional side quests and goals, and often even expanded world and new catchable pokémon.) There are a myriad of other staples and stock features that appear in all of the games, but I won't make this paragraph any longer by listing them.

Every single core game in the series, all 27 of them (so far), use the that exact same core game mechanic, and follow that same core plot. All of them. Their graphics have advanced with the hardware (even making a quite successful jump to 3D), and each new generation has additional features to them (lots of new pokémon, new battle modes, new side quests, etc.) but essentially all follow the same pattern. One could pretty much say that if you have played one of them, you have played all of them.

Yet, somehow, against all logic, each game is as enjoyable to play as ever. Somehow they avoid a sense of endless repetition, even though that would describe them quite well. I have a hard time explaining why. That's the genius behind these games.

For example, when I bought my Nintendo DS, one of the very first games I bought for it was Pokémon White. A year or so later (and mostly inspired by Twitch Plays Pokémon) I bought Pokémon White 2. Being in the same "generation", it's a very, very similar game (much more similar than games in subsequent generations). The story is different, but other than that it's really similar. But I still found it really enjoyable and addictive, and I played it for even longer than the first one.

These games, from the very first ones, are really well designed. You could just pick up the very first games of the first generation, in all of their monochrome graphical quality, and enjoy it as much as the latest ones. All the essential game mechanics are there.

Not many game series succeed in this. People often laugh at game companies essentially releasing the same game year after year (usually sports games), and how people still keep buying them even though it doesn't make sense... but in this particular case, it does make sense, because each game is as enjoyable as ever.

One thing I like about the pokémon games is how relaxing it is to play them. They avoid frustration and stress (although this can go so far as to often make the games too easy). They can be played at a leisurely pace, without rush nor pressure. Somehow the game mechanic just works.