"Idle" games. Sometimes called "Clicker" games or "Incremental" games or even "tap"/"tapper" games. You basically sit and wait while the number rise. Usually you have to tap, tap, tap, tap until you get some sort of "auto-tap" then you just keep spending your in-game currency to upgrade and make your money go up progressively faster. Usually the game continues, to some extent, when you go off the game. You come back and "claim" the money, usually a smaller amount than if you sat there with the game on or only for the first 4 hours, or however long, that you were off the game. Your money is going up at 10 coins per second, you save up 1000 coins, upgrade your money producer, and now you get 11 coins per second. You buy new money producers, or upgrade your existing ones, you but or upgrade something else that increases your money production speed. Eventually it takes so long between upgrades that it is no longer practical to do it, so you reset/prestige and you are back to the start of the game again. You have to tap-tap-tap again like you did back at the start of the game. But you now have some sort of permanent upgrade that survives a reset. So your money already goes up a bit faster than it did the first time. Now when you get to that same point that seemed impassable last time, you get past this bit and get bogged down a bit further. Each progressive reset lets you get a further each time.

I would describe this type of game as "addictive", not "fun". Often this seems to be a selling point. "This is the most addictive game I've ever played". But that's not the same as "fun". It feels like you've boiled away the "fun" aspect of something to just the bare minimum.

I had half a dozen of these on the go at a time.

• Balls drop and fall down to the bottom, progress is made by increasing the ball quantity and reducing the size of the obstacles.
• Your character walks along auto-killing the enemy ahead of you. You increase the attack damage.
• Your little man goes down the mine, does some mining, then brings up gold. Buy extra mines and speed up the miner to progress.
• Customers come to your theme park and go on the rides. Buy more rides and upgrade existing ones.
• Your chickens lay eggs, increase their speed and the egg's value.
• Attach cogs and other machines together to make air come out of underwater stones.

I played these types of games for quite a while, but afterwards realised that all I've done is watch number get bigger and bigger.

If you enjoy these types of game I'm in no way mocking you - play and enjoy, I've just decided that I want to play games that feel more "worthwhile" to me. Something with a story-line I can get into. Characters I can care about. I want a game I look forward to playing, not just a game that I feel I'm missing out of in-game earnings if it's not on my screen all day.