I've spent so much time on Adventure Capitalist. Countless hours tapping things to upgrade them so I would get enough money to buy more things and upgrades to get more money to do that ad infinitum. Then you reset your things but you get even more money next time. And the numbers go really really high and you can buy things to make the numbers go even faster. It's basically the only iOS game I've played so far that made me watch its ads gleefully - because it made the numbers go faster, and watching a 30s ad is always worth it to do that. If you like idle game - which I'm not sure what that says about you, or me - you gotta try this one.
Much like I said in my opening paragraph, this is an idle game at its best. You start by tapping on things to make them produce money at a fixed interval - from a few seconds to a few hours - then you buy more things, then you buy Managers that automatically 'tap' your businesses for you. At certain business thresholds, you get bonuses (usually getting more money from your businesses, but sometimes you also increase their production speed), and you can also buy upgrades to get more money. There are in-app purchases, but another way to support the game developers (and to get 2x boost for four hours) is to watch ads. I've done it constantly. It made me feel a bit gross because I was willingly watching ads in a mobile game, but it gave me a substantial reward to do so.
After you've earned a bunch of money, you get 'angel investors', which give a base 2% bonus to your profits each, although this can be upgraded. To collect your angel investors, you need to reset your businesses to 0 and start over, but it goes much more faster the second time around, so it's totally worth it. The managers you buy are a early-game kind of treadmill; At first, you can't buy most of them, but when you have a huge cashflow, you buy them all almost at the beginning and then the manager tab is useless, they do three things; either they click automatically your businesses for you, either they show your cash per second (and lower the price by 10%) or they lower the price of a business type by 99.99999% (which seems a lot, but with the numbers we're talking about here, it's not that much)
Of course, when you leave the game and come back, you have raked a bunch of money in, so you don't have to keep the game open at all times. With the gold you can buy for real money, you can get cash multipliers, or even angel investors without needing to restart from scratch. Speaking of the angel investors, you can also buy upgrades with them, and while at the beginning it's a balance act between the loss of revenue you get from selling the angels and the benefit of the upgrade, the game nicely gives 'safe' upgrades that cost less than 1% of your angel investor total.
After a while you unlock the opportunity to go to the moon. This takes a bunch of time and/or resources, but you unlock it eventually. I didn't enjoy the moon, it's much slower than the normal place, I've had to wait days before I could buy enough businesses to have a bonus. The big problem on the moon is that everything is super slow and businesses give weird amounts of money. You can trade your cash for megabucks and use them to boost your businesses. It's recursive-iffic!
Big numbers, tons of achievements that you will probably never obtain, countless hours of tapping on things and watching bars fill and numbers grow, Adventure Capitalist is the quintessential idle game, it has everything. Give it a shot!