A very limited time with parental supervision as long as the game isn’t particularly violent.
So let’s take an account of games my five and under kids like to play. We have a tablet with Android at home with a few and they like (in no particular order)
- Ticket to Ride
- Jetpack Joyride
- Super Hexagon
- World of Goo
- Plants vs. Zombies
Of course we also have a computer which they play
- Peggle
- FTL (with some help from me)
- A few others to varying degrees of interest
Soon I’ll probably introduce them to Super Mario and Tetris. In my personal opinion, as long as there’s known a limit to how much time they could spend playing, there’s nothing wrong with giving them a computer/phone/tablet and letting them let out a bit of steam. It’s even better when said device has a strong password for any and all Internet uses (dedicated Linux laptop sudo iptables -A INPUT -m owner --uid-owner TheKids -j DROP) and a handful of pre-approved non-violent games on it.