The thing is, if you have to walk out of the house with only one gadget on you, you don't take a Nintendo DS, you take your telephone - it'll give you some gaming on the go, whilst keeping you connected, allowing you to take photos and have a GPS.

Nintendo has to compete against that, and it is not easy. On the other hand, Nintendo could make an absolute killing by selling a gamepad accessory for the iPhone - extra battery life plus a decent d-pad/thumbsticks would be an easy sell for gamers. You could probably even price it at a pretty steep mark-up and make nearly as much profit as they must be making on the DS. Make all Nintendo games compatible with it, and run a licensing scheme so that other game companies can list themselves as compatible with the hardware.

This strategy allows Nintendo to continue innovating where they have successfully done so in the past - specifically with clever input devices. It's been a long time since Nintendo could claim to rule the roost for things like raw processing power, so leave Apple to do the heavy lifting there.