Random guess 80-85

One thing a lot of people don't seem to realize is that the DS/PSP generation was vastly larger than any previous generation and 3DS/Vita is actually pretty similar to pre-DS/PSP levels. Also Gameboy and it's 118 million sales doesn't really tell the whole story as it was a 2 generation device that had shown huge declines and was about to be replaced before Pokémon came along and revitalized sales.

Oh I realise that but the point is in the past when the gens were this big they didn't have mobile on the brink of taking over.  

The same logic could be used for consoles but the core seems to actually be growing (ps3/360 < ps4/X1).  Last gen was boosted by the Wii anomaly.  

The PSP had a wii like effect on the dedicated handheld market in terms of greatly boosting it,  the only difference is it was a device that captured core gamers where as the Wii captured casuals. 

I really don't believe the core console market is notably growing, more like PS4/XB1 are more front-loaded than PS3/360 were, lifetime sales for PS4+XB1 will likely be similar to PS3+360 which in turn is similar to PS2+XB. But that's getting off topic.

As for PSP, a huge selling point was that it wasn't simply a gaming device but a multimedia device. A portable device that could play games+watch movies+listen to music+surf the Web was a pretty big deal back when PSP released.

A lot of people act like handhelds are dying but I firmly believe there is still a market for them, 3DS going on to sell 65-70 million or so shows there is still quite a bit of people who like dedicated gaming handhelds.

Considering that the Vita is basically already dead and may sell around 3 million units until it will be discontinued and considering that Nintendo will most likely launch there next handheld this year, I expect no more than 85 million.

85m.

86 Million both are great handhelds.