out of the 250m home console users of this current gen, how many do you think are real core gamers?

That's a good question. Maybe 1 in 5?

One, me.

20 million Nintendo ones (Gamecube), 30 million Xbox ones (Xbox and converted PS), 50 million Playstation ones (waaaaaay more expensive). I say 100 million. Most of Wii's audience was casual (grandma, soccer mom, little kids that only play party games). A lot of early Xbox users were most likely casual (COD and Madden that didn't want to pay for PS). Playstation caught some of those as well but is least likely because they were most expensive and didn't have a casual gimmick to attract casuals. Most of their exclusives cater to hardcore as well.

Depends on your definition of core gamer. But there are so many variables with just a number of 250m, like people who bought more than 1 console, 2 of the same, etc. So it's very hard to say, but just to guess...maybe a 40%-50%.

Edit: after thinking for a while I think the numbers are probably between 20%-30%

Around 20-25 million. You can use Xbox 1 and Gamecube's numbers.

After the Wii, I'm pretty sure that the solid core base Nintendo had has diminished. They almost lost me. 

I'm a quad-core gamer... it doesn't get much more core than that!

This doesn't affect the question, but with the Wii Nintendo definitely gain a lot people (not necessarily casual). Granted most are probably young kids and teenagers.

50m Sony fans
20m Nintendo fans
10-15m Xbox fans

I think around 80-90m, rest are casuals.