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Switch is currently at 61.44 million as of June 30th.

So far, VGChartz' tracking has the Switch at roughly 4.61 million units sold from July 1st to September 19th, with 11 days of tracking left in this fiscal period. Safe to say, it'll pass the 5 million threshold of units sold to consumers, and rather comfortably too. Somewhere around 5.2 million units sold is what I'm guessing. If that tracking is accurate, then the shipped total for this FY would be roughly 6.2-6.7 million. Depending on how much Nintendo has improved their ability to meet demand.

That would bring the Switch's overall shipped numbers somewhere between 67.64-68.14 million heading into the holiday quarter. Last year, Nintendo shipped 10.82 million units in the holiday period from October-December 2019. Granted, this year they don't have a super, megaton S-tier title like Pokemon or Smash Bros. in years past. But, demand is so through the roof right now that they don't really need one of that caliber. Hyrule Warriors and whatever title they have left to fill December will do just fine. So if Nintendo is able to, I think they could ship 10.82 million again, if not slightly more. Which would bring them to right around 79-80 million by the end of the year. From that point, they would need roughly 20-21 million to achieve OP's projection.