"Infrastructure", which includes z mainframes (called out by name) and I assume iSeries also (though not called out), is the smallest segment of IBM's revenue.

See page 17: https://www.ibm.com/annualreport/assets/downloads/IBM_Annual...

Much, if not most, of their consulting revenue is for mainframe support and much of their "hybrid cloud" is just hosting mainframes.

My semi-educated guess is that mainframes are a much bigger chunk still.

(AS/400 is midrange. They are called something else now, I heard. Maybe I-series.)

A lot of those indispensable infrastructure systems we all depend on, such as insurance, income tax, etc., run on mainframes, as they have for decades now.

So don't diss big iron / Big Blue.

I, for one, hope they have many years left, though I guess they could do with improving their corporate culture and business practices some.

Those z-boxes can comfortably run 5000 instances of Linux as your very own virtual data center. Makes you wonder what inference on mainframe would look like, though you don't have GPUs.

Do people use them for that, and is it cost-effective?

There was an interesting point in the recent Acquired podcast about Microsoft vs IBM. Supposedly IBM revenue only decreased after 2012 and Microsoft only passed it in revenue in 2015.