I am quite likely to do a more formal writeup in the next few weeks, unless Zvi beats me to it. (He had, apparently, directionally similar results.)

Any idea what the actual deduction it supposedly found for private school?

You can pay for K-12 with 529 or Coverdell ESA funds. But neither allows deductions for contributions. Only growth in either is tax free (assuming it’s spent on education expenses).

Many states allow a state tax deduction for 529 contributions, which could net you up to an 8ish% discount if you’re in a high tax locality (e.g. NYC).

See: https://tax.illinois.gov/individuals/credits/educationexpens...

Okay I was thinking only of federal taxes (for which there’s no deduction). Thanks for the detail.

I've also saved a bit of money on taxes just by thinking about possible deductions and asking LLMs whether they exist. Of course to actually claim such deductions I need to follow instructions from the IRS/state tax agencies so it's hallucination proof: I'm still manually reading the instructions from the tax agencies to understand how to claim them.