There is no certain, mathematical threshold that must be crossed. Rather, most courts hold that the taxpayer understated his tax liability by a “substantial amount.” Again, not all courts agree. For example, if you live in California, the government need only show that “some tax deficiency” existed. In United States v. Marashi, 913 F.2d 724, 735-736 (9th Cir. 1990), for example, the Ninth Circuit only required that a reasonable “trier of fact could have found some tax deficiency beyond a reasonable doubt”.