You can claim that you rolled dice, but that won't be sufficient - the distrimination law explicitly puts the burden of proof on the employer to demonstrate that the firing was because of a non-discriminatory reason, so if it's just the employer asserting that it was because of dice and the employee asserting that it was because of race, then the employer automatically loses unless they have convincing evidence to state their case.

That's part of why you'd often see lots of HR bureaucracy regarding firing process, documenting infractions, performance improvement plans, etc also in states where technically you can be fired without a reason.