Nothing stopping you from firing someone for being black, then claiming you rolled a dice, however.

IANAL but I believe juries tend to be biased towards the plaintiff (terminated employee) in wrongful termination suits simply because there are far more low level employees in the jury pool than there are managers, not to mention how expensive it can be to litigate. Hence all the CYA measures like performance improvement plans and so on.

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.

Attorney here who has handled a number of similar wrongful termination claims here. You can try this, but you better have a lot of good, clear documentation backing up your non-discriminatory reason for the firing which, if you're just making it up as a pretense, you probably don't. And if it's found that you did fire for a discriminatory reason and you attempted to lie about that fact, you're opening yourself to a world of hurt.