I read a post on a different forum, years ago, about steps to take to rename anonymous if you win.
Some states require that you give your legal name and photo, and they publish it. California is one of those states. So you have to work around that.
step 1: put the ticket in a safe deposit box or some other inaccessible place till you complete several more steps.
step 2: contact a lawyer about LEGALLY changing your name. Let the dust settle and open an account in the new name to receive the funds.
step 3: If you are a man, grow (or shave) facial hair to get a different look. Both genders, dye your hair, change your glasses (or get rid of them if you wear them, or add them if you normally don't.
step 4: You have a new name, a new look, new bank acount. Contact the lottery office and arrange to come in. Wear clothes that are a disguise. Wear a wig if necessary. Do not look like your normal self. Sign all the forms with your new name, and get your picture taken with your new look.
Step 5: deposit the check in the account under the new name.
Step 6: contact the lawyer about changing your name back. Dye your hair back to the normal color, shave, return to normal eyewear.
In theory, you have thwarted some of the financial fraudsters who stalk lottery winners.
I don't know if any of this would really work, but if I won, I would definitely ask a lawyer about it.
As for the math - I had a college math professor friend who played regularly. He pointed out that a $1 investment improves your odds infinitly... Because it's now non-zero. FWIW, I did not play, so I definitely didn't win.