As someone who knows what it's like to be on the other side of this deal, there is probably a better way to arrange this. I would start with finding an attorney that could draw up a contract. 500k home in Cali is much less than a 500k home in other areas.
As far as how to set up the deal, I would just ensure there are contingencies and you are protected. A 50/50 split is reasonable, and you simply need to ensure that your money and credit are being put to good use. Make sure this person has the skillset and knowledge to properly do the work. Trade references are a good starting point. I would think a smaller amount to start would be completely possible. You want to find the worst home in a good neighborhood that needs to be updated. Simple stuff like flooring, cabinets, paint, appliances. You don't want to get into a project that needs things like walls moved, adding and removing plumbing and electrical. Dont get an older home. Something built in 1985 or after. Try to stay away from things like drywall where matching texture would be involvled. Anything past scraping popcorn off ceilings can be tricky, especially if this is your first venture with the person. He needs to have connections with other trades in the area, vendors, etc.
Last piece of advice, make this person get all supplies, materials in his or her name, not yours. That is where this person getting 50% of the profit takes risk away from you. At the end of the day, if something goes wrong, you don't want to owe a bank, hardware store, subcontractors. You're basically partnering with this person to be the general contractor for what your money can buy. A few other things you will need are an established realtor that will list the house at the right time and sell it fast and check comps before you buy, a backup contractor in case this other person doesn't follow through or needs help finishing in a timely manner and possibly secondary financing in case you need more money just to finish and protect your initial loan.
Best of luck. No risk, no reward!