Okay. So, in this case 1/2" hardware cloth is your new best friend. It can be pricey, I know, but so is replacing chickens, so I figure it is worth it. I'm not sure what snakes are able to fit through, maybe some of our fellow southerners can speak to that, but you basically want no hole or gap to be bigger than a quarter. It might be even smaller depending on the snakes where you live.
You will also want what is called an apron around your run. It is essentially 18" of 1/2" hardware cloth on the ground around your run. We stapled the hardware cloth to the wooden base of our run with brads and then secured it to the ground (with rocks and dirt, but most folks use landscape stakes). This prevents digging predators. Our birds don't stay in here 24/7 for us, but when we need them to be safe, like at night or when there is something prowling around and we won't be home, we have that space to use.
If there is just chicken wire on the run, you will want to secure the hardware cloth on there, too. The name is misleading, but the smallest of the weasels and the hands of raccoons can get through chicken wire. We only use chicken wire to barricade our chickens from one another inside the coop and run that is protected by hardware cloth.
You can also use cement to secure the bottom of your run.
Your vents should also be covered with 1/2 hardware cloth as well. I have seen raccoons that will rip the hardware cloths out of the vents, so you want to be sure that stuff is super secure there.
If you post pictures of your setup we can give exact advise and troubleshoot any weaknesses. Let me know if you can think of anything else.
