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It's like planning the "perfect" murder: impossible to do, but entertaining nonetheless.
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Well, you could use a piece of food, and then eat the murder weapon.
The only problem is that you can't really kill someone with a piece of bacon or toast. Perhaps a rather large watermelon.
Anyway, like SeaRex said, we'd all have a rather small chance of survivng. Multiple factors kick in, such as food, safety, weather (cold), the amount of undead, weapons, and (the most dangerous) desperate people.
These people are panicking, desperate people who are mindlessly driven for safety. If they see your safe area, they'll go nuts trying to get in even if there is no danger nearby.
Given the choice, they will probably kill you to get into your fortress. And then, they'll devour the resources in and around, then move on. They'll be worse than the zombies.
I'll post a more comprehensive analysis later, if I ever get bored.