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From your description I thought this would be a trash experience. But no, it clearly isn't. This is a great basis for a game!

Some feedback if you want to continue working on this: 

- Try to explain the game inside the game. When I originally started the game I didn't even know that you could pick up stuff. Needing to read the downloadpage is never a good sign.

- Please don't close the game if you die. Just open a startscreen so I can get back into it again.

- Implement some kind of healthbar. I didn't know at first if the zombies even hit me or not

And finally, if you want to expand on this, maybe implement some kind of score / an online leaderboard.

Again, I had a great time playing this, so don't discourage yourself :)