We created a Mystery Box app and you can do things like collect emails while your customer plays a Mystery Box game, charge customers to pay to play the game, create a full product Mystery Box page and other features.
Here is the Shopify app link - https://apps.shopify.com/hero-box
Also I would suggest Stocky for an inventory app, they have a lot of features to help maintain your inventory levels but it could be a bit pricey.
Please let us know if you have any questions.
If there is anything else I can help you with, please let me know.
This would work really well if there was an option for multiple boxes. I am looking to move my website to shopify so i need an app with the ability to provide the same features as my current site: beast-boxes.com