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I would have to set up a database, and it wouldn't be possible to run the code locally any more. The app works without any connections to 3rd party servers, everything happens between you and a steem node. You can download the code and confirm once that it doesn't connect to any other server, and keep using it safely after that.
Besides that, I'm not interested in managing users' funds. In a worst case scenario the bank would just be shut down.

Another option for you would be to simply play from your steemit wallet. Transfer your bet with a memo in the following format:
{"type":"lower/higher","number":50}
That's what the app does.

If you could post a guide on how to play purely doing transfers, I suspect you would get a lot more action. I'd love to play, but I'm in the camp of being too paranoid to give out my keys.

Here's a link :)
https://steemit.com/steem/@pharesim/steemdollar-casino

And once more, the key never leaves your browser, you do not "give it out". I even considered an option to use your own node, but as the transaction is signed and nothing confidential is transmitted I left it out (for now).

You have the right to your reservations. After having my vote used in a way I didn't like a while back I decided to never hand my posting key to anybody again

I agree! In addition to that: Is there any way the user can verify that the algorithm is fair? For example, by displaying hashes of the next roll?

The hashes and the resulting number are displayed at the bottom of the screen

Awesome, thank you!

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