Upon winning or losing you will get the number that you have rolled via a dm message.

Then go to the nonce account and fetch the nonce of your round. (published every 10 minutes)

Now create a sha256 hash out of the following information ( nonce | your npub | your zap memo | index)

You can also do this using online tools like https://emn178.github.io/online-tools/sha256.html?input=%5Bnonce][your npub][your zap memo][index]&input_type=utf-8&output_type=hex&hmac_enabled=0&hmac_input_type=utf-8

The result will look something like that 9d6b99966ce4ff8ccc8c7d73058aa3273cb782adc86b3bdfee7a7f134d1135be

Now take the first 4 characters of that hex and convert them to a decimal number. You can again use an online tool like that. https://www.rapidtables.com/convert/number/hex-to-decimal.html?x=9d6b

Now you can verify that the number you've rolled actually adhered to an entropy provided by you.

Before a round starts nostr dice also commits to the nonce upfront, so it can't cheat you by finding a nonce that suits them best afterwards. You can find these announcements as well on the nonce account

Here is an example from a previous round with a nonce hash commitment of 7ff33d5c47cb2fedf918461659b482359e142085ab28d3d42b2be46e6d3c059c.

After 10 minutes nostr dice published the nonce (pre image: cb3f8358ac79f4329a486d93021a71262293cfb36e6e89609ec2ff5d114ff3d9), which you can then verify comparing the sha256 hash of the published nonce and the nonce commitment.