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 Rolling a die gives you a random output for a given input. If you input the same nonce on a block template, you will always get the same output hash.

It is guess and check, not rolling a dice. And the "check" part is... Wait for it... Math. 
 No. It is not like rolling dice.

It is guess and check.

Guess nonce, then do math to figure out if the resulting output meets the difficulty requirement. If it doesn't, replace the nonce with a new guess and run the math again, over and over, until an output hash meets the required number of leading zeroes.

nostr:nevent1qqsfglayjd6k564vm58q5xweypz806lajsz8h7nfxct7hr7q5nkf6hcpr4mhxue69uhkummnw3ezucnfw33k76twv4ezuum0vd5kzmp0qgstwf6d9r37nqalwgxmfd9p9gclt3l0yc3jp5zuyhkfqjy6extz3jcrqsqqqqqpugaen6