The 11th roll is dependent on the server seed, client seed, and nonce and the previous rolls.
An important property of hash function is avalanche. With that, two almost identical inputs would create completely different hash output (the optimum is that each output bit has 50% chance to change) , and that's why a small change in nonce is enough to create a new random number independent of the previous numbers.
For example, knowing sha512(12sPa15STZ4:j8mEOhZKHYWMcCmwvIJkdOc4ZRxMsLgrfPec4vpIMMMOiyEz08:
0) is
ad0d3d199ba3d6a8d577d32d596c3188be5ab134e1f9d1d7234807f26d65d9d5cd1f5a6e68ed23b 76d51f025be13dd7baedcb2e3029c207b767da215a945f371 will not help you predict sha512(12sPa15STZ4:j8mEOhZKHYWMcCmwvIJkdOc4ZRxMsLgrfPec4vpIMMMOiyEz08:
1)