Litecoin - Merkle Root

[deforation]

I have a question about the uniqueness of the merkle root.

In the litecoin wiki, i have read, that each miner will create a different block sequence,
otherwise the fastest system would always win.

Now it is mentioned, that this is achieved by creating a unique merkle root based on the unique litecoin address
This raises one question to me.

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Assume i have 2 computers with each 1 GPU.
The mining process on both systems is started.
Both systems are configured in a way, that they mine into the same Litecoin address.

Does this now mean, that they will mine the exact same sequence?
According to my understanding of the text, this should be the case not?


Thanks for your time