Proof of work: optimal number of transactions?

Question

I've been struggling with this Q for a while: My initial understanding was that miners start to work on PoW for new block immediately after the previous round's block is confirmed. My Q is this: given how the SHA-256 works, we know that each new transaction added to a block that is being worked on will change the hash in a apparently random way. To me this means, that every time a new transaction is added to the block that the PoW process of "guessing" the nonce needs to restart.

Given that the probability of finding the correct nonce will be marginally higher if you've already tested thousands of nonces for a given merkle root, at some point, is there an optimal number of transactions in a block, after which a miner would be better off not accepting new transactions to a block?

I recognize that this Q may reflect a fundamental misunderstanding of the PoW, so any guidance is very welcome.

Thanks,

Answer 1

Given that the probability of finding the correct nonce will be marginally higher if you've already tested thousands of nonces for a given merkle root

This isn't true. No block header is guaranteed to return a solution. (In fact, most do not.) Each attempt to hash a block header is equally likely to result in a valid block, regardless of how many nonces have already been checked.