Do Larger Mining Pools Waste Fewer Hashes?

Question

I wanted to check my understanding of the PoW consensus algorithm as it pertains to ETH and BTC mining.

1. Mining pools pool together resources from many miners to search over nonce values to create the next block. The first miner to find the right nonce wins, therefore all the search performed by other miners is "wasted", and they need to move onto mining the next block.
2. If there are two mining pools attempting to solve the same block, and one is substantially larger than the other, the larger mining pool will tend to find the block (and receive the block reward).

I understand that the intent of PoW coins is to avoid mining centralization, but if the above two assumptions are true, isn't it beneficial for miners to always join the largest mining pool?

Answer 1

...therefore all the search performed by other miners is "wasted",...

For Ethereum this isn't quite the case. (Though, yes, largely it is. See some of the answers here: Why does Ethereum plan to move to Proof of Stake?)

If two (or more) miners, or pools, find blocks at approximately the same time, then they both submit them to the network. The protocol consensus mechanism ensures that only one of these blocks is eventually considered the true block. (See: What is the exact "longest chain" rule implemented in the Ethereum "Homestead" protocol?)

The other block is discarded, and becomes an orphan. In Ethereum these are called uncle blocks, which themselves have an associated reward, and which means the work isn't completely wasted (see: Why am I getting less than 5 Ether per block?). In Bitcoin orphaned blocks aren't rewarded.

isn't it beneficial for miners to always join the largest mining pool?

Yes, but their reward would be proportional to their relative contribution to the pool's hashing power.

If everyone joined one big pool, then they'd receive very little in the way of reward when that pool mined the block. By splitting into smaller pools they are trading a guaranteed small reward for the chance to win a potentially much bigger one.

Further, one of the aims of the previously mentioned uncle blocks in Ethereum is to incentivise miners not to join one big pool. (Miners can still earn a reward by coming second place.)