I think there might be confusion about some facts:
- As @MattewSteeples pointed out, you have to mine on the same wallet ID to “share the load”
- Exploring a given walletID “nonce space” is not better (or worse) than exploring several individual “nonce space”. More on that below.
- The difficulty (aka the number of leading zero of the output hash you should have to get a reward) is dynamically adjusted so that blocks are mined every 10 min (on average)
(1) tells us that to cooperate, you have to trust the wallet iD of the group. Whoever have control over it have power. If you get rewarded only when you find, you have no interest in cooperating (see below) but have the risk of being robbed by the pool leader (mathematically it’s a pure loss). If you share the reward, you have the same amount on average, but the income is much more regular. That’s why mining pools exist in the first place, at the cost of having to trust the pool leader.
(2) For a given block, any pair (walletID, nonce) have the same chance of giving a winning hash and give you a reward. This is counter-intuitive but important to understand: Having explored 10^20 nonces for your wallet ID without having found a winning nonce DOES NOT increase your chances of finding a good one in the next N tries. Exactly as loosing 10 times at the roulette wheel in a casino DOES NOT increase (or decrease) your chances of winning the next round.
(3) but all that is not really important: the network will adjust its difficulty so that a winning (walletID, nonce) is found every 10 min. Wether its because of dumb uncooperative nodes doing the same computation again and again, or a fully cooperative network all computing on the same wallet ID and never trying the same nonce twice (will never happen, but you get the point).
No matter what, the energy spent for a block (network-wide) will be 10min * electrical power of ALL the mining nodes… Whatever their strategy. Having a good strategy only increase your cake share at the expense of the others. No effect on electrical consumption.
So. If you want to optimize electrical consumption, you only have two options: reduce the number of nodes (nothing you can do about that) or reduce the energy required for computing one hash (via new hardware, etc).