Quote from: Forp on October 05, 2011, 10:18:43 AM

The original paper from 1996, Rivest, Shamir, Wagner (see above) provides some nice real-world examples here.

1 woman needs 9 months to give birth to a baby. So 2 women will have twice the power and will need 4.5 months to produce a baby.

A bus full of passengers stands in the desert. They ran out of gasoline. The driver discovers that the next gas station is 50 miles away. This is no problem, since there are 50 passengers on the bus. They will just split the task and every passenger will walk his share of 1 mile.

The examples show that there are tasks where you do not get 2X power by doing Y twice. In my above posting there are references to mathematical examples in the literature.

Come on man you are ignoring the entire concept of a reward.

A pool doesn't "get more" it isn't trying to get 2x. It still gets x. It simply gets x more consistently.

A better example would be a lottery (real world) pool. In a lottery (lets ignore the lesser prizes) you either win nothing or you win a HUGE prize. However the odds of you winning in each draw is so low that even if you played every day for the rest of your life you may never win. Rather similar to the bitcoin lottery right?

So you and 19 friends get a great idea. Instead of playing individually you pool your 20 tickets and if any ticket wins you SPLIT THE REWARD 20 ways.

Has the lottery pool gained 2x? No. Do bitcoin pools gain 2x? No. In the long run (say 100 years of solid 24/7 mining) a solo miner and a pool miner (assuming same hardware, downtime, and fees) will earn the same amount. They both earn X. The only advantage of a bitcoin pool is reduced volatility. You reach the "long run" (where expected value and actual value converge) much quicker.

Any problem no matter how non-parallelizable can be pooled. Each "miner" would work completely independent and if/when he "wins" he shares the reward with the rest of the pool. That is unavoidable. If you think the biggest risk to bitcoin is pools then your proposal does nothing about that (and creates a large number of new problems).