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Can a pool keep blocks for itself without giving out rewards to miners? Can it do this in secret?

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Yes. This is one of a few problems with current pool implementations.

Miners are trusting pools to:

  1. give miners their fair share of any blocks the pool mines
  2. payout on all blocks mined
  3. not censor transactions
  4. give miners hashing blobs for the main chain they want to mine
  5. not be performing a 51% attack
  6. display accurate information about the pool (e.g. its hashrate, payouts, etc)
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