So lets say we are currently at block 240,000. If I were to say I will use the hash of block 240,010 as the seed to a random number generator (or some number of bits from the hash) for a number guessing game, would this be a secure mechanism for seeding the RNG?
The trick would be to keep the reward lower than the block reward. If someone "wins" block 240,010, they get 25BTC in a reward. If your lottery pays 1BTC in a prize, it is more profitable to publish a block.
An different attack occurs to me. They could join a mining pool and would get credit for their hashes. However, they could still throw away the winning block, if they didn't actually win.
However, I think mining pools probably have checks so that if someone has 2-3 blocks worth of shares without any win, they are flagged as suspicious.