I have seen a few game-Dapps (e.g., lotteries) that extract randomness for the game from the least significant bits/bytes of the hash of some blockheader in the blockchain. One complaint I have seen is that miners trying to win the game could choose to only submit blocks with least significant bits/bytes that let them win. I.e., the miners can try to influence the randomness.
I would like to know if anyone has seriously analyzed this complaint? It seems to me that it is not necessarily something to worry about unless the reward is very large.
For concreteness lets assume a game where players pay a small fee to play and have to guess the least significant byte of the hash of some future block header (say a block header 1000 blocks in the future). If a player guesses correctly he wins x Ether. Now a miner could try to mine the given block so that the least significant byte matches his guess in order to win the x Ether with certainty. However, in doing so the miner is trying to mine a block that is roughly 256 times harder to mine than a regular block. Almost certainly some other miner will mine a regular block before this happens.
My point is that the reward x would have to be enormous (I suppose around 256 times the block reward) in order for this attack to be profitable for the miner. However, my intuition could of course be wrong.
Does anyone have some thoughts about this problem?
I am new to Ethereum and this board, so please excuse me if this has been discussed before.