With your scheme, on Ethereum at least, miners have an advantage since they choose which transactions to include in a block they mine. So a miner would only pro

With your scheme, on Ethereum at least, miners have an advantage since they choose which transactions to include in a block they mine. So a miner would only process the random numbers sent in 2. if it results in a win for them. Of course there is more than one miner etc., but having a positive expected outcome is enough to be worth it to play.