As per proof-of-work: Miners will need to find a hash which contains the right amount of zeros to match the difficulty. If a miner found the right hash in time but it does not match the hex number that he placed the bet one, than he can choose to not submit the block and instead continues to search for a different nonce/hash. This will likely take him on average twice as long and even then there is still a 15/16 chance that if he found a new hash that it is still not the hex number that he placed the bet on. However, meanwhile the miner risks that someone else finds the correct hash - so he is risking his block reward doing this.

The odds are entirely different if the house allows to place bets exactly until the block is announced. In this case the miner could just place a bet before announcing the block to the network. However, it is unlikely that the house would allow these last-minute bets.