This depends on casino or during deposit you could be asked to choose an option and you went on and choose the other network and when you confirm that you are depositing to ERC20 instead bep20 they auto just direct it to the network you chose, and even though they are same address, but they wouldn't credit it to network as you may have think. What you must know is that casinos are too stringent with their policies regarding to financial mistakes or mismanagement of funds during deposit, so you must learn to recheck your deposits address before proceeding.
You are right with the fact you mentioned, that online casinos are too stringent with their policies and they are always on the look out for gamblers who make this type of mistake and frequently too 😁
Since the erc20 and BEP20 receiving address are exactly the same, what this mean is that both of this networks also share the same private key, if the casino waited to help retrieve the money, it's absolutely possible but unfortunately, they might not.
I've once made a similar mistake while sending money from my wallet to an exchange, I was to send from bep20, but on the exchange, I mistakenly selected erc20 receiving address, I sent the fund before I realized the mistake I had made, I was looking for a way to reach the exchange's customer care but to my amusement, the fund dropped, the deposit turned out successful and was deposited on the exchanges bep20 network, which simply means that both the erc20 and bep20 addresses are the same.