The commitment scheme solves "cheating" in the sense of "dealing cards in a different order depending on how the game goes".
There are other types of cheating, e.g., leaking the order to players and perhaps picking a non-random order in advance. Those will take longer than a parenthetical in a conversation about Bitcoin to address. Do you think that a blockchain is capable of solving any of these types of cheating more than some offline stateless scheme could?
Does the process you are referring to automatically give a refund to the player? It's hard for me to follow your logic because you mention Bitcoin which doesn't have a smart contract language like Ethereum.
Oh, I was going off this thread being about Bitcoin. Ethereum is probably a better example, sure.
If your constraint is "I want a transfer of money based entirely on the output of this algorithm on this data," then a blockchain platform is probably the right approach, sure. But I think you only need that for an internet gambling site... if you're trying to restore trust in a physical casino, the wagered money is right there on the table, it's clear who should get it. (The other participant trying to physically attack you to get money they don't deserve is out of the threat model, I think.)
FunFair looks cool but I think it mostly follows this design: the actual game is off-chain and it's only settlement that happens in Ethereum itself, if I'm reading right. You're doing a commitment scheme on your shared RNG, you're just also adding in a smart contract that can verify the game (or a partial game, hopefully) and determine who should get what money. If all players trusted a third party to escrow the funds (where the third party could be an API or a table with a pile of money), then you could do the game with no blockchain at all.
