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Yes, my understanding of ethereum is you need to pay a fee to do anything so I would be interested to know as well

My understanding is the game itself doesn't run on blockchain. Only the card market and digital asset aspect will down the road, utilizing ERC 5511 and ENJ. I'm playing on Rinkeby test net and haven't had to visit a faucet, and looking at my meta mask history there's no transactions at all recorded on blockchain.

@philippekiene posted some gameplay recently if you want to check that out --> https://www.battlegames.io/dtube/@philippekiene/b7235bntkdc