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I can point you to a few examples of centralised blockchain designs that make sense, but one that is (imho) easy to understand is what Loom Networks uses.

Essentially, users money is kept in the public Ethereum blockchain so all the cryptoeconomic security properties are assured but the games are developed (and played) in a centralised side-chain using a technique called Plasma that doesn't charge users per tx and has very fast block times (~1 second iirc).

Plasma is a way of extending (for scalability or any other reason) a main-chain such as Ethereum with a new app-specific or industry-specific blockchain, in such a way that the users can always trust their money without having to fully trust the side-chain owner's best intentions.

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