If I have a decentralized ledger I can authenticate tokens in (at least) linear time with the total number of tokens I have ever distributed. The ledger is also public so competing arcades know intimate details of my business. In some cases they might even know which games are most popular. My customers will also know the relative scarcity of tokens and how much they should be valued, potentially limiting my profits.
Why should I use a decentralized ledger for my arcade?