&gt; A tax would be if a certain class of people were forced to pay for the monopoly service, in this case some people would be forced to play the lottery.<p>If the government taxes a particular non-monopoly service, no one is forced to buy the service, but the tax is still recognized as a tax.<p>Mandating a monopoly on a class of service, which monopoly then extracts monopoly rents -- especially where the state receives the rents, or a share thereof -- is pretty hard to meaningfully distinguish from taxing the class of service. Sure, no one is compelled to purchase the service, but a tax on alcohol or tobacco doesn&#x27;t stop being a tax because no one is forced to purchase alcohol or tobacco.