Like we mentioned above, you can technically mine Polkadot by allotting computer power to the network. This would make it more or less free beyond the energy expenses, which are relatively low for this particular coin.
More likely, however, you will do it the “old-fashioned” way and buy it on one of the crypto exchanges like Coinbase, Binance, or Bitpanda, and then manage your coins from the integrated wallet there.
Many casino operators make things even smoother for those making a last minute decision, allowing you to purchase crypto through an external service provider like MoonPay or Banxa, direct from the casino cashier.