I have thought of ways I could link this game to Bitcoin
People tried to link Bitcoin to S&P500, Nasdaq, Gold and more but it is not true at all. Bitcoin is unique and your linking can be not correct.
Here are some steps one could take to set up a cryptocurrency payment system for your pool game, incase one has an interest in such kind of business endeavour:
1. A cryptocurrency payment processor system that fits this kind of need may include selecting between several companies that offer this kind of cryptocurrency payment processing service. Some are CoinPayments, BitPay, and Coinbase Commerce.
Using payment processor services is good but it costs expensive fee.
2. A payment button or QR code would also need to be added to the game interface so that the system of payment can be functional.
It is more matched if you want to run a store, shop, business which need to show QR code for users to send their coins to you as their purchasing fee. For a pool game, I am unsure it is necessary.
3. A cryptocurrency wallet to receive payments from players would also need to be setup. This can be a software or hardware wallet, depending on your preferences.
I am not sure if you already use Payment processor service and you will have to use their given wallet for your account or have to connect supported wallet to their processor service.
using a stablecoin like Bitcoin, or better still converting cryptocurrency payments to fiat currency immediately upon payment might have to suffice.
Bitcoin is not a stable coin.