If you take a look over fiat vs stablecoin Bitcoin markets on CMC, you'd notice their prices vary wildly. If a Bitcoin is sold at $20,000 for a USD pair, it could very well be sold at $20,500 for a USDT pair at the same time - but having such wild differences makes it easy for traders to make a profit. Hence, with high liquidity and trading volume you automatically have smaller and smaller differences between fiat and stablecoin Bitcoin pairs.
In the end however, the main idea of this system is making sure that if you have received 20,500 USDT for your Bitcoin, the value of those USDT are constantly equal to 20,500 USD. That is done through a centralized system. Meanwhile, trust is obviously part of the game. Say you had a USDT/USD pair. Although you and everyone else knows that 1 USD = 1 USDT at all times, you decide to sell 1 USDT for $5. Would anyone ever purchase it from you? If they would, then it is likely that nobody else would purchase it from them at a higher price than one buck. It makes no sense to sell or purchase a stablecoin at a value other than $1.00 per coin.
This is why the only way you can sell 10 USD banknotes for 20 USD PayPal balance is when the said buyer is in an emergency. The constant centralized price pegging is there, but it cannot realistically be enforced without our common sense. Makes sense?
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