How the peg is held
The issuer takes a dollar, issues a token, and stands ready to redeem the token for a dollar. Arbitrage does the rest: if the token trades below par, someone buys it cheaply and redeems it at par, and the buying pressure closes the gap.
That mechanism depends on redemption actually working and on the reserves actually existing. Both are claims about a company, which is why stablecoin issuers publish reserve attestations and why people read them.

What has historically moved a peg
Doubt about reserves, a redemption channel becoming slow or restricted, and contagion from an unrelated failure elsewhere. Large stablecoins have traded below par for short periods and recovered; algorithmic designs that held no reserves at all have failed outright.
The lesson is not that stablecoins are unsafe but that they are a credit instrument rather than cash, and their stability is a property of an issuer rather than of the chain they move on.
What it means over a casino session
Very little, honestly. The exposure lasts hours or days, and the risk being discussed here plays out over longer horizons than that. The reason to hold a stable unit during a session is that the arithmetic stays legible, and that benefit is immediate.
The reason not to keep a large balance parked in one indefinitely is the same reason not to keep it parked at a casino: it is somebody's obligation, and obligations have counterparties. The comparison in full.
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