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It varies according to the version of video poker you're playing and that game's volatility. The rule of thumb is to have a bankroll that's equivalent to at least two royal flush payoffs for your denomination. For quarters, that would be $2,000. Some experts recommend two to three royals, which would mean somewhere between $2,000 and $3,000. Jean Scott, however, experienced an episode where she came close to losing her entire bankroll, which was the equivalent of three royals, so ever since she's felt more comfortable with a bankroll of five royals ($5,000 for quarters).
For dollars, that would be somwhere between $8,000 (two royals) and $20,000 (five royals).
This is just a rule of thumb based on denomination. It's important to understand, however, that if you don't have a long-term advantage in the game you're playing, any size bankroll will eventually be exhausted.