Lots! (You've seen Ocean's Eleven, right?)
But you're probably looking for a little more detail than that. OK.
You're correct in the assumption that casinos have to keep a certain amount of cash on site to pay out big winners, whether a whale or someone who gets lucky and hits a huge progressive jackpot. It's a matter that falls under the jurisdiction of the Audit Division of the Gaming Control Board. The relevant regulation is number 6.150, which you can look up in its entirety on the GCB's website.
And it's not just a guess at the possible maximum payout a casino might face on any night with a random number of zeros on the end; precisely defined formulae apply, depending on the size of the property and the type of gaming it offers -- of course, the more gambling you have, the more money you need available.
Regardless of how big or small you are, you must stay in compliance with the rules, or alert Gaming Control immediately should your available bankroll fall even $1 beneath the required amount. When we asked the extremely helpful chief of the Audit Division whether this ever happens, he explained that a sizable safety cushion is built into the dollar amount required, so that a temporary shortfall still enables a property to operate, but properties that do violate the regulation generally go out of business shortly thereafter. It's not a sign of good financial health.
The bankroll that a typical casino (as opposed, for example, to a stand-alone video poker bar) must have is divided into two types. There's the money that they must keep "on-hand," i.e., hard currency in the cage, booths, and vaults. And then there's the money that falls into the "next business day" category -- in other words, funds that they're good for, but would need to issue a check or wire transfer for, being too large to be handled via a straight cash transaction.
For the purposes of Reg. 6.150, "currency" is defined as paper money issued by the United States government -- coin and foreign cash don't count. And the "next-business-day" stash includes all the "on-hand" cash, plus any coin, foreign currency, chips/tokens, personal checks, payroll checks, cashier's checks, government checks, and traveler's checks, and any money held at financial institutions that can be converted to currency and be at the casino by tomorrow (or Monday if it's the weekend). It excludes counter checks, markers, any cash that patrons may have placed on deposit (that's your money and not theirs to borrow), and unpaid race and sports tickets (if you place a wager on the Super Bowl in July, that money is technically still yours -- or at least not the casino's -- until the game has been played).
As far as the actual formula is concerned, it's not that complicated to calculate, if you have all the relevant figures at your disposal -- the GCB supplies an Excel spreadsheet that has all the codes embedded in it and works it out for you, once you type in the required information.
Relevant figures include all the cash the property has available, plus its gross gaming revenue for the previous year, the number of slot machines (and their denominations) and table games, plus other gaming options offered, such as keno, race and sports, and bingo. The embedded formulae calculate how much you're required to have on property or within 24 hours per machine and game, plus how much you need in "variable amounts" to cover such eventualities as the highest possible slot payout, any progressive jackpots throughout the casino, contest/tournament liabilities, and miscellaneous promotions.
There are also some helpful "look-up tables" that give you some definite figures: For example, if your gross gaming revenue is greater than $130 million, you need to have available $1,000 per .01-.50 and multi-denomination machine, plus $1,800 per $1 slot, and $5,000 each for slots of higher denomination.