Get special "casino use" low-limit credit card
You can get a credit card with a very low limit, like $200. Use that only for casinos, and only if you absolutely must, so that if they try to renege on comps and charge everything to your card, the most you can be scammed out of is the amount of your low credit limit on that card.
Some banks now have "prepaid" cards that look and act like credit cards, but only up to the amount you loaded into them, like a prepaid calling card. These are useful for this purpose, since the credit card company will never let you go over the "credit limit."
DD's point is very well taken. If you absolutely must use a card for whatever reason, don't risk the hassle if you expose a card with a normal credit limit to a casino. They could scam you out of a lot, as they did DD'.
Usually, the clerk is satisfied with the explanation, "I don't plan to charge anything, so I don't need to give you a card." Or you can put up a small cash depsoit, which usually quickly resolves the situation.