Problems at White Gloves Society

When I played through this it took many tries, so first and foremost: save often. If you take one of the guys out, save before you start on the next one.

There are a few ways to do this:

• Take some Unarmed books with you. These will help if you haven't focussed much on skilling in Unarmed.
• Some people in the Mojave will teach you special unarmed moves. The NCR Ranger (with the injury) in Novac will teach you one, for example. These may come in handy here.
• Run away and heal up outside of the casino. It is entirely possible to escape and get out alive, but the two men will still be there when you return.
• Holdout weapons & the sneak skill. You might be able to pull off sneak attack criticals, which are extremely powerful.

Unarmed companions are also extremely useful when dealing with this situation - Veronica, for example.