Some of the responses are a bit naive, although I have seen them taught or explained in the literature in multiple places.
Most of the mugging (Give me yoru wallet) scenario responses assume there is only one bad guy. According to stats provided by the Dallas Police, that accounts for only about 40% of the time. The other particiipant(s) may not be directly in your view and may be serving simply as lookouts or as backups to the person with whom you are dealing. In other words, just because you see only one threat definitely does not mean that only one threat is visible. So, for the scenarios where you try to toss the wallet as a distraction or want to hand over your wallet to excercise the bad guy's mental function such that you can draw and fire on the bad guy really may be a bad idea because he may not be the only guy with a gun trained on you. The question at that point becomes one of just how good is your situational awareness such that you think you will out draw on a drawn gun or knife of the bad guy known to you and still evade being injured or killed by the potential bad guy not known to you? Are you sure you are actually dealing with just one bad guy?
So you want to toss your wallet as a distraction to give you enough time to draw and fire your gun before the bad guy can react to your movement. Here, you are drawing on a drawn gun or knife, maybe a club. If you hand is not already on your gun, just how quickly can you cold draw your gun from concealment and fire that first shot accurately enough to strike the bad guy, hopefully accurately enough to incapacitate him? I have run through this with several folks, some multiple times. We would have guys come in to our range sessions and without downloading carry ammo and changing over to range ammo we would have them come out to the firing line, put on muffs and glasses, and time a Mozambique (2 chest, 1 head) at 7 yards. Granted, mugging distance is much closer. What many fail to realize is that the location of their gun may change during the course of carry or may be in a slightly different position on one pair of pants versus another. Maybe they are wearing a sweat shirt to conceal their gun instead of a vest.
Keep in mind we didn't give the guys a chance to stop, adjust their gun, cinch up their pants, or anything... just straight in, drop gear bad, come to firing line for muffs and glasses and shoot timed. We found guys to be as much as a half second slower on their first shot when drawn cold than after they had warmed up. In shooting cold at 7 yards, we had guys actually miss 1 or 2 of the three shots made as part of the drill and surprisingly, the first body shot was often the shot missed. Unfortunately, it was rare to have a shooter make all three shots in the correct areas in a time that was within 3/4 of a second of their shooting after warmed up. Overall completion times were up to 1 second slower than after the shooter had warmed up and hitting all three shots in the correct areas.
One of the biggest problems was getting that initial grip on the gun for the draw. Unrealized to many shooters, tucked shirts usually close to the body can become untucked during the course of a day and the initial grips on the guns sometimes included a wad of shirt that hindered proper manipulation of the gun. While I don't recall any range safety issues that actually put any shooters in harm's way, one shooter (my name withheld) managed to shoot a side wall of the indoor range, completely missing the target by about 5 feet and a result of the wad of shirt gripped with the gun being pulled taught just as full extension shooting postion was reached, causing the gun to twist to the side as the first shot was being made.
It was suggested that handing the wallet to the mugger will require more fine motor skills on his part, thereby allowing one to draw and fire. It is a novel idea that assumes the guy has poorer motor skills than you have, which may or may not be true, and assures that if you are already not in very close proximity to the bad guy that you need to be closer. The motor skills of a teenaged mugger may be a good bit better than that of a 40 or 50 year old intended victim. So by being close and having the bad guy use more of his fine motor skills, you are able to draw and fire a gun carried concealed in 1.5 to 2.5 seconds against a drawn gun or knife? Let's see, even if the bad guy had a slow response and it takes him a full second to start pulling the trigger of his drawn gun after you start your draw, he will still be firing before you. Maybe you will benefit from his being drunk or stoned such that his neural responses are slowed. Then again, maybe he is hopped up on speed and has faster responses.
The one thing that trying to hand over the wallet will do, if you are already not there, is to put you in that much of a closer position to the bad guy. The closer your proximity to danger, the greater the likelihood of you getting hurt. A lack of distance to the threat can negate the need for skill by the threat in order to harm you. Sure, your chances of hitting the threat improve as well, but it isn't about whether or not you hit the target better than the target hits you, but about not getting hit. It does little good to kill your attacker if you are similarly mortally wounded as well, or suffer debilitating injuries that destroy your ability to enjoy life.
A few years ago, there was a great article that really brought to light the fact that proximity negates skill. In the article the intended victim was an elderly paraplegic who was confined to a wheelchair. Some guy figured the codger in the wheelchair would be an easy score and threatened the codger who did not give up his wallet. Keep in mind that the paraplegic old guy wasn't just paraplegic, but also legally blind. The bad guy started beating the codger in the wheel chair who managed to grab his attacker with one hand and produced a revolver from under the blanket in his lap with the other hand and placed it into the side of the attacker where he fired just one shot that produced a "one shot stop."