While I agree that incrementally decreasing Mr. Lucky's available Edge would be a valid experiment, I should also point out that the Sam should do the same. When I've played Mr. Lucky, I can only think of two times where he's spent more than two points of Edge in a game, which is generally on par with the other characters.
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The target group works well within the mission (SRM-13 pg. 9 IIRC). I´d prefer the original, documented scene over a pre-run description of the environment (number of cars parked, lighting, people, info about the targets capabilities...).
Here it is to the best of my recollection:
The job's first part was to intercept a team of runners and take their place at a meet. We chased them off, but we spread out to try and finish them off. Due to a lucky (go figure) perception test, I locate them on a street corner, arguing about what to do. Unfortunately, we don't have the time left to assemble the team to take them on. I order my van to drive casually, to speed up on a verbal command, and start a drive-by.
The opposition consists of a Street Samurai, a Gunslinger Adept, a Face, and a Decker. AFAIK, they were the archetypes straight out of the book, except for the fact that the gunslinger was packing SMGs. At any event, I get a surprise action, and shoot the street sam full in the face. (Direct hit, although not a called shot, with a disgusting number of successes behind it, too much to soak even with Edge.) My second shot isn't nearly as cool, and only wounds the Gunslinger Adept. (Read: She uses Edge.) As a free action, the van starts to acellerate.
First pass. I win initiative, and unload on the Adept. Needless to say, I hit, but she spends more Edge to survive/reduce the damage. It now goes to her turn, which is an ouchie for me. She fires four times, using her ambidexterity to good effect. However, I'm behind good cover; and even though the GM penalizes me for dodging in confined quarters, I manage to escape with only two hit points taken. Some Edge was used, but the good luck I had was that the adept botched on her last shot, causing her to drop her gun. Well, maybe not so lucky, since I now had to face her full dice pool. The face's shot gets me for one hit point, taking me to a Moderate wound, and the decker is frantically trying to locate my wireless signal.
Second pass. My first shot only wounds the adept, but she's now out of Edge, and the second shot finishes her. The face hits me, but I manage to dodge/soak the shot. I honestly don't recall what the decker was doing next. At this point, the GM rules that the van has pulled too far away to make another shot, so I'll have to turn around for a second pass. While I'm doing that, the Face and Decker decide to run for it. The adept is still alive, but the sam went into serious overflow; they grab the Adept, trigger her Docwagon, and run. I'm not about to take on Docwagon, and by the time I turn around, they're effectively out of combat range.
So, the original claim was that Mr. Lucky took on a team of Prime Runners and won. He didn't exterminate every last one of them, but he did beat them. If the Face and Decker had decided to shoot it out, any dedicated Combat character would have mopped the floor with them. My point is basically while a high Edge is no match for smart tactics, a high Edge combined with smart tactics is the win.