"He said, 'Bill, I'd like to have an opportunity to take a shot at least 500 yards on a deer,'" Cobb said.
Brown had made an incredible free-hand shot of almost 300 yards before, hitting the doe right between the eyes. Still Cobb had his doubts about accurate shots out to 500 yards, but he shrugged and dropped off the Baton Rouge gynecologist at a stand where he had a clear view for hundreds of yards.
It wasn't long after Cobb left Brown and headed for another stand that a loud pop sounded.
"He shoots a .308, and with that bull barrel it sounds like a .22," Cobb said. "So I said, 'Well, he shot something' and headed to check on him."
When he arrived, Brown was standing over a doe that had a red plastic bag over its head.
"Randy was kind of red and kind of embarrassed," Cobb said. "He told me, 'Please, please keep this between us. I made an extremely bad shot.'"
The befuddled Cobb pulled the bag from the doe's head, and couldn't believe what he saw.
"Rather than hitting the deer right between the eyes, he was off to the left about a quarter of an inch," he said. "This was an 85-pound doe looking at him when he shot: You figure how wide that (doe's head) is.
"You can't even see a deer at 500 yards. With the naked eye, all you see is a brown dot."
Still, Brown was embarrassed. That's because he takes pride in the ability to make shots others wouldn't even contemplate.
Here are a couple of stats that prove his abilities: His longest head shot was on a doe at 813 yards, while his longest shot period was at 1,200 yards. Those aren't estimated yardages: Brown lasered each deer before shooting.
"That was just a so-so shot," Brown said of the longer of the two. "I was 2 inches off in windage and 1 inch off in elevation, but it was still a kill.
"I did that just to see if I could do it."
Brown isn't new to precision shooting. He cut his teeth in the early 70s as a member of the LSU shooting team, specializing in handguns.
But when he began hunting later in life, he came to what seemed to be two logical conclusions.
"I realized I could get more deer if I could shoot farther," Brown said. "And I also realized that if I made head shots, I wouldn't have to track them: They'd run 2 feet straight down."
There also was another consideration related to his job, which keeps him extremely busy.
"I don't hunt that well," he said. "I don't know where the deer are; I don't have the time. If I'm in the middle of a field, they can come out anywhere. I don't have to find them."
So he started playing with rifles and scopes, looking for the right combination.
His go-to caliber is the .308, with his guns of choice being bull-barrel Remington Model 700 and 40-XB offerings, along with the Savage Model 10.
"That .308 cartridge is still the most accurate cartridge ever made," Brown said. "It's got low vibration, and it has all the best ballistics."
He matches these guns with Nightforce NXS 12-42x56mm (yes, that's a maximum of 42 power) or Tasco 12-60x56mm custom scopes. The Tasco is no longer in production, but Brown said the 42-power scope is more than adequate.
"With that (42-power) scope, you can see the eyelashes (of a deer)," Brown said.
But when he really wants to reach out past about 800 yards, Brown turns to another round designed for use by military snipers in Afganistan and Iraq.
The .408 CheyTac is massive, measuring 4 ¼ inches long and holding enough powder to push solid-core bullets weighing 419 grains to incredible distances.
"Those bullets cost $5 a round," Brown said.
The only disadvantage to the bullet is that they punch right through the deer.
"This bullet is not going to hit something and mushroom," he said.
That makes it very important to know what's behind any deer shot with this massive round.
"That bullet will go through tank armor," Brown said. "It's not designed for that purpose, but it'll go through tank armor."
He couples the Nightforce NXS scope with his CheyTac M310 rifle.
Although such scopes can cost in excess of $1,500, Brown said they are vital.
"You have to have good scopes," he said. "I recommend using the finest scope that you can afford. You want one that transmits light at low ambient levels near dawn and dusk because you can't hit what you can't see."
So he's got the equipment to reach out and touch a deer, but is that all there is to his success?
Brown has spent untold hours learning the peculiarities of how each gun shoots.
"You can't go by the (ballistics) charts," he said. "Every gun is a little different, even with the same round, so you have to know how each one shoots."
He said one of the major mistakes hunters make is going to a range and firing repeated shots through their rifles to "group" the bullets.
"I never fire more than one shot," he said. "When that barrel heats up, it changes the POI (point of impact). Almost all guns will walk the bullet slightly as the barrel heats up.
"You might have the first shot out of a cold barrel hit over here, and then the rest of the shots group off to the side."
The difference might be less than an inch at 100 yards, but that offset grows dramatically as yardages increase.
"At a hundred yards, it won't matter, but at 500 yards, that one inch could mean a miss," Brown said.
Besides, the hunting world is by and large a one-shot business.
"How many times do you shoot more than once at a deer?" Brown asked. "Not too often."
While short-range deer (under a couple hundred yards) often take off when they hear a shot, animals at extreme ranges often just stand there. That should allow another shot, but Brown said he normally doesn't even attempt a follow-up after a miss.
"I'm so mad that I missed that I couldn't hit it if I tried," he said.
So his normal sight-in practice is to fire a round through his rifle, and then put it up until it thoroughly cools. That means it might take several days to get his gun properly sighted.
Brown said he also checks each gun every time he goes hunting to ensure the point of aim hasn't changed.
Another mistake made by hunters is trying to take a 500-yard shot on a deer without practicing at that distance.
"People practice and they sight in, but they never, ever shoot their guns at their intended range," he said. "If they're trying to take a head shot at 400 yards, there's no way to do that unless they practice at 400 yards."
His goal is to consistently shoot at least ½ minute of angle.
"That means your rifle should shoot within a 3-inch circle at 600 yards consistently," Brown said.
Long-range shooting is such a finicky ordeal that Brown said even atmospheric conditions can affect a shot.
"If it's ranging in the 80s or 90s, it's not that big of a deal, but if I get to the camp and it's 19 degrees, I'm going to fire every one of my guns to see what they do under those conditions," he said. "At 100 yards, the temperature change won't matter, but if you get out there at 600 yards, you might be 8 inches off."
Even rain or dust can cause problems, he said.
"I condom my rifle," Brown said. "I use (latex) finger cots you can get at a drug store and put them over the barrel (even when hunting) to keep any dust out of the barrel."
He also keeps his rifles in hard cases until he's ready to climb into a stand or onto a large, round hay bale (one of his favorite tactics).
"It takes so little to knock a scope off," he said.
He even carries a laser bore sighter into the field so he can check out his POI.
"I know where the crosshairs are supposed to be at 500 yards, and if it's not right there, I go back to the truck and get another rifle," Brown said.
After he's satisfied, Brown puts a rain sleeve around his rifle until he's ready to shoot.
"If you get a couple of rain drops on the barrel, your hunt is over," he explained. "When you're shooting long range, it's vital to keep every bit of contaminant off the barrel."
While most of his guns include magazines, Brown said he rarely uses them.
"I load each round by hand, making sure the bullet doesn't touch any metal," he said.
The reason is simple: Any nick can change a bullet's ballistics.
"If you've got a burr on the tip of a bullet, that vortex of wind will make it not follow the right track to the target," Brown said.
To ensure that there won't be any issues with deformities, he runs his finger on each bullet before chambering it.
He also uses premium bullets, and doesn't understand why other hunters scrimp on the very tool used to actually kill their prey.
"People spend thousands of dollars on their rifles and hunting leases, and then they go and buy cheap ammo," Brown said. "It just doesn't make any sense to take a chance of missing a deer of a lifetime."
Brown is so meticulous about details that he even prepares his trigger finger.
"I usually sandpaper my finger just to get a little more of a feel," he said. "You have to marry your finger to that trigger break; I have to feel that trigger break. When you use sandpaper on your finger, it increases the sensitivity."
While some shooters like very light triggers, Brown said he doesn't like anything less than 4 pounds.
"It helps me feel that trigger break," he said.
Another secret to Brown's success is that he never estimates where the round should hit by elevating the crosshairs above the intended point of impact: Every time he fires, he's moved the crosshairs to compensate for yardage (vertical changes) and windage (horizontal changes).
"At 200 yards, a .308 drops 4 inches," he said. "At 400 yards, it drops 36 inches. To try to shoot above a deer and use 'Kentucky windage' is incredibly difficult.
"It'll work, but it's very hard."
Instead, Brown uses a range finder to predetermine ranges on different topographical features (trees, hay bales, etc.). He often marks these yardages with tape, reflectors or small flags.
He also carries a small, inexpensive wind meter to keep up with the wind.
"I'll shoot in wind up to 10 to 15 mph, but that's it," Brown said. "If it's steady, I can compensate for it, but if it's variable, you can't compensate for that."
If wind is too finicky, gusting and dropping off unexpectedly, Brown will often simply put up his equipment and head back to the camp.
However, if he's got a steady wind under 15 mph, he's ready to go. Brown does continue to check the wind regularly throughout the hunt to ensure nothing has changed.
While he often will hunt an open field, Brown said his favorite long-distance setup is actually a straight pipeline.
"You have trees on both sides of the pipeline, so you have a natural wind break," he explained. "That takes wind out of the equation."
When a deer pops out, he carefully glasses it with Zeiss 10x56 binoculars to determine if there are antlers and, if so, how large the rack is. If it's a shooter buck, he has a much stricter standard for shooting.
"The longest kill I've made on a buck was right at 500 yards in Texas," Brown said. "And I only took that shot because he came out and stood broadside. I knew I was never going to see this buck again."
But at his West Feliciana Parish hunting camp, he normally won't even take that long of a shot on a buck.
"I just worry too much about wounding a buck," Brown said.
But if he's decided to take the shot, especially on a doe past about 400 yards, Brown pulls out his range finder and double checks the range.
"A lot of times, the laser won't read on a deer if it's too far away, so I have to find something close to it," he said. "That's also why it's important to pre-mark your ranges."
However, it's vital that the distance is ranged to within a few feet.
"If your estimate is off by 20 feet, that can be a miss," Brown said.
Once he's satisfied with the yardage, he reaches up and clicks in the appropriate changes to his scope.
"When I fire, my crosshairs are on the (intended) POI," Brown said.
The specific number of yardage clicks is determined by the manufacturer's settings (normally 1 click equals ¼ of an inch at 100 yards) and practice, while windage adjustments are determined using charts and practice.
His scopes have tactical turrets that make it easy to get dialed in quickly. For those who haven't shelled out $1,500 to $2,500 for tactical scopes, Brown said aftermarket turrets can be purchased to retrofit their hunting scopes.
"You can make the changes with the slotted turrets, but the tactical turrets are so easy," he said.
He then places his gun on small sandbags he carries into his stand or uses bipods, solidly braces himself and puts the crosshairs on the target.
If the animal is moving, Brown stops them with a whistle he carries.
"Whistles are natural, so it doesn't scare them," he said. "They'll stop and look, and you've got maybe 20 seconds to get a shot off. That's plenty of time."
He then begins a practice with which any military sniper would be familiar.
"I only pull on target," Brown said.
What this means is that he puts the crosshairs on the deer, recognizing that the point of aim is going to move slightly with his heartbeat and his breathing. So he doesn't shoot immediately.
Instead, he takes a moment to get a feel for how the crosshairs are moving.
"It will move up and down or side to side," he said. "When the crosshairs are on the target, I'm pulling the trigger. If the crosshairs move off the target, I let off the trigger."
Once he has minimized movement and knows how the crosshairs are moving, Brown squeezes the shot as the POI touches his intended target.
"If you aim small, you miss small," he said.
Body shots are pretty simple, but it comes down to inches when taking long-distance head shots. Brown said all deer have a distinctive mark that allows him to know exactly where the eyes are, even if the light is poor.
"I pull even with the whites of the ears," he said. "That puts the point of aim right between the eyes."
At that point, there's nothing left to do but find the deer. That can actually be more difficult, he said.
"At those ranges, you sometimes don't know exactly where they went down," Brown said. "You fire, and then keep the scope directly on the target so you can see some sign of what happened to the deer."
After seeing a tail or leg flopping, Brown will try to locate a landmark before heading out to collect his kill.
Cobb and the other Woodlawn members have learned to expect a lot from Brown, and they always look for a deer with a bag on its head when he comes back from the woods.
"I use plastic bags to put over the deer when I head shoot them," Brown said. "There are kids and women at the camp, and I don't want to gross them out. If they see a plastic bag, they know what I've done."
However, he also only takes shots in which he's confident.
"Safety is the No. 1 concern," Brown explained. "If I have people (hunting) around me or there are people who might be coming in late and cross in front of me, I won't take a long shot.
"Once you let a bullet go, you can't pull it back."
He also refuses to push the envelope on conditions.
"If everything isn't perfect, I don't take the shot," Brown said. "I don't want to wound a deer."