This has certainly been an event for outsiders in recent years so I'm not rushing to pull the trigger on the seven players at 25/1 or lower.
Viktor Hovland at 11/1 looks incredibly short while backing Jason Kokrak at 14s doesn't smack of a smart play.
If forced to play the front end of the market, perhaps Sungjae Im would get my vote but I will steer clear.
With eight each-way places on offer, there's real scope to scroll down the odds and one I like at 80/1 is Cameron Tringale.
On first glance, he has a trio of missed cuts on his last three visits but rewind further and you'll find a pair of fourth places in 2011 and 2014 so he can definitely score well at the Old White.
One standout season from last season is that he finished 54th - i.e. in the top 25% - for Strokes Gained: Putting.
That was his best ever performance on the greens as a pro and provides a clue that he's ready to win after banking a second place on the PGA Tour in each of 2014, 2015 and 2016.
While he lasted just one round of the FedEx Cup playoffs after a missed cut at The Northern Trust, Tringale had played some fine golf over the previous months.
Starting from April's Texas Open, he had two top fives, four other top 20s and a T23 in 10 starts up until the Northern Trust.
In July, he said: "I've felt like my game has been strong really this whole season or this whole year at least, and definitely a little bit more momentum as the summer started."
This has been a good event for first-time winners - two of the last three editions went to a maiden - so hopefully Tringale can become the latest.
Take the 80/1.
David Hearn turned 40 at the start of the summer and he enters his fifth decade still without a PGA Tour win.
That will put plenty off but, to me, he's a definite each-way proposition at 90/1 here and, who knows, maybe the significant birthday could just help him refocus enough to get over the line.
If the Canadian is to win, the Old White is certainly a likely venue.
Hearn was runner-up here in 2015 and has also finished T12, T14 and T18 in his seven visits. Last year he was T30 after falling back on the final day.
One of the keys is that he always seems to putt well on this par 70. He ranked 1st for SG: Putting in 2015 and has been in the top 10 for that category on three other occasions.
Always a straight hitter, Hearn's iron play has looked particularly strong in recent starts and he was top 10 for GIR in all three Korn Ferry Tour events he contested recently.
As for this week's venue, he said a few years back: "I've always enjoyed playing here at the Greenbrier. I think it's one of the nicest stops we have on tour. I just really enjoy this week. I just feel like a lot of these holes set up nicely for me."
A course where lack of length isn't the negative it is at so many PGA Tour layouts, it's no surprise to hear those words.
The bonus is that he returns to the West Virginia track on the back of a fourth place at the Korn Ferry Tour Championship a couple of weeks ago which secured his PGA Tour card.
"Never give up. Never stop trying to get better. PGATOUR 2020 here we come!," tweeted a delighted Hearn soon after.
Hopefully he can ride the wave of optimism this week.
Having selected players at 80/1 and 90/1, I'll complete the sequence with a 100/1 shot.
There are a few at that price I like, including Anirban Lahiri, Lanto Griffin and Brian Stuard.
But the one that gets the nod is Fabian Gomez.
For starters, there is the little matter of the Argentine being a two-time PGA Tour winner.
The most recent of those was at the 2016 Sony Open and the Hawaiian event has some good correlation with this one - the obvious link being that Seth Raynor designed both Waialae and the Old White and they're par 70s.
Gomez is another straight hitter who much prefers the playing field to be levelled by a shorter track so I think he has the ability to go well here even if it hasn't quite shown yet.
He made just one of his first three cuts at The Old White although, after a gap, returned last year and opened 67-68 before fading.
What must surely help this time is that he has some hot Korn Ferry form heading in.
Gomez was T7 at the Portland Open in August and started the current month by finishing runner-up in the Korn Ferry Tour Championship thanks to a pair of closing 66s.
I'll play the momentum angle and hope it catapults him to a big finish.