Well, to make you feel better, you have much better odds if you exclude the 15% ed bonus. Sure, it’s nice, but really anything between 5-15% is decent. 10% ed is not going to make or break your faith, it’s just a min maxing caprice.
Also, Matriarchal bow may be better, depending on how easily you can hit that IAS breakpoint.
In my 100 hours of solo player 1 chaos runs, i found 2 GMB and 2 Matriarchal all with +3 bow skills, none of which had sockets. All went in the cube, none came out 4 sockets. It is going to be a LOOOOOONG journey to get that 4 socket one.
Ah… fixed. Changed it to increase.
I think 1 in 18, based on 1 in 3 for socketed, then 1 in 6 for correct number of sockets. It’s significantly better but you’re right it’s still quite rare!
Even then, highly likely that I won’t even roll the dice anywhere near enough to satisfy the mathematical odds. We’re talking about 180,000+ cow runs to find this baby.
These relate to the same thing. Set the Ed and +bow skills to their minimum values, you will see what I mean.
Also, I think the 1 in 6 and 1 in 396 numbers are wrong, since it includes durability mods in the possible rolls which bows can’t roll. So it should be:
This item is in a different league of rare items compared to runes. Rarer than Tyreal’s Might 
I already have a couple of 4 socket GMB’s and some plain GMB’s 
It’s not hard to get the max IAS breakpoint with a faith GMB. I was thinking of MB to use with Atma’s but after the synergy buffs, that’s a redundant option now.
And those are plain ones, not superior as I said, it’s the equivalent odds of finding 48 Zod Runes… it’s pretty dumb how rare this is.
Updated my maths with the enhanced damage chance.
I think the mod odds are looking right, it’s really the drop odds that we’ve got different numbers for since we’re using different data sources. Either way, it is looking like finding this is in the “not a chance in hell” basket.
Whatever the base item drop chance is, multiply it by 17,820 for running 750+% magic find, and 8910 if running with 0% magic find, and somewhere in between if running a magic find amount somewhere in between 0% and 750%. (@Players 1) With what I’ve figured anyway… There’s probably something else I’m overlooking. Brain starting to hurt again. 
Still a bit unsettled with Silospen and Maxroll are showing different numbers, the differences aren’t small either. Don’t know how to verify which one is right…
Here’s the drop tables for dark archer players 8:
https://d2.maxroll.gg/d2-drop-calculator#p8,1;monster=normal,12,cr_archer3
https://d2.maxroll.gg/d2-drop-calculator#p8,1;monster=normal,12,cr_archer3,minion (minions)
Then filter for “Grand Matron Bow”.
It then tells you the drop odds of the base, and what the percentage distributions between normal, superior, magic, rare (ignore set) if that base drops.
Probably the best way to find this is either use a javazon or CE necro to do P7/P5 cows all day and find jewels, runes, charms alongside. It’s a 1 in 9.5 million chance to find a 15max/15ias jewel for example, which realistically 3 of them can be found before finding this GMB base. And then need to gamble like 15 billion gold to get a 3s tiara of speed. God help me…
The original devs weren’t kidding when they designed the drop system to make every playthrough of the game a different experience.
Since you’re on single player, you have the advantage of farming weapon racks on the same map. Google weapon rack farming.
I am contemplating this too, if the numbers are good enough I could try it 
Still might need to jump online regardless to trade for other items like charms and jewels.
After 500+ p=1 cows runs, and thousands of other end game farming runs, I’ve only ever seen TWO GMB bases drop. One was +1 skills, the other +2. Neither were superior and neither came with sockets.
You’re never gonna get a perfect GMB except by trading so forget about it.
I just dropped 4 socket Grand Matron Bow in hell cows. Do I win something?
Did it have +3 bow skills and 15% ed?
Only +3 skills no ed
For solo self found Ide be more then thrilled to find that with the 4 sockets, GJ!
Thanks, I play online but mostly ssf, didn’t do much trading so far.
Sadly no, welcome to the club
I found a guide on this. Looks like it’s not possible for Grand Matron Bows 
oh well
Guide link
https://www.purediablo.com/forums/threads/1-07-1-08-racking-guide.1564/