I get about 30 blues per day (3 hours) and 3-8 legendaries depending on if I have milestones or not.
1 Gunsmith mat per blue, 3 per legendary. That’s approximately 30 + 24 on a good day. So 2 days for a Gunsmith rank-up and 200 for 10,000 mats.
32 weapons in the loot pool with even chances of it being any of them + the additional 1 worth of exotic weapon chance. That means you have a 1/33 chance to get the weapon you want per rank up. That means you should get the weapon you want roughly every 3300 mats. This means once every 66 days. Combine that with the tons of perks perks on weapons and it becomes less and less likely that you’ll get he weapon you want with the roll you want without serious grinding.
If you want mats fast, grind the strikes playlist or blind well as they have good blue drop rates and have a decent chance to earn legendaries for the amount of time they are.
An easy way Bungie can help is to remove world drop weapons from the Gunsmith pool. That would remove 12 slots and drastically increase the chances of getting a Gunsmith Weapon.
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Props to you for working all that out!
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Or they can just decrease the amount required, hopefully down to about 30 considering how bad the weapons you get tend to be.