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Pineapple Grenade applies vulnerablity.  After that the goal is essentially to get rid of all of our charges while the buff from 
The Whole 9 Yards is active.  Rocket-propelled Grenade and Magnum should be used first to help maximize the execute on Sniper Shot, in what order doesn't really matter.  If you're feeling fancy you can even weave the two in order to abuse animation cancelling and save time.  After your charges have been expended throw the second Pineapple Grenade to re-apply vulnerability then use Ol' Painless to use up ammo.  You should be able to Rapid Reload with under 25% ammo remaining but before running out.  Use The Davy Crockett whenever it's off cooldown.

Slot 1:

 Fragment of Twilight (Recommended) - I feel some people will argue that Sword Gun is a better choice here.  It's true that the two items have very similar damage output but this is my argument for Fragment of Twilight.  When we look past the damage stats Fragment of Twilight has up to 2700hp, health on hit, and a cheat death proc while Sword Gun has nothing, it's only damage.  In terms of utility it's really no contest.

 Sword Gun - Punisher has some amazingly good uniques with high stats.  The availability of this item also means it isn't too difficult to get one with a good roll which makes it more accessible than Fragment of Twilight.

 Bow of the Einherjar - I feel this is worth a mention because the stats on it are favourable towards Punisher.  It's not as easy to acquire as Sword Gun and lacks utility stats like Fragment of Twilight but the damage is up there with both of those items.

Slot 2:

 Kraven's Lion Vest (Recommended) - We won't be activating the melee proc but it's still +9 attributes, up to 483 damage rating, a decent health roll, and some power duration.  Pretty solid overall.

 Standard Issue X-Men Uniform - It's not too hard to acquire a good one from Danger Room and still offers a nice mix of damage and utility.

 War Zone Flak Jacket - Punisher's personal slot 2 is a bit of an odd assortment of stats that are overall inferior to Kraven's Lion Vest.  Maybe the strength will get changed to something more useful in the future.

Slot 3:

 The Whole 9 Yards (Recommended) - Damage rating, health, critical hit, brutal strike, attack speed, and six attributes.  That's a lot of good stats to ask for and this item raises them all in pretty decent amounts.  Since this is also easy to acquire there is no reason to use any other slot 3.

Slot 4:

 Standard Issue USMC Jungle Boots (Recommended) - Much like The Whole 9 Yards this offers a lot of good stats and in generous amounts.  For that reason, once again there is no reason to use any other slot 4.

Slot 5:

 Davy Crockett Nuclear Device (Recommended) - Most of the damage in this rotation comes from skills with an 'area' tag. Combine that with the insanely high critical damage and sizeable number of attributes makes this one of the highest damage slot 5s in the entire game.  Once more, there is no reason to use any other slot 5.

Punisher is in an odd place when it comes to artifacts due to how Fighting isn't abundant in artifacts and Intelligence is usually tied to mental damage.  This doesn't leave too many options.

 Gem of the Kursed (Recommended) - Provides much needed critical hit and brutal strike

 Nick Fury Was Right T-Shirt (Recommended) - The only artifact in the game that raises both Fighting and Intelligence and fortunately it's a good one for ranged heroes.

 Crossbones's Teaching Credentials (Recommended) - Both the cosmic and Intelligence versions of this artifact work here.

 The Broken Crown (Recommended) - It's hard to say 'no' to that collection of good stats.  Unfortunately it's also a bit hard to get ahold of.

 Kevlar Plated Helmet - Having a hard time getting a The Broken Crown?  This is almost as good.

 Flag of the Skrull Empire - It's good but the proc is not super reliable and we really need to make up critical hit and brutal strike with artifacts which are two stats this item doesn't really provide.

 Advanced S.H.I.E.L.D. Motion Analyzer - I'd have an easier time recommending this if  'maximum range' was in any way clearly defined in this game.

 Mental Focus Headband - Don't be fooled by the +5 Intelligence, the damage output isn't that great even factoring in how the proc scales off of your stats.

 Edge of Infinity - Pretty good and easy to acquire stop-gap solution.

1. (Mind Gem) Intelligence:  +6 Intelligence. (150 points)
2. (Soul Gem) Fighting: +6 Fighting. (150 points) 
3. (Time Gem) Temporal Loophole: +20% Attack Speed. +20% Move Speed. (160 points)
4. (Power Gem) Strike Through: +75% Brutal Damage. (150 points)
5. (Mind Gem) Mental Focus: +30% Critical Damage. (150 points)
6. (Reality Gem) Potency: +75% Base Damage to Signature Powers. (150 points)
7. (Mind Gem) Intelligence
Filler: (Reality Gem) Potency: Base Damage to Signature Powers.

- S.H.I.E.L.D. Agent Medallion and Infernal War Skrull Medallion seem pretty equal but the latter is easier to acquire and reroll -

- Hela blessings work better than Loki blessings.  Probably because of the hero's passive and low inherit brutal strike -

- Power Doop seems to work better than Bowazon -

- An invisibility catalyst helps a lot with survival, highly recommended to use one even if the archetype isn't perfect -

- Punisher's ultimate is a single target DPS loss even when maxed. -