if all players sit intop of each other and you throw large portion of gold on the ground who auto-picks it ?

Gold drops are just like item drops: per-player

The gold that drops for you, drops for you. The gold that drops for your buddy, is for your buddy. There's no sharing or splitting when you pick it up. And if you have some +gold find stats on, you're going to get more gold than someone in your party who doesn't.

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Q u o t e:
Do you only see the drops that are for you? Or will I wind up running over other peoples stuff trying to pick it up?

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You only see items that you can pick up. Whether that's your individual drops, or items someone else threw down that everyone can see.

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Q u o t e:
So it's similar to WoW whoever the 1st person is to engage the enemy, they get the loot? Or maybe whoever does the most damage to an enemy? Or last hit on an enemy?

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No, everyone gets their own individual drops. We kill an enemy and you may get 5 gold while I get a legendary sword. Drops are individual for every player. The game only requires proximity to the dying enemy to be considered for a loot drop.

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Q u o t e:
Like, does playing solo give you the exact same chance at gold and magical items that playing with a group does?

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Yes, it's exactly the same.

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Q u o t e:
And my Gold Find and/or Magic Find gear has NO EFFECT on anyone else in a party?

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Correct. Each person affects their own drops.

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Q u o t e:
(aka - Why should we bother playing in a group?)

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Because your kill rate goes up. Despite the difficulty increase you simply kill stuff way faster in a group. More 'drops per hour' means you want to be in a group.