Last night when I was honestly just trying to get the Sterling treasure from doing the weekly crucible I was match made into a group, because none of my friends were online, and it ended up being a group where the guy was friends with the other team... I played it out because I actually wanted to try to win, and I finished with a 1.7 kd while both of the players from the other team had like 0.7.. I consider that decent either way, but the guy on my team had 0 kills and 0 deaths and he was shooting at me while I was trying to shoot them making my aim go all over the place.. I reported all 3 of them for cheating because they are just farming for rep and rewards... it was enough to put me off of doubles for the rest of the games existence...
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There are 2 weekly pvp modes but only 1 of them shows on the main navigator shortcuts. Go into the crucible navigator and hover over the different game modes at the top. You will see that 2 of them give you the weekly rewards (the one on the shortcut list and another one)