Ok, it seems that I may have found a bug, at least with my DIR-878 using v1.12B01 FW.
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Both a single and two xbox consoles, 1 non MS Preview Program, 1 MS Preview Program no matter what order they are turned on, power button OFF reset, all 4 buttons on xbox controller reset, 1 xbox Instant ON enabled while the other is disabled, disable and re-enable of uPnP on the router and reboot of both 878 and ISP modem, both are showing STRICT NAT on the dashboard networking settings. Nothing else I've tired will not change to any other NAT status on the consoles. One console reports port 3074 and the other reports a random 4#### or 5#### port number.
This is not good.
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I can put other routers online and get OPEN NAT on both dashboards.
Both console should have OPEN NAT on the dash board and in game> one game would be OPEN NAT and the other game would be Moderate due to the NAT kind D-Link now uses.
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I'm hoping that D-Link will take a look at this and consider making some changes where needed. I hope I can be of help if more information is needed.