The Teladi Outpost (TO) is Down-Loadable DownLoadable Content available for X Rebith via Steam.
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Generally speaking in Rebirth, the higher our reputation with a Faction, the more they like us. Leading This leads to improved trading discounts, the availability of Licenses in the more lawful systems of Albion and Omicron Lyrae (resulting in increased mission variety, rewards and cash bonuses for shooting hostiles), and not getting shot in the face.
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TO offers unique but initially confusing gameplay relating to levels of reputation with the local 'pirates'. They're an easy-going but sociopathic bunch. Appearing : appearing in photos with babies one day, stealing their prams the next. They come in two factions, Uguras Armaments and The Cartel.
Both factions are initially neutral (blue) towards Otani and seemingly disinterested in him. Their ships, Marauder Phoenixes, happily wondering wander around Fields Of Opportunity nuking passing cargo ships without a care in the world. Also without intervention from the Teladi Union, who are seemingly unwilling or unable to do anything about it.
The confusing part is that even while blue, they'll do that to Ren's ships too if they are designated as Trade or Mine in the encyclopaedia and if they are carrying trading wares (including just jump fuel)... Typically our capitals will return fire at that point and if their Marauder the Marauder Phoenix is killed , either by Ren, his trader, his other ships or by NPCs, our standings will drop. At which point, once red, normal standings reputation rules apply if standings continue to drop.
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Maintaining, gaining or regaining standings reputation with Uguras Armaments and/or The Cartel is possible but it's tricky and isn't really compatible with treating Fields Of Opportunity like other systems. Without wanting to provide too many spoilers, it is worth noting that the TO-specific mission, The Rising Tide, is Uguras Armament-related. So it might be worth holding off from war, at least initially.