Patrol

A new feature (as of April 2020) is the ability to send your units on patrol. (See also the official announcement here.) While on patrol, your units will discover new resources and items. However, patrolling is risky; the longer your units are on patrol, the more likely they are to take casualties.

Starting a patrol
To start a patrol, visit the "First patrol" location on your world map, just to the west of your command center. A patrol consists of six types of units, one each of infantry, stormtrooper, heavy infantry, special, vehicle, and heavy machinery. You can send as many as you want of the unit that you select, however. The patrol may be accompanied by one hero.

Each unit you add to the patrol increases the patrol duration, in a similar way to expedition success. (That is, for a given unit, the amount it increases the patrol duration, in minutes, is equal to the expedition success chance, in percent.) In order to start the patrol, the patrol duration must be at least 6 hours, and it cannot be longer than 24 hours.

Sending the patrol also costs some steel, recruits, and ammunition. This cost is determined by the unit type, but is less for basic units (generally half the cost, although not always).

On patrol
While your troops are on patrol, they will gradually take casualties (indicated by the decreasing number of troops on the left area of the screen). They will also discover new items while on patrol, which get placed in the area on the right. If all of your units get killed, then all of their items discovered are lost. Heroes increase both the chance of your units surviving, and of the chance of discovering items, with the effect increasing with the rarity of the hero.

At the end of the patrol, you may extend the patrol duration by paying either gold, repair kits, or medkits. This part of the patrol is more dangerous, but provides higher rewards. The patrol may then be extended a second time for gold only. When the patrol is complete, it will return to base. It will still continue to take casualties during this time, although you can accelerate the return by spending gold.

If the patrol returns safely to base, all surviving units are returned to you, as well as whatever they found on patrol.

Strategy
Given the costs of sending different unit types, and that the more expensive types do not contribute anywhere near as much more time, it is clearly most cost-efficient to send the cheapest unit types. If you accompany your troops with a gold hero, and you don't extend the patrol, your troops will take no casualties, so in that case the best is to simply take your infantry units with the highest chance of expedition success. The ober-traitor of Old Reich is currently the best; if you don't have enough, regular Old Reich traitors are also a good choice, or you can supplement with stormtroopers (Old Reich units are also a good choice here).