Travel and Exploration Rules
Players have access to the World Map which they will slowly fill with information about the terrain and the contents as they explore.
Hexes on the world map are 6 miles from one side to the opposite side.
Each day, your journey is divided into 7 parts. While traveling you can engage in light foraging without slowing down (see supplies below). (Horses move 11 parts per day)
Easy terrain (grassland, light forest and savannah): 2 parts
Medium terrain (hills, forest [including the Dark Forest], wetlands, jungle, rocky desert) : 3 parts
Hard Terrain (dense forested hills, heavy jungle, sandy desert): 4 parts
Very hard terrain (mountains without passes, sand dunes): 5 parts
If you don’t have enough movement to complete a hex, you will make partial progress through it.
Variations in Travel Speed
If party members are encumbered you can only travel 5 parts / day. If you choose not to forage you can travel at 8 parts / day, and if you also push your endurance you can travel at 9 parts / day, but you run the risk of becoming exhausted (see Encumbrance and Exhaustion). If everyone in the party has horses, you can travel at 11 parts / day (you must carry fodder for your horses).
Searching A Hex
Searching is the process of looking through a hex for things that are not apparent while travelling across it. It involves looking for high ground, inspecting unusual terrain features, etc. It ordinarily takes a number of days to search a hex equal to its movement cost, though there may be exceptions (for example if you climbed a high mountain you would have a good chance of spotting anything in the hex, although things that were actively concealed might escape your notice).
Stealth While Moving
If the party wishes to sneak up on a group of enemies (spotted at a distance), the group makes Stealth rolls. The median result is the Stealth of the party. This is compared to the passive Perception of the enemy group, plus one active roll if they are especially alert, or two active rolls if they are guards specifically on look-out duty (3+ for a huge castle). If the party succeeds on its stealth roll, it can close to a reasonable distance (200 feet in plains, 50 feet in a forest, 30 feet in jungle) before starting its surprise round. If the party loses cover at any time while moving forwards, they are spotted automatically (e.g. if they are stealthing up on a group relying on the cover of darkness but the group has darkvision). During the surprise round, PCs have advantage to hit their flat-footed foes (who stop being flat-footed once initiative is rolled). If the stealth rolls fails, the party is spotted X rounds away, when X is the margin of failure x2 in open terrain, x1 in forest, x0.5 in dense terrain. They don’t get a surprise round, but low initiative foes are still flat-footed until they act.
If an enemy group wishes to sneak up on the PCs, compare their median Stealth roll to active Perception rolls by all party members. Any PC that beats the median Stealth roll can act normally in the surprise round, and is not flat-footed. If a PC beats the median Stealth by 5+, they have X-4 round to react, and can choose to warn other party members, cast preparatory spells, etc (all at the risk of tipping off the ambushers that they’ve been spotted).
Note: being trained adventurers who only venture into the wilderness a few days out of every month, PCs are far better at remaining alert for extended periods of time than their foes. This also explains why PCs get worn down (penalty on drop rolls) as expeditions drag on. PCs choosing to forage, catalogue plants and animals, or engage in other activities while moving forfeit their active Perception rolls against ambushes.
Sleeping in a hex
Your likelihood of having an encounter overnight while sleeping in a hex depends on how secure your position is. You can find a secure position with a good survival check, or by choosing one manually (such as if there is a cave you find or something).
To determine whether you have a night encounter in an average hex, I will roll a D20, and check the result against the following set of values:
In the open: 1-4 two encounters, 5-11 one encounter, 12-20 no encounter.
Somewhat secure: 1-2 two encounters, 3-8 one encounter, 9-20 no encounter.
Very secure: 1 two encounters, 2-4 one encounter, 6-20 no encounter.