In OD&D and B/XD&D you check once per day to see if there's a random wilderness encounters (Cook/Marsh Expert has allowances for multiple checks per day, buts it's kind of vague).
That's fine but what about in adventure stories where the encounters don't stop? One dude gets eaten by a giant snake, another gets a poison dart in his neck and a third drowns in quicksand. Before noon no less.
To account for this I've worked out an "exploding die" derived wilderness encounter check that uses the sum of an infinite series calculations to maintain roughly the same odds as the original check.
The idea is every day you roll a wilderness encounter check; if there is one, roll another wilderness encounter check and than roll again and so forth (don't worry, probabilities ensure that there won't be 154 encounters). This determines the total number of random wilderness encounters the party encounters over the course of that day.
Clear, Grasslands, Inhabited, City: Was a 6 on a d6, now 1-2 on a d12 or 14%.
Woods, River, Desert, Hills, Barren, Ocean, Aerial: was a 5-6 on a d6, now a 1-3 on a d12 or 25%.
Swamp, Mountains, Jungle: was a 4-6 on a d6, now a 1-4 on a d12 or 33%.