Rather than use wandering monster rolls, as I've heard some people do, just assume that any hunter will eventually find non-threatening game. The real question is "when?" Roughly divide animals into small, medium and large game; based on the area, decide what animals would fit into each type.
- Small game is stuff like pigeons, mice, and other tiny animals; they're common, so finding them (or traces of them) takes turns of time.
- Medium game is a little larger, like rabbits or raccoon; large enough to make a small meal for more than one person. Finding them takes hours.
- Large game is deer-size and will feed an entire adventuring party, perhaps for more than a day. Finding them takes a number of four-hour hunting periods (really big game takes days.)
Ask the player what kind of game the hunter is looking for, to determine the base time period of the hunt. Some areas like mountains or deserts also shift the time unit up one or two categories. Roll a d6, adjusting up or down based on background and difficulty of hunting in the area. On 5+, the hunter find game or a game trail in the very first time period. If the roll is lower than 5, describe how poorly the first time period of the hunt went, then ask the player how long they wish to continue the hunt. Don't roll again; each extra time period adds +1 to the die result, so eventually the result would be 5+. If the hunter doesn't hunt long enough, no game is found.
Once found, the player can decide how to actually catch the game. Set traps along the game trail? Roll 1d6 per trap every 4 hours, with a 5+ meaning a trap worked. Stalk game and ambush? Might take a while (use the evasion and pursuit rules.) Drive game towards a trap or ambush? Quicker, but takes a lot of manpower and effort.