City: Must be on a tile where a city can be founded (no marsh, mountain, volcano, etc)
Gold: The tile must not have any type of resource or luxury on it.
Maps: always available
Nothing: always available
Settler: Player must not have a settler (active or in production) or any unit with the Settle AI strategy.
Player must have less cities than (TotalCities / NumActivePlayers).
Mercenaries (skilled warrior): There must be a unit available to the Barbarians as well as the player and that unit must be able to be built (or have been built) by some player in the game.
Tech: Player must still be in Ancient Times.
Barbarians: Player must not have Expansionist trait. There must not be a city within a 1-tile radius. The player must have at least 1 city. The player must have at least 1 military unit. The unit popping the hut must not have the "All Terrain As Roads" ability.
To determine your odds of getting a item, sum up what's available when the hut is popped and divide what your looking for by that number. Example: Your playing a Monarch game as a non-EXP tribe. Your popping a hut while researching Ceremonial Burial when you have no military units and are equal to the average number of cities. You can only get city (5), tech (15), gold (10), maps (10) & warrior (10) so 5+15+10+10+10 = 50 and you'll get a tech 15/50 (30% of the time)