Per the yaku's name, kan must be called three times; and as a result, the tenpai hand has at most four tiles remaining as closed. If necessary, the hand can call as far as a single tile remaining.
Of all the standard yaku, sankantsu is the most difficult and least frequent. Its rate of occurrence is comparable to that of some yakuman. As the name implies, kan must be called three times before the end of the hand. A fourth kan converts the hand to the yakuman, suukantsu. The difficulty stems from the need to call kan three times; but overall, the use of kan is risky play due to additional kan-dora, which may benefit the other players. This is true even for a single kan call, let alone three times.
Sankantsu's difficulty stems from its various pitfalls during hand development. For starters, attaining the tiles necessary to call kan three times is difficult onto itself. In order to call kan in the first place, a player has to draw three out of the four tiles. In terms of frequency, games do not involve calls for kan all that often, let alone more than one instance in a hand. Even when someone is tenpai for sankantsu, the hand can end in the event another player calls kan for a fourth time, invoking an abortive draw.
No sequential based yaku can combine with sankantsu. Three out of the four possible tile groups must be called for kan, and they can be referred as "triplets plus one extra". This rules out pinfu, iipeikou, ryanpeikou, ittsu, and sanshoku doujun. Chiitoitsu is incompatible due to its usage of pairs. Every other yaku is compatible.
This yaku is set at 2 han. However, the number of kans significantly increases the hand's value. Even with the minimum 3 open kan of simples, they generate a fu count of 8 fu each, for a total of 24 additional fu to the base 20. So, at a minimum, this yaku is valued at 2 han and 50 fu, which is the equivalent of 3 han and 25 fu.
Even with a base of 2 han, the number of kan calls adds the probability of additional dora, which may have an immediate impact on the hand value. Just one dora and adequate fu may bump the hand already into mangan. If any of the tiles used for kan became dora, that's instantly 4 dora.
- Sankantsu in Japanese Wikipedia