Toitoihou 「対々和」, often shortened to toitoi 「対々」 is a standard yaku. In English, it is referred as "all triplets". That's due in part with every tile group to be composed of triplets. This hand is immune to any requirement involving the numbered suits or honor tiles. Simply, any group of triplets would suffice. In terms of han, this yaku is not devalued while open. Players, whose hands containing multiple pairs, may be encouraged to call on tiles to complete triplets. With in mind, this yaku also acquired the nickname of "pon palace".
If this hand wins by tsumo, then it counts for the suuankou yakuman. Otherwise, it's a toitoi mixed with sanankou.
As the name implies, this yaku requires koutsu. Usually, this yaku is called open due to the ability for pon to claim discarded tiles from any player.
^ Ippatsu requires riichi to be of any use.
Toitoi with mentsumo and junchan actually form yakuman, as suuankou and chinroutou respectively. Toitoi with chanta forms honroutou instead.
Toitoi is incompatible with any yaku requiring a sequence, meaning pinfu, iipeikou, ittsu, sanshoku doujun, ryanpeikou, and chankan (since it can only win on a sequence wait). It also cannot be combined with chiitoitsu, since it doesn't use mentsu.
Naturally, this yaku can be developed when the start hand, or later subsequent tile draws, produces a number of pairs or even triplets. As the yaku requires, every tile group must be a triplet, which may be acquired via the tile draws or player discards (pon). However, if the hand happens to develop with a concentration of pairs (normally 4 or 5 pairs), then a player may actually opt to develop chiitoitsu instead. A hand with 6 pairs is already tenpai for chiitoitsu, which renders a chase for toitoi to be rather pointless.
- Toitoihou in Japanese Wikipedia