The name is the recipe, in three words. Sata is sugar, anda is oil, agi is fried: sugar, fried in oil. A batter carrying a great deal of sugar is dropped into oil that is deliberately not very hot, so the inside has time to cook through before the outside sets hard. Rushing the oil is the one way to get it wrong.

As it fries the ball swells and the top splits, usually into three. The split is read as a mouth opening in a laugh, and that reading is why the thing is considered lucky. A batch that comes out smooth and unsplit has, in the local formulation, failed to laugh, and is regarded as a poor omen as well as a poor cake.

The origin usually given is Chinese. Cooks from the Ryukyu court who travelled to China some five hundred years ago are said to have brought back a fried cake called kaikoushou, the open-mouthed laugh. The name and the split came together, from the same place.

In Okinawa it is still sent as part of a betrothal gift, and handed round at weddings. It also keeps for days without going stale, which is part of why it works as a gift at all, and it means the laugh stays on the plate for the whole length of the celebration.