Ten Thousand Year Ko
A ten thousand year ko is a kind of ko position where either player can initiate the fight but the player who does is at a disadvantage, since the other player will then be the one to take the ko first. One player (or sometimes both) also has the option to make the position into seki instead, the likely outcome if neither side has the stomach for the ko.
Since neither player may be eager to fight the ko, it can remain on the board for a very long time (ten thousand years). In fact, the game can end with the position remaining unplayed, in which case it is considered a seki. (See Life and Death example 12 of the Japanese Rules.)
White cannot fill the ko because she dies (bulky five). Often this will become seki when Black takes and fills the ko at the end of play.
Despite its name, it is not uncommon for the ko to be fought before the end of the game and not become seki. In particular, the ko typically favors the player with fewer stones in it, because that player has less to lose by comparison with seki. See /Fighting the ko.
A ten thousand year ko is hyperactive, which means that its evaluation depends upon the ko threat situation.
For an example of a position that can lead to Ten Thousand Year Ko see Long L Group.
Here is a /complex example.
Whether a position is a ten thousand year ko can depend on outside liberties. In the initial example on this page, if white is only loosely surrounded with plenty of outside liberties, white can be considered alive unconditionally, as white can initiate the ko fight to kill black with 胀牯牛 (oshitsubushi).
oshitsubushi is possible when white has 3 or more outside liberties prior to the ko fight
Ten thousand year ko is a direct translation of the Japanese mannen-ko. Mannen here means "perpetual" or "prolonged" (referring, in this case, to the period until one side makes the situation into a direct ko). The Japanese term is recognized and used in the West. The less-preferred English alternative thousand year ko is also in use. See /Terminology for details.