If White takes the ko she raises the local temperature from 1 2/3 to 2 1/3.

This kind of sente ko is fairly common. They do favor the player with sente, but the sente threat is not so large that they are unfightable, as a rule.

2) A ko such that winning it is sente for one player. Here is an example.

Sente ko (iii)  

If Black fills, the White group dies. But if White takes and wins the ko,

Sente ko (iii-a)  

White threatens to kill the Black group with White 1. This is worth 16 1/3 points, miai, hotter than the original ko position, in which a play is worth only 12 2/3 points.

Sente ko (iii-b)  

If White wins the ko in sente, later Black 1 is a 1 2/3 point sente ko, where taking the ko is sente.

3) An extreme form of one-sided (hanami) ko fight. The capture by one of the players, Black say, has such a large potential follow-up that White must treat it as a sente play.

Such a ko position, at a given stage of the game so that it really is a sente ko, will not give rise to an extended ko fight. But it is possible sometimes for White to capture once, even in such a fight. The reason is that Black must find some ko threat. White therefore has a chance to make Black use one threat.

Double sente ko?

Double sente ko?  

Here, few points are at stake locally (both sides can live, e.g. black 1, white 2), but the winner of this ko saves his own group while forcing his opponent to defend, so the winner gets the first opportunity to play elsewhere. This contrasts sharply with gote ko, in which the ko loser gets the first two plays elsewhere.

Bill: This is a rather hot ko (17 2/3 points miai value). If there are no ko threats, or Black is komaster, Black will be able to take the ko with sente when the ambient temperature is between 13 1/3 and 1 2/3. I. e., under normal circumstances. That will leave a sente ko worth 1 2/3 points for later.

In the unlikely event that White is komaster, when White takes the ko back Black will normally defend at a, leaving a sente ko.

So when there are no ko threats or Black is komaster, Black will normally be able to take the ko in sente, but when White is komaster Black will defend in gote. If it is White's move instead, Black dies.

This is by contrast with double sente, where the player with the move can play locally with sente. Under normal circumstances Black can take the ko with sente, that's all. Otherwise he will end up having to play at a in gote.

BTW, this kind of ko is not that uncommon.

"Double sente" ko  

Bill: Here is something that is more like it. When Black is komaster is sente.

"Double sente" ko  

And under many circumstances (double sente always depends upon the rest of the board) Black will be able to play with sente.