Ko Threat Functions
Why make a ko threat?
Well, obviously, to win the ko (if you can).
But that is not the only reason. Suppose that your largest ko threat is not large enough to win the ko. Do you refrain from playing it? Of course not. You play it so that, if your opponent ignores it, you can carry out the threat and get something in exchange for the ko. That is the second function of a ko threat, the one that gives it its name.
I (Bill Spight) call threats that enable a player to win the ko primary ko threats, and those that merely enable the player to make a gain in exchange for the ko secondary threats. Which are which depends on the situation. Primary and secondary threats are sente.
There is another, more subtle reason for playing a ko threat, and that is to avoid winning the ko now. Suppose that your opponent has just played his largest ko threat and you have one more primary threat. You answer his threat and then, when he retakes the ko, play yours so that, when you win the ko, he will only get to carry out his second largest threat, which is smaller. Your gain from playing your threat is the difference in his gain between his two largest threats. If the two threats are carried out as simple gote with miai values A and B, respectively, this gain equals 2(A - B).
Similarly, you can use a primary threat to make a gain even if your opponent does not play a ko threat. Suppose that he has just played the largest gote. Instead of winning the ko, you play the current largest gote. He takes the ko and you make a primary threat and take the ko back. He now takes the next largest gote and you win the ko. Your ko threat has enabled you to take the previous largest gote instead of him. Your gain is twice the difference in miai values between the gote you took and the gote you let him take. This kind of gain is a function of primary threats.
There are three offensive functions of ko threats:
1) To win the ko (primary threat);
2) To make a gain in exchange for the ko (secondary threat);
3) To make a gain from delaying the win of the ko (primary threat).
Ko threats also serve to defend against the offensive functions of the opponent's threats. Preventing your opponent from winning the ko means that you will win it, so that defensive function is the same as the offensive one. Preventing your opponent from making a gain in exchange for the ko is the same as the third offensive function: you gain by delaying the win. But preventing the opponent's gain from delaying the win of the ko is something new. Ko threats which do this I call tertiary threats.
Tertiary threats are not strictly sente, because they do not make a gain if ignored. Instead, they prevent loss by maintaining the value of the largest play (see ambient temperature). (Remember that the gain from delay by playing one primary threat depends on there being a difference between the values of the two largest plays.) Tertiary threats are therefore ambiguous.
If the two largest gote are the same size (are miai), then they prevent a single primary threat from making a gain from delay. In a sense, then, they function together as a tertiary ko threat. Such a miai pair I call a virtual ko threat.