In this thread I want to share some interesting things that can happen under simple rulesets such as Tromp-Taylor. Sometimes I may consider different variations of rules, and often the exact details won’t matter much, but unless otherwise stated we’re assuming:
- Positional superko (passes do not lift ko-bans).
- Suicide is legal (this very rarely matters).
- Two consecutive passes ends the game, and all stones on the board are assumed alive.
This last point may seem extreme if you’re not familiar with Tromp-Taylor rules, but all it means is that dead stones need to be “manually” removed from the board before passing. Even if you introduce a dead stone agreement phase as a practical shortcut, this is what would happen if both players stubbornly insist that all their groups are alive, requiring the other player to capture to prove them dead.
- Bent four in the corner (see below)
- Frozen life (aka 1-eye-flaw)
- Zombie groups (dead groups coming back to life)
- Cycle tampering (starting a cycle and then tricking the rules that it was the opponent who did it)
- Long cycles of the eternal flavor (eternal life, eternal ko, triple/quadruple hot stones)
- Unremovable ko for both sides (what happens if neither side can finish the ko?)
- Molasses ko (ko beast that can slow the game down to 20% playing speed)
- No-pass go (ruleset without passing and scoring)
- 23 eyes can die
- Three basic problems about ko under area scoring
- 1 > 1.5
- A single stone living in seki
Let’s start with a well-known example before I get into the more controversial stuff
This is the go-to example to highlight the difference between Chinese and Japanese rules, so a lot of people will already be familiar with it, and I’ll only go over the basic shape quickly. If you want a better introduction, the sensei’s page has some more variations.
In this shape, white has no continuation, since both A2 and D1 are self-atari. The best white can hope for is seki.
But black can at any time start a ko to kill the white group, and black will take the ko first (5 at 1):
This means that as long as the surrounding black stones are alive, the white group will usually die. Black can leave it until no other point-gaining moves are available, then remove all ko threats, and only then start and win the ko.
Some people might even accept the above as a proof that Bent four in the corner is always dead. But there is an important flaw in the “proof”, it’s not always possible to remove all ko threats!
A relatively common example of an unremovable ko-threat is a seki which one side can afford to sacrifice, something like this:
White can use B2 as a ko-threat. It loses 7 points, but can easily be worth it to win a big ko. And there is no way for black to remove the ko threat!
So let’s put these two situations on the same board and see what happens:
If both sides pass here, the score on the board is B+3. Can black do better by starting the ko?
It’s a one-way street up to here, where white is forced to use the point-losing threat:
Now black has two options: respond to the threat or finish the ko.
If black responds to the threat, white will take back the ko, and there are no more threats:
Black will pass, white will play C1, and the final score is B+2, one point worse than before!
Black gained 7 points in the upper right, but lost 8 points in the lower left
Then how about black ignoring the threat?
Black kills lower left, white kills upper right. The final score is W+2, even worse for black!
In summary: Black could kill the lower left in this game, but will lose points in the process. Black is better off leaving it as the seki in the first diagram, so this is a case where Bent four in the corner is not dead.
If you’re familiar with Japanese rules, you may note that they allow black to claim the benefits of killing the lower left group without paying the price of giving up the upper right group! For fans of simple rules this seems really unfair.
But this is a matter of subjective opinion, and if you prefer the Japanese result that’s perfectly fine!
In particular, I really hope this thread won’t devolve into heated debates over which rules are better.
I just want to share and discuss some interesting positions since I know there is a small group of people out there which enjoy them as much as I do
The fact that we used a point-losing unremovable ko threat to construct the above position made it quite a close call whether black should start the ko or not. As it turns out, there are several ways to have unremovable ko threats which are not point-losing, but I’m saving those for later installments in this series where they are actually needed!