Molasses ko
It is black to play in this position. We note that:
- If black passes/plays elsewhere, white can take on E1 and then capture the whole group with F2 after that.
- Black E1 and F2 are both self-atari.
Therefore the only promising local move is E5 (or equivalently E4), to which white’s only response is taking the ko:
3 and 4 are also forced:
Now there is no local move for black. If there is a large enough ko threat on the board, black could use that threat and then take back at E2 - but let’s assume there is no such threat.
Luckily for black, black can simply play away (say, F8), and white does not have a way to “win the ko”. Instead, white can only exchange a similar sequence of four moves as black just did:
And so it continues:
With the moves 5, 10, 15, 20 and 25, we saw a normal sequence play out on top. But the players had to exchange a 4-move sequence between each move, or else lose their big group. Thus we see a normal game continue, at 20% speed. Sounds kind of tedious right? This 5-move sequence took 25 moves, imagine playing out the whole latter half of a game in this way…
But wait, it gets worse! Let’s go back to the last diagram above. Black has played the final move at 29. There are no normal endgame plays left on the board, so can white finally pass now? Nope! If white 30 passes, black plays 31-33…
…and white cannot capture on F2, because this would repeat the exact position we had after move 25, just with black to move instead of white to move.
This is one of the rare cases where the difference between positional and situational superko matters.
Positional superko says that the board position may never be repeated under any circumstance.
Situational superko only says that the position may not be repeated with the same player to move.
So under situational superko, 34. F2 would be legal: it would be a repetition of the position, but not of the situation.
Since there’s no way for black to make headway after white passes, we can assume that the game could end with (30. Pass 31. Pass), with both big groups involved in the ko left alive for scoring.
But in this thread we are always assuming positional superko, so let’s get back on track…
What we now realize is that playing away from the molasses ko is safe, but passing is not! The moves you make elsewhere don’t have to be ko threats, but they do have to change the board position (and of course all non-passing moves meet this requirement).
For move 30, white may play inside her own territory, or even better, inside black’s!
We will now enter a long phase where both players throw in obviously dead stones into each other’s territory, to be able to make as many moves as possible. And remember, the game is still going at 20% speed! Some time after move 200 we’ll reach a situation looking like this:
Now it is again white to play, but every empty intersection on the board is either illegal or self-atari (note that even if suicide is legal, single-stone suicide is illegal under positional superko). It has finally become clear that white lost: she could resign here, or pass to end the game, in which case black will take the E3 group off the board before going to scoring.
Going back to the previous diagram, you can see that black had more territory before the territory-filling started. It is generally the case that the player with more territory will be able to make more legal moves, but because playing into the opponent’s territory can gain you extra moves, it is not easy to play this phase of the game correctly, or to predict which side is going to win.
In conclusion: The molasses ko can slow play down to 20% and turn the game into no-pass go, introducing a territory filling stage after the normal endgame. Weird and wonderful indeed, but probably not something you thought you signed up for when starting a game of go! Luckily they are exceedingly rare (Sensei’s only mentions one known example in a casual club game, is anyone aware of other examples?), so even if you’re playing with positional superko your whole life, you will most likely never have this happen to you.
(See Molasses Ko at Sensei's Library for some discussion on the status of the molasses ko under other rulesets)
We have now seen two different types of beasts which effectively turn the game into no-pass go: the unremovable ko for both sides, and the molasses ko. Next up we’ll take a closer look at no-pass go in isolation, to get a better idea of how these endgames would play out in practice.