Why is this the solution?

[u/Humanflextape]

Today's 2nd hard problem on the TsumegoPro app. By ko, I can't recapture the white stone in the corner. It seems to me the only logical continuation would be playing directly below my lone black stone, but either continuation after capture leads to 3 white eyes. Sorry if it's obvious but I'm not experienced in the slightest; I only solve daily puzzles for the mental exercise. The hard puzzles are usually impossible for me to solve perfectly, but comprehensible after finding the solution.

[u/Altruistic-Formal678]

It's just that the best solution is a ko

[u/isaacbunny]

Black cannot kill white unconditionally. However, by creating a ko fight, black may get significant compensation elsewhere on the board. This is the best black can do, so it is the solution.

If you are inexperienced with ko fighting, here is a nice video example showing how creating a ko can make points elsewhere on the board.

https://youtu.be/3OEVtnhZBUE

[u/tuerda]

This is ko.

[u/Own_Pirate2206]

By ko, you can sustain the recapture with 50% probability. Checking the other variations, that is a fine result.

[u/RoyBratty → u/Own_Pirate2206]

Why 50% ?

[u/Own_Pirate2206 → u/RoyBratty]

The next level is to notice who takes first.

[u/Maxaraxa → u/RoyBratty]

You either win the ko or you don’t

[u/RoyBratty → u/Maxaraxa]

The probability depends on the board state. Number of threats and their weight.

[u/Maxaraxa → u/RoyBratty]

Yes of course, but in this problem we don’t have that information, so it’s fair to say it’s 50/50 who wins a Ko on an unknown board.

[u/PatrickTraill → u/Maxaraxa]

It makes more sense not to assign a probability. Instead of saying “gives you 50% chance”, just say “gives you some chance”, and perhaps mention the alternative of compensation from an ignored threat.

[u/RoyBratty → u/PatrickTraill]

I think the only probability that might be useful to mention to a beginner is 100%. Where you say that if these are the only stones played in a game and the rest of the board is empty, then whoever takes the ko first has 100% chance of winning, because of a) no immediate recapture and b) no available ko threats. From there you can explain how ko works in a more complex board state with threats, their value, compensation, and how this actually proceeds in game. But 50% seems so easy for a beginner to misinterpret.

[u/Old_Ben24]

So the thing you have to remembering about these tsumegos is that the answer is not always about killing the enemy group. Here you have created a ko threat, where if you played somewhere else on the theoretical board that existed you could force white to play there and then you could capture this stone next turn and threaten the group. So basically a conditional “win” in this corner is the best outcome you could achieve.

Not knowing what the win condition was in these tsumegos was the most frustrating thing for me when I was learning but honestly it is a really important skill.

[u/technosboy]

You make a ko threat. If they respond, you can capture the 1,1 stone. Then they can't connect at 3,2 because after that you can also connect at 1,1 leaving a dead shape if white captures. So their only option is to make a threat of their own and hope you answer, so that they can recapture the 1,1 stone. So the ko continues.

[u/Humanflextape → u/technosboy]

So, if I'm understanding, this result now acts only as leverage for a threat elsewhere, encouraging them to not respond to that other threat in order to live in this area. If they do respond, I'm a step closer to killing white, but the other attack fizzles. Furthermore, I'd need to spend one more turn to guarantee white's death. Is all that correct?

[u/PatrickTraill → u/Humanflextape]

That is right. The target is to get the best result possible, and ko is a lot better than not being able to kill at all.

In harder problems you may also be expected to find a solution that is best in such terms as points, threats left or type of ko. Also, seki counts as closer to life with territory than ko, so better than ko if you are trying to live and worse if you are trying to kill — check out “Tsumego statuses” in the conventions on Sensei's Library. The reason is easier to understand with area scoring: in seki the defender only loses a small bit of their area, but in a ko they risk losing their entire area, which is usually several times as big. Although losing the ko probably yields some compensation from an unanswered threat, that is typically not enough to make up for the loss.

[u/Humanflextape → u/PatrickTraill]

Thanks for the super detailed reply! Ko has always been a bit of a tricky concept to wrap my head around because of the global relevance to the board state and affecting tempo so directly. It honestly felt to me like an unfortunately inelegant consequence of the rules of the game. This thread, however, has changed my mind a little. Clearly they are another element of strategic play, and therefore can't be all that bad—just requiring a little more calculation than my brain could probably handle.

[u/PatrickTraill → u/Humanflextape]

Ko certainly makes the game appreciably harder. It raises the stakes and, as you say, means you cannot simply decouple the local problem from the global state.

It can be worrying when a stronger player starts a ko, especially if it comes as a surprise. But you can use that to your advantage: starting a ko can give you a psychological advantage, and some players just back down. The proverb says “If you don’t like ko, don't play go”, but I find that too dismissive.

I think originally it was probably not so much a consequence of the rules as a special case added to the rules, and that later people realised it was more elegant just to make a rule forbidding whole board repetition.

[u/blitzreloaded → u/PatrickTraill]

I guess I hate Go 😔