commit 6b4ea98163cecda8935ac77c1e318e4b663a246e
parent d95e547982e446b04cef630f24edeb0c895b3baf
Author: mpizzzle <m@michaelpercival.xyz>
Date: Thu, 18 Aug 2022 22:56:17 +0100
minor tinkering, fixing links
Diffstat:
8 files changed, 104 insertions(+), 99 deletions(-)
diff --git a/content/bent-four-in-the-corner-for-dummies.html b/content/bent-four-in-the-corner-for-dummies.html
@@ -1,78 +0,0 @@
-Chess is notoriously a game of perfect information, and can be approached with purely deductive reasoning.
-
-I found the rules of Go to be nebulous, which was off-putting coming from a 'more logical' game like chess; it didn't seem to be clear in many common cases how territories could be defined. If I have a line down the center of the board, which side is the inside of my territory and which side is the outside? If there's no way to define this then surely there's no way to count a score of what's 'inside' vs 'outside' a group right? Why does a group need two eyes to be alive? There is nothing in the ruleset saying that a group needs two eyes to live. And if I have some territory with two eyes and my opponent still plays inside it, what the fuck is happening? wait, my group with two eyes managed to die???
-
-As it turns out the rules are in fact very well defined; the consequences of these rules however can be nebulous for a new player, and therefore can be a lot harder to get an intuition for compared to chess.
-
-When I first learned to play Go, I started by doing life and death puzzles (tsumego).
-
-The outcome of each puzzle is also very logical, of which there are exactly four:
-life, death, seki, ko.
-
-getting an intuitive feel for life and death comes quite naturally coming from chess, as it's the same binary severity as being checkmated. Can you checkmate your opponent in this position? Can you defend against checkmate in this position? Very easy to understand. Seki is somewhat analogous to stalemate, and can occur when two weak groups are attacking each other at the same time. If neither group has a significant advantage in the fight, then it's possible to reach a situation where if either player tries to kill the other, that player would end up killing themselves first by shorting their own liberty count. As such, the best option for both players is to live peacefully in 'mutual life' (seki), which, while doesn't net you any points in some rulesets, is better than dying.
-
-ko, however, is a fascinating result; however, when first learning the game the nuance of ko was lost on me. It was hard to get an intuitive grasp of 'ko' compared to the other three results as it doesn't have an analog in chess, and I remember when first learning the game thinking "yes I can sort of see that the shape of this result is a ko, but what the fuck is a ko?". The light-bulb moment came during live teaching game, where the implications of an evolving ko fight became apparent to me. You mean this fight can affect every single other fight happening on the board? mind blown! a Queen in the middle of a chess board certainly has a lot of influence, but there will still be pockets of the board where her presence is not felt.
-
-Anyway, if you look on online-go.com, early on in the puzzle lists you encounter many 'bent four in the corner' problems, and when first learning the game these puzzles stood out to me as making no sense; I found this 'bent four' concept to be even more opaque than ko fights, and unlike ko fights didn't seem to have very much significance. There is a lot of complexity to unpack with the bent four (we'll break it down), and they do have some interesting significance, however personally I found it unhelpful to have this puzzle introduced to me so early on while learning; if I was teaching go to someone I would wait WAY longer before showing them bent four in the corner problems.
-
-Complexity layer 1:
-So here's the scoop. This is seki right? if Black plays either X or Y, they are reducing their own liberties from two to one, and next turn White will play whichever move Black didn't play reducing Black's liberties from one to zero thus capturing the group. Ok, so Black doesn't have a move, it's seki right?
-
-Complexity layer 2:
-Well, no. What about White's moves?
-If White plays Y, then Black plays at X and captures. This makes a straight 4 in the corner, and this is a shape which White cannot stop from making two eyes.
-However if White plays at X, Black plays at Y making a bent four in the corner. Can you see what's about to happen? Lets continue:
-
-White plays at Z. Now Black has only one move which can potentially still make two eyes at A. If White were to play away, Black could capture the stone at Z and be alive. However, White isn't a dumbass and instead takes the stone at A. Next opportunity White gets, White will play at A reducing the shape to a bent three in the corner, which as you can see is pretty trivially a dead shape.
-
-But it is Black's turn. and do you notice anything about the shape? it's a ko! White has started a ko fight, and therefore if Black can find enough threats elsewhere on the board he has the potential to make life!... right?
-
-Complexity layer 3:
-Well, no. Think about the initial position of the puzzle; remember that Black has no way to initiate this ko fight, only White does. So theoretically, White can keep the pseudo seki on the board until the very end of the game, neutralize any remaining ko threats, and then start the sequence above. When Black tries to find a ko threat, he will find that no move on the board forces White to respond, and therefore White will simply ignore it and play at A, thus finally killing the group.
-
-So, finally, here is the conundrum. What is the result of the puzzle? alive, dead, seki or ko?
-we can rule out life for Black pretty easily, so this leaves death, seki and ko.
-
-If White so wishes, she can leave the seki on the board and that's that. However, at any point she has the option to force a ko fight, including waiting until the end of the game where she can 100% guarantee that Black will lose the ko fight. So is it dead?
-
-Complexity layer 4:
-The weird answer is, it depends on the ruleset! The strangest case is the Japanese ruleset, which in the UK is also the most common (although the AGA ruleset, which I believe to be superior, seems to have gained traction)
-
-In the Japanese ruleset, the bent four in the corner shape is declared to be unconditionally dead; there is literally a special case in the ruleset for this shape. You don't even have to initiate the ko! despite it technically being a seki, Black is declared to be dead if there is a bent four on the board.
-
-Wait, how is that fair? it's a seki on the board, so surely at the very least you need to reduce it to a dead shape before it can be declared dead, right?
-Well, no. Again, it's a special case baked directly into the rules, so it is dead. So why does a rule for this case exist?
-
-Complexity layer 5:
-Imagine the following scenario when there is no bent four in the corner rule:
-
-We are (almost) at the end of the game and there is a bent four on the board. White needs to kill the bent four to win the game. In order for White to kill the bent four, she has to reduce Black's group to a dead shape. But as we have highlighted, this involves winning a ko fight. Therefore, she needs to preemptively neutralize any remaining ko threats before initiating the sequence, otherwise there's a chance that she might accidently let Black reach unconditional life which could be the difference between winning and losing. Eventually, White manages to do all this and capture the group successfully. She won the game right?
-
-Complexity layer 6:
-Well... It depends. How much is capturing the bent four group worth? How close was the score before the above scenario started? How many ko threats needed to be neutralized?
-
-Lets say the group is worth 15 points, White is down by 0.5 points, and she had to preemptively respond to 15 ko threats before starting the ko. In this case, the 15 points of territory gained is offset by the 15 extra moves she needed to make, each of which is worth -1 points (It's possible for this not to be the case, e.g. the preemptive move was dame, but suppose all were worth -1). She still loses by a half point, even though objectively there's a group on the board that she can kill that would win the game, but the amount a stones she needs to invest makes it not worth it.
-
-In the Chinese ruleset, this problem does not exist. each extra move played in your own territory is worth 0 points instead of -1, as your stones + territory count towards your score, where as in the Japanese ruleset territory + prisoners are considered. This means that in the Chinese ruleset playing preemptive ko threats doesn't reduce your score and therefore you are free to clean up the bent four, winning by 14.5 points.
-
-The Japanese saw this flaw in their ruleset especially when compared to the original Chinese rules. rather than throw out their ruleset entirely, they introduced a rule to handle this so that this very odd circumstance wouldn't force outcome of the match to diverge radically between rulesets.
-
-Ok, so under some rulesets the rules of Go are a bit less elegant, but it solves the problem right?
-
-Complexity layer 7:
-Well... no.
-While they are much, much rarer than the bent four, there are other shapes that share this 'bent fourness' quirk of being technically dead at the end of the game, but having to go through one or more ko fights before eventually being reduced to death. While this scenario is more complex, it could again feasibly be the difference between winning and losing, and again being another wedge between the Chinese and Japanese rulesets, especially since only the special case for the bent four exists! No other shapes, despite their similar properties are covered.
-
-So... yeah. Unfortunate as it is to say, but the Japanese ruleset is inelegant. The Chinese ruleset is more elegant in some ways, but it too has it's own problems.
-
-Is there a middle ground?
-Well... yes! It's the AGA ruleset, in my opinion the best ruleset, and they fix this entire problem with a solution that is so elegant (as Go is supposed to be) that I'm genuinely surprised that the Americans figured it out before anybody in Asia.
-
-The rule is simple: passing your turn is worth -1 points. That's it, that's the entire rule. No bent four in the corner special case. See if you can figure out how that fixes the problem before we continue.
-
-Here's how it works: imagine the bent four scenario again. White needs to capture a 15 point bent four territory, is behind by 0.5 points, and needs to fix their shape preemptively against 15 ko threats.
-The situation is exactly the same: Every time White neutralizes a ko threat, it's -1 point to her. However the small detail is that when Black passes the turn, it's also -1 point for him. So no net loss has occured. If there are any dame (zero point moves) then both players need to fill those in first before White starts neutralizing threats. So if Black passes it's -1, and no matter else where Black plays it's also -1 points. Therefore, at the end of the sequence after the bent four has been captured, White has +15 for the territory, -15 for the ko threat neutralizations, however now Black also has -15 for passing 15 turns (or playing 15 unnecessary moves). Therefore, White wins by 14.5. Genius!
-
-There are more subtleties to this ruleset, but basically it combines the best of both the Japanese and Chinese rulesets while still managing to be more elegant. Notice that this rule doesn't just fix the bent four in the corner, but any other variations of 'bent fourness' that might not technically be covered by the Japanese ruleset.
-
-The irony of it all is that this kind of complexity arises BECAUSE the rules are so simple, allowing difficult edge cases where small subleties make all the difference.
diff --git a/content/hardware.md b/content/hardware.md
@@ -10,6 +10,6 @@ Hardware:
- OS: [Manjaro](https://manjaro.org/)
+ IBM Thinkpad T60
+ OS: [Parabola](https://www.parabola.nu/)
-+ [Librebooted](https://libreboot.org)! this is the only machine I own that rms would approve of.
++ [Librebooted](/thinkyboi.jpg)! this is the only machine I own that rms would approve of.
- Lenovo Thinkpad W540
- OS: [Arch](https://archlinux.org/), though I plan on replacing it with [OpenBSD](https://www.openbsd.org/) at some point.
diff --git a/content/library.md b/content/library.md
@@ -4,5 +4,4 @@ date: 2022-08-07T11:48:24+01:00
draft: false
---
-Fiction
-Non-Fiction
+Coming soon.
diff --git a/content/pgp.md b/content/pgp.md
@@ -1,4 +1,5 @@
---
+title: "Michael Percival's PGP Key"
date: 2022-08-07T00:15:31+01:00
draft: false
---
diff --git a/content/posts/my-first-post.md b/content/posts/my-first-post.md
@@ -1,17 +0,0 @@
-+++
-title = "Site maintenance"
-date = "2022-05-19T19:07:16+01:00"
-author = "Percy"
-authorTwitter = "" #do not include @
-cover = ""
-tags = ["", ""]
-keywords = ["", ""]
-description = ""
-showFullContent = false
-readingTime = false
-hideComments = false
-+++
-
-BLEP
-
-BLEP BLEP
diff --git a/content/thoughts/bent-four-in-the-corner-for-dummies.md b/content/thoughts/bent-four-in-the-corner-for-dummies.md
@@ -0,0 +1,100 @@
+---
+title: "Bent Four in the Corner for Dummies"
+date: 2022-08-12T10:30:59+01:00
+draft: true
+---
+
+Go is a game of perfect information very much like chess; to a beginner though, unlike chess, the rules can seem nebulous.
+
+When I first started learning Go, it wasn't clear to me in many common cases how territories could be defined.
+- If I have a line down the center of the board, which side is the inside of my territory and which side is the outside?
+- If there's no way to define this then surely there's no way to count a score of what's 'inside' vs 'outside' a group right?
+- Why does everyone say a group need two eyes to be alive? There is nothing in the ruleset saying that a group needs two eyes to live.
+- If I have some territory with two eyes and my opponent still plays inside it, what the fuck is happening? wait, my group with two eyes managed to die???
+
+As it turns out the rules are in fact very well defined; the consequences of these rules however are not trivial, and therefore can be a lot harder to get an intuition for compared to chess. For getting a basic feel of the rules I would recommend trying a few life and death puzzles (tsumego).
+
+The outcome of each puzzle is one of exactly four possibilities:
+life, death, Seki, Ko.
+
+Intuition for life and death comes quite naturally if you've played chess before, as it's the same binary severity as being checkmated. Can you checkmate your opponent in this position? Can you defend against checkmate in this position? Very easy to understand. Seki is somewhat analogous to stalemate, and can occur when two weak groups are attacking each other at the same time. If neither group has a significant advantage in the fight, then it's possible to reach a situation where if either player tries to kill the other, that player would end up killing themselves first by shorting their own liberty count. As such, the best option for both players is to live peacefully in 'mutual life' (Seki), which, while doesn't net you any points in some rulesets, is better than dying.
+
+Ko, however, is a fascinating result; however, when first learning the game the nuance of Ko was lost on me. It was hard to get an intuitive grasp of 'Ko' compared to the other three results as it doesn't have an analog in chess, and I remember when first learning the game thinking "yes I can sort of see that the shape of this result is a Ko, but what the fuck is a Ko?". The light-bulb moment came during live teaching game, where the implications of an evolving Ko fight became apparent to me. You mean this fight can affect every single other fight happening on the board? mind blown! a Queen in the middle of a chess board certainly has a lot of influence, but there will still be pockets of the board where her presence is not felt.
+
+[OGS](https://online-go.com/puzzles) has some decent puzzle collections, and I'd recommend trying *Cho Chikun's Encyclopedia of Life and Death - Elementary* if you are a beginner. Early on into a lot of puzzle lists, a weird class of so called '[bent four in the corner](https://senseis.xmp.net/?BentFourInTheCorner)' problems start to appear that I'd like to talk about, see [this](https://online-go.com/puzzle/102) puzzle for example.
+
+I initially found the whole 'bent four' concept to be utterly confounding, because it certainly looks like a Seki.
+
+Here is how OGS describes it:
+
+- This solution is a special case called “Bent Four in the Corner”. While it looks like Seki (dual life) to a beginner, Black is in fact dead. But how does it work?
+
+- If Black plays either D1 or A2, then White can capture him easily with the next move. Black can not approach White!
+
+- However, if White waits until the very end of the game and no more Ko threats are on the board, he could finally play A2 as an approach move to start a “safe” Ko fight. Play A2 now to see the variation.
+
+Ok, so it's a sort of Seki that can actually be killed at the end of the game. Why is it in so many puzzle lists?
+
+that is even more complex than Ko, and unlike Ko didn't seem to have very much significance. There is a lot of complexity to unpack with the bent four, and it *does* have some interesting significance, however personally I found it unhelpful to have this puzzle introduced to me so early on while learning; if I was teaching go to someone I would wait WAY longer before showing them bent four in the corner problems.
+
+Complexity layer 1:
+So here's the scoop. This is Seki right? if Black plays either X or Y, they are reducing their own liberties from two to one, and next turn White will play whichever move Black didn't play reducing Black's liberties from one to zero thus capturing the group. Ok, so Black doesn't have a move, it's Seki right?
+
+Complexity layer 2:
+Well, no. What about White's moves?
+If White plays Y, then Black plays at X and captures. This makes a straight 4 in the corner, and this is a shape which White cannot stop from making two eyes.
+However if White plays at X, Black plays at Y making a bent four in the corner. Can you see what's about to happen? Lets continue:
+
+White plays at Z. Now Black has only one move which can potentially still make two eyes at A. If White were to play away, Black could capture the stone at Z and be alive. However, White isn't a dumbass and instead takes the stone at A. Next opportunity White gets, White will play at A reducing the shape to a bent three in the corner, which as you can see is pretty trivially a dead shape.
+
+But it is Black's turn. and do you notice anything about the shape? it's a Ko! White has started a Ko fight, and therefore if Black can find enough threats elsewhere on the board he has the potential to make life!... right?
+
+Complexity layer 3:
+Well, no. Think about the initial position of the puzzle; remember that Black has no way to initiate this Ko fight, only White does. So theoretically, White can keep the pseudo Seki on the board until the very end of the game, neutralize any remaining Ko threats, and then start the sequence above. When Black tries to find a Ko threat, he will find that no move on the board forces White to respond, and therefore White will simply ignore it and play at A, thus finally killing the group.
+
+So, finally, here is the conundrum. What is the result of the puzzle? alive, dead, Seki or Ko?
+we can rule out life for Black pretty easily, so this leaves death, Seki and Ko.
+
+If White so wishes, she can leave the Seki on the board and that's that. However, at any point she has the option to force a Ko fight, including waiting until the end of the game where she can 100% guarantee that Black will lose the Ko fight. So is it dead?
+
+Complexity layer 4:
+The weird answer is, it depends on the ruleset! The strangest case is the Japanese ruleset, which in the UK is also the most common (although the AGA ruleset, which I believe to be superior, seems to have gained traction)
+
+In the Japanese ruleset, the bent four in the corner shape is declared to be unconditionally dead; there is literally a special case in the ruleset for this shape. You don't even have to initiate the Ko! despite it technically being a Seki, Black is declared to be dead if there is a bent four on the board.
+
+Wait, how is that fair? it's a Seki on the board, so surely at the very least you need to reduce it to a dead shape before it can be declared dead, right?
+Well, no. Again, it's a special case baked directly into the rules, so it is dead. So why does a rule for this case exist?
+
+Complexity layer 5:
+Imagine the following scenario when there is no bent four in the corner rule:
+
+We are (almost) at the end of the game and there is a bent four on the board. White needs to kill the bent four to win the game. In order for White to kill the bent four, she has to reduce Black's group to a dead shape. But as we have highlighted, this involves winning a Ko fight. Therefore, she needs to preemptively neutralize any remaining Ko threats before initiating the sequence, otherwise there's a chance that she might accidently let Black reach unconditional life which could be the difference between winning and losing. Eventually, White manages to do all this and capture the group successfully. She won the game right?
+
+Complexity layer 6:
+Well... It depends. How much is capturing the bent four group worth? How close was the score before the above scenario started? How many Ko threats needed to be neutralized?
+
+Lets say the group is worth 15 points, White is down by 0.5 points, and she had to preemptively respond to 15 Ko threats before starting the Ko. In this case, the 15 points of territory gained is offset by the 15 extra moves she needed to make, each of which is worth -1 points (It's possible for this not to be the case, e.g. the preemptive move was dame, but suppose all were worth -1). She still loses by a half point, even though objectively there's a group on the board that she can kill that would win the game, but the amount a stones she needs to invest makes it not worth it.
+
+In the Chinese ruleset, this problem does not exist. each extra move played in your own territory is worth 0 points instead of -1, as your stones + territory count towards your score, where as in the Japanese ruleset territory + prisoners are considered. This means that in the Chinese ruleset playing preemptive Ko threats doesn't reduce your score and therefore you are free to clean up the bent four, winning by 14.5 points.
+
+The Japanese saw this flaw in their ruleset especially when compared to the original Chinese rules. rather than throw out their ruleset entirely, they introduced a rule to handle this so that this very odd circumstance wouldn't force outcome of the match to diverge radically between rulesets.
+
+Ok, so under some rulesets the rules of Go are a bit less elegant, but it solves the problem right?
+
+Complexity layer 7:
+Well... no.
+While they are much, much rarer than the bent four, there are other shapes that share this 'bent fourness' quirk of being technically dead at the end of the game, but having to go through one or more Ko fights before eventually being reduced to death. While this scenario is more complex, it could again feasibly be the difference between winning and losing, and again being another wedge between the Chinese and Japanese rulesets, especially since only the special case for the bent four exists! No other shapes, despite their similar properties are covered.
+
+So... yeah. Unfortunate as it is to say, but the Japanese ruleset is inelegant. The Chinese ruleset is more elegant in some ways, but it too has it's own problems.
+
+Is there a middle ground?
+Well... yes! It's the AGA ruleset, in my opinion the best ruleset, and they fix this entire problem with a solution that is so elegant (as Go is supposed to be) that I'm genuinely surprised that the Americans figured it out before anybody in Asia.
+
+The rule is simple: passing your turn is worth -1 points. That's it, that's the entire rule. No bent four in the corner special case. See if you can figure out how that fixes the problem before we continue.
+
+Here's how it works: imagine the bent four scenario again. White needs to capture a 15 point bent four territory, is behind by 0.5 points, and needs to fix their shape preemptively against 15 Ko threats.
+The situation is exactly the same: Every time White neutralizes a Ko threat, it's -1 point to her. However the small detail is that when Black passes the turn, it's also -1 point for him. So no net loss has occured. If there are any dame (zero point moves) then both players need to fill those in first before White starts neutralizing threats. So if Black passes it's -1, and no matter else where Black plays it's also -1 points. Therefore, at the end of the sequence after the bent four has been captured, White has +15 for the territory, -15 for the Ko threat neutralizations, however now Black also has -15 for passing 15 turns (or playing 15 unnecessary moves). Therefore, White wins by 14.5. Genius!
+
+There are more subtleties to this ruleset, but basically it combines the best of both the Japanese and Chinese rulesets while still managing to be more elegant. Notice that this rule doesn't just fix the bent four in the corner, but any other variations of 'bent fourness' that might not technically be covered by the Japanese ruleset.
+
+The irony of it all is that this kind of complexity arises BECAUSE the rules are so simple, allowing difficult edge cases where small subleties make all the difference.
diff --git a/content/penrose-tilings-part-1.md b/content/thoughts/penrose-tilings-part-1.md
diff --git a/layouts/partials/navigation.html b/layouts/partials/navigation.html
@@ -6,7 +6,7 @@
</div>
<div class="nav-element">
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+ <a href="/thoughts">thoughts</a> |
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