What is squeeze/finesse/endplay in bridge? Why does direction make a difference and how do you best exploit it?
Properties of bridge play (ignoring trumps):
- Each trick, each player places a card. The players play in clockwise order. The highest card of the leader's suit wins the trick.
- Everyone must play the same suit as the first player (leader) unless they have run out of that suit, in which case they can play any card.
- Upon winning a trick you have to give back by playing from your hand again (leading). Within a suit, this is often self-damaging, which balances the advantage that you still have of choosing which suit to play. This adds stability by preventing a positive feedback loop. In Go, locality helps prevent positive feedback but it can still occur when big weak groups are next to each other.
- Whoever plays earlier in a trick has a disadvantage (in Go playing first in a position always gives you a non-negative advantage)

However, you work with a partner ('s hands), so if you want your hand to play later, you have some control by getting your partner to lead (and vice versa). This in turn means having the power to access each others hands is useful, with some kind of high cards in each. (Weirdly, this property is called "having enough bridge".) Having enough bridge is also critical if your partner has a long suit and is the only player that can access that suit.

Finesse: You lose something compared to expected if your high card is covered by opponent's. You finesse your opponents if you lead, partner has say AQ (with a gap of K) and the K is on your left. You don't know where the K is, but you can take a 50-50 bet that it is on the left and play the Q unless left plays K, in which case you win with A. We say the K is covered and can never win unless the hand with AQ plays that suit first. It is called a finesse because you have to take a bet, more advanced than beginners who just play winning aces.

Squeeze: One of your opponents holds all the key cards in two suits that you might be able to establish. However, they need more cards that they have to defend both suits. You watch what they discard and play that suit accordingly, in order to win more from that suit.

We can say that you establish a suit if you can win all the long cards in that suit. However, this term can be generalised to any example where special play can gain an extra trick or two from a suit. For example A always wins 1, but AJ.. might win two if you can push out the K and Q. This might occur with two finesses or if the opponent has one of (KQ) singleton (possibly from a discard/squeeze) and you can finesse the other opponent.

Endplay: You play out all suits until your opponent only has zero or one card in a suit where some critical interleaving occurs (e.g. they have KJ, you have AQ)(both have strength in the suit). They must play that suit first, which gains you at least one trick (and maybe more if it helps you establish).

Advanced: Merging all these concepts in tense situations where there are several different paths with different risks, and managing the bridge and which hand is expected to have to play first later. More advanced is maximising your own information and minising your opponent's.

Edit:19/01. Strange feels around sarcasm, mania and random rapidly fading illnesses day by day over the last two months. Thoughts about what "God" might be, and parallel patterns in all aspects of life from the Amazon to neural networks etc., from Wijk an Zee to my rating points and much more I'd rather not share (werewolves, Blackadder, etc.).
Naturally I rationally blame local personal/work life etc., but I can't help but wonder if it is related to the Hunga-Tonga eruption somehow. This is especially weird given I felt better after the major eruption, though I haven't managed to get much work done until today.

Edit: 29/01.
1. Why is it easier to push a door than to pull it open?

2. Why is it easier to pull on a rope than to push it?

My answers

1. Because your body and the door are solid objects with internal defences to keep their structure. These repel each other upon contact. Hence the pushing interaction does more work than pulling. In order to pull a door open, each component needs to attract the next, such as your hand hooking over the door handle which is hooked into the wooden door. However, this can damage your hand (indentations), and the relation between the handle and the door.

The regularity of the internal bonds means that messages (push/pull) from one end are passed on quickly with its own resonating sounds. There are many regular modes of vibration/sound. It is hard, so it tends to reflect energy rather than store it, and when it does store it, it is normally only because the environment (air) is vibrating with the same energy.

2. A rope has interweaving threads which pull on each other by friction and support each other. The flexibility of the rope means you can knot it around your hands when you pull. It allows both a lock shape and a line shape. However, it isn't a strong solid shape overall since pushing it merely causes it to compress inwards rather than affecting the other end. It has one critical mode - taut, and chaotic other modes (slack). There are ways to hide heat/messages inside the rope.

Advanced:
In a sense, a sound wave is orthogonal to the bonds in a solid block (especially if crystal or metal, though it may diffract due to speed changes etc.) so it passes straight through. In contrast, a push is parallel to the bonds, so the whole block is pushed.

Similarly, a pull on a taut rope pulls the whole rope while a transverse wave is transmitted. In a taut rope, there is little room for large transverse effects and all threads are independently pulled taut. But a push encourages splaying, since each thread has strong attraction holding it together, much more than its attraction to neighbouring threads (unlike a solid piece of wood/metal where attraction is close to even in all directions) so much of the push pressure/energy goes into sideways collapse of the rope. This is quite random and very much depends on the subtle unseen internal/external state of the rope at the time of collapse. It can be difficult to extract the information from the rope after it collapses.

A neural network is much like a mould that tries to fit into a multi-dimensional solid block. It predicts the output of the rope.

A rope is so flexible it can be used to hook around itself. By tying a knot, it forms (at least) two hooks by itself. Then even if you pull on the ends, the knot only gets tighter. If you push on the ends, it splays. The knot can be moved sideways and keeps the same topology.

A neural network is like the opposite of a knot. At the slightest force, it unravels and changes shape, like an amorphous multidimensional blob. Instead, the environment acts more like a knot. Or a host.

Just fate? Veritas?

I suppose the go game is just a sort of knot, a graph with cycles, bouncy castle atoms. a1 (is the beginning) (graph theory)(adam).

Think of go as 361 dimensions that can be black, white or empty. (That's very much in the box, but do you dare to leave the box even if there is a scar inside, or a rift has made a crossing impossible?)

[Hide][Hide][Hide]Today I heard.
[Hide]______[Hide]Sometimes I wonder if I'm inside a whale[Hide]Heed[Hide]A ray of hope.

Iron-56 is most stable. But it bonds with oxygen (rust) naturally on Earth. Circles. There are many cycles on Earth.

Is physics a form of light itself?

Today, the pressure of pipes can be measured by letting flows out sideways (which releases pressure) and putting a filter on it, but it normally can't be easily measured by filters perpendicular to the flow because they change the flow rate. Instead, only the voltage difference can be measured.
(alignment)
(deny all means that the water level can't rise above a fixed level, like a tuning fork keeps pitch, or a force field can keep a quota.)

If fingers are like chopped teeth, are canines a form of recognition between mammals/reptiles.

___
(Blue/jupiter/out)

220329

Entropy: Most of the time, the more you measure something, the more you try to measure it, the more it disappears. What remains can be quite revealing, even if you call it a heat death. "Hopefully not pointless, even if beyond your control."

Are all science equations local balance equations? Philosophy suggests the flaws in our thinking, if that is where you want to push yourself?

220417

Some slightly strange patterns today, black birds swooping, one plane showing a dark line in the clouds before it, another plane only having the normal white streak that disperses behind it. The full moon yesterday was encased in clouds that looked like <o>. Apparently it was a strong pink moon.

I also keep getting childhood dream memories returning, and later I find that the news tells me something that is true in the world very similar to the dream but not quite the same. For example, the tree growing project in China at the edge of the desert (when I thought of the Sahara). Presumably these were common dreams like a tsunami, or were they personalised like Santa, though how could I know? (though I don't recall ever mentioning such dreams to other people, and for many years now, I don't notice having any dreams).

20220422
The stories I feel

Human bones:
leg: thigh and calf fused as one to support meeting the hard ground.

feet: they face forward, pad flexing allows an extra push. More efficient to run forwards than backwards.

heel: this is reinforced to allow the connection, but even if slightly pierced, the weakness can spread even as healing encourages stress to bypass the fracture.

arm: two bones together means weaker for walking on, but they allow a new fixed dimension of rotation without cartilage that might slip under stress. This allows the body to make connections with the environment, channelling a form of stress relief and allowing mutual control/influence by the body/environment. It only rotates the thumb towards the face, not the other way around, allowing cupping the hands to the mouth (good for drinking).

hands: allow grip (forest), digging, holding (spears to extend reach), sacrifice (frostbite), identity (fingerprints), and probably much more language interface that no single person is aware of (shadows?). They are renowned for controlled tool use, guiding and directing all we know to do as we will (generally surviving together, food). They require stretching, practice, protection, healing, rest.

lead: held in bones, can replace calcium, increases confusion, memory loss, but allows learning new things. Much heavier and dissipates gradually downwards until it decays or escapes.

20220515

I would protest more at strange messages in Go games, especially at some blatant graffiti on PETC results. I can't accuse individuals of match fixing if it is occurring over such a long time and space and I have no idea where it is coming from. I'd protest more if the UK's position at the bottom of league 2 wasn't also partially my responsibility. My main defence for not playing is that I have been unusually forgetful (and sometimes busy) during match times. My main defence for the result fixers is that Go isn't all about winning and I hardly understand what is going on.

2022/06/08
Probably not go related. But yesterday my computer clock didn't automatically sync, so it was off by 7 hours. Then today I slept for perhaps 16 hours (almost consecutively) despite alarms. I'm unsure whether I am ill though I doubt it. I think something else entirely is happening.

Was it a year reference 536? to 12--? Or only minutes? I'm scared. Or is it only a history lesson?

2022062022

How to measure the value of each move. Its still on my mind? It gets difficult when there are weak groups (and hence several potential attacks and directions). When one direction is clearly biggest, consider if it is worth taking in gote, or reducing in sente. When multiple are, play a bit more flexibly elsewhere in order not to damage your weak groups. That is, attacks that you opponent must defend against will also hurt your groups neighbouring it (unless they can connect and coordinate with your attack), so this loss must be taken into account. It remains a good idea to imagine a fuzzy set of B/W stones around potential attack points and play accordingly. Many things are semi-sente (i.e. locally sente if not for the loss on the other side).

For example, even after the 3-4 gets approached, it still has some eyespace in the corner and expects to be able to counterattack. Even after the low approach, you still expect a wall of space around. This is the reason why the AI likes to play the 4-4 attach, since the 3-4 is likely forced to defend the 3-4 stone itself with 3-3 for eyespace and territory, and so the 4-4 reduces the local attack power of the 3-4, with some local eyespace and remaining threats on the 3-4 too, so the 3-4 is likely to get local territory, strength, but in gote.

20220627

intuition: every move is like a bubble. when choosing direction bear in mind that tighter moves leave stronger local follow ups, but every move makes larger moves around for the opponent to attack, especially in a fight where the opponent might sacrifice a weak group. Boundary attack moves can be attacked themselves, but locally, they build a growing bubble where the opponent needs more moves to surround it, and it helps cut the opponent's counter attacks.

a lesson: when building at the boundary of groups, often there is only one key point. However when reducing, consider preparing first. If you are able to invade, then it is probably going to be valuable to settle there, and there is probably only one area you are trying to reduce, so it is worth it with big follow ups, and all connected until the opponent cuts. Just avoid facing a double attack.

20220628

A rubik's cube is centres then edges, then corners, then it depends. A Go board is corners then edges then centre.

This is because the components of a rubik's cube are based on a finite set of components that combine in discrete ways. Permutations are the vertices of a large graph which has fairly small diameter. The goal is a faster time. Edges are closer to centre, and better for fixing a reference point for your eye. Whereas moving an edge into position where two corners are already there is harder to get your head around (though perhaps it is symmetric). It is easier to memorise how to put an edge into position (barely any thought required), and then build on that: how to put a corner in without changing the edge.

However, values in a Go position can be chopped up into fractions of 1/2 1/4 etc, making it much more complex. However the values get attracted to the corner for almost the inverse reason that it is easier to fix the corners since they are closer to the "outside" of the board (closer to the human solving it).

20220629
Can hardly be a happy day to hear of the death of a younger student. At least I'm alive.

Back to contemplating the meaning of life?

A few tears, though I'm not close to anyone, I did invest more time on him than most. Anger, upset, tired, hatred, lost, why, determined? Today, I found a dead spider in my room, and saw a green eyed cat and climbing squirrel which I've never seen before.

20220701

again, a failed time sync, last at 03:57. I can't see anything special about that year this time.

20220707

Guesses. Wet sand holds form as though the water and sand chemically bonds for a time as a film that is stronger than its own gravity. Lower pressure can liquify to quicksand. Footprints remain like sandcastles and memories. Shears leave most of the chemical bonds so it remains not the hardest to crack. But perhaps footprints are a sign that it likes to bond with the foot (the body part closest to wet sand?)

Water is so liquid (not as self bonding as a solid) and prevalent and simple that it has familiar interactions with almost anything.

Dry sand acts like many individual particles, each following gravity since they dont bond with each other sufficiently beyond space occupation. They can absorb impact smoothly since there are less hidden bonds, so mathematical understanding may be easier. With all the gaps for air, it isn't so dense, though in order to have remained rather than windswept, they likely remain denser than what left, or form local bonds. Sandbags are good moveable defenses.

Sand isn't a liquid though as dunes tend to form. It is unclear to me why this is lower energy state than completely flat, but perhaps sand responds to manipulation by the environment. Perhaps this question is too similar to why does life exist.

The slowness to cave in compared to water allows caves. Is this sand's so called empathy.

It is very prevalent in 3d form, too weakly bonded to find much in 2d (requiring heat to form glass for example and even then brittle) unlike many of our plastic and metal tools. Metal is strong enough that even 1d swords hold lasting form, but that also means it requires a lot of energy to form. Though arguably sand particles are even stronger like 0d, resistant to wind, heat, pressure, like a miniature planet. But in order to have survived they must have gone through a lot of pressure, selection and erosion (often rounding them).

20220711

Read chem today. Recalled Pauling's electronegativity point, and the relativistic speeds of electrons in heavy atoms, and plasma shielding, with curious anomaly of Cr,Cu in valence electrons.

Sun and wind trying to get man to remove their coat reminds me of AC/DC. Both the Sun is much more powerful, and also the medium of air isn't great for focused blowing. However, heat is unavoidable and seeps into almost all things. It doesn't even hold that much energy since vibrations are local, but being everywhere has its own power.

It reminds me that a solid is low entropy state (inclined to melt), since although bonds make it low energy, they also provide a lot of constraints to motion. This is why you can push a solid but not so easily push a liquid (the push spreads into waves and too much leads to chaotic eddies). At the same time, Pauling's point that A and B almost always have stronger bonds than A by itself and B by itself seems to both be related to entropy and also that different shapes often tile more compactly (but not necessarily). Or at least with more possibilities that can better fit with changing environments.

The case of wet sand bonding well (probably denser than dry sand with air gaps), and yet caving into the shape of a footprint more readily than dry sand probably represents this point. The flexibility of liquid makes it less likely to kill us directly except in large quantities? But it attracts competition.

The natural question arose as to what is the underlying difference between extreme covalent and extreme ionic bonds?

In this case, compare bond between A and empty space. Intuitively, the balance seems to mean that in a bond, we expect electrons to shift until there is balance between their attraction to A, B (3rd law), and this drop in energy is accounted for by (assuming linear elastic force) the square of the distance changed. This can turn a covalent bond into an ionic bond if the electron is mostly ripped off.

I feel this has non-zero relevance to influence functions.

20220721

just watched Demis Hassabis, David Silver's discussions with Lex Fridman. On the topic of weaknesses of neural networks, which seem very strong, I wonder if the fact they are static blobs that can't combine or dissipate is a limitation to reasoning. But it depends on the relation between the structures you can make and the structures in the environment. (actions+sense act like similar dimensions, perhaps with opposite sign), but reward functions are one dimensional. This connects with the one dimension of time/energy. Whereas optimising over space seems a bit different. I suppose it optimises a functional rather than a function.

I read the definition of a Turing machine. Why is it so powerful in our world? Compressing a series of changes into a (1d) list of instructions in order makes me think of the bijection between R and R^2. Instructions may not commute so perhaps this adds more possibility than is necessary. The "head" needs to be able to read/write arbitrary functions into the cells.

Obvious fundamentals to note are cells must be distinguishable, not mix nor mutate except by the control of the head.

The question asked was what are the limitations of such a machine in our world?

20220731

just did a bridge calculation. If you can draw m rounds of trumps with n remaining and you need to catch a key card, the chance of catching it tends towards the err function (assuming n is small enough compared to the total number of cards) (in reality if trumps are badly distributed, so are other suits, so even distributions are slightly more likely which also means catching a key card is more likely). Hence if n=2m, then this gives 50% (or slightly higher). This is better than finessing, though consider other information about points and distribution. Otherwise if n>2m finessing is likely better.

why? Well WLOG left holds the key card. There are n-1 cards remaining. If n=2m. Your only chance is if left has at most m cards. This allows (0,n-1),...,(n-1,n) which is a symmetric half of the combinatorials.

20220801

If I can try to make the algorithm of "weak point theory" explicit before I forget. It should be that every empty space contributes up to 2 points swing between B control and W control. How does this connect to the values of moves? The swing of a chain will be the sum of the number of intersections its stones occupy. One move that captures or saves it will have this swing. We see that moves get very big if they are one move away from switching control, especially if the influence connects to a large area. The way to think about this is that every intersection needs to connect to a living group (and hence normally two eyes of its own or shared seki dame) in order to live and when one move kills/saves a large group, all its stones depend on that group, so that one move has influence over all of them. However, the potential must be counted in general. For example, one move in an empty corner already has a swing of around 28pts because one move almost makes the whole corner all territory.

On the sides, control tends to be closer to getting one eye etc. However, value only matters if two eyes are possible (note that one way to get an eye is to capture the opponent's surrounding stones) not just one. For example, cutting a two eye group into two groups with one eye has positive value. Each group then only lives if it can extend to another eye on the other side of it (which could be quite a wide area), so large move value accumulates at the easiest places for it to make eyespace. Note this is treated as sente-gote in endgame theory, and it refers to the direction of value flow. In particular, the value of such moves must also take into account the large values of the opponent they induce that continue to threaten the eyespace, as well as the potential if any such moves will have other than having local eyespace. This could be high from open space access, or high from being near other weak points, or high from simply being the last move to living, switching from territory for the attacker to neutral points.

Any error reducing algorithm should first focus on the life and death of the largest groups, checking how many moves they may need to live as well as the opponent's gains from threatening (checking if they are sente or not). If such groups may be disconnected, then such value must be considered by splitting as mentioned above. The easiest to count is "gan mu" "dry points" which doesn't have any additional eyespace value since they are simply worth

lambda * points
i.e. aliveness of group * size of group.

But groups that also change the eyespace of the surrounding area that supports it (rather than just size/points) are more valuable to fight over. Note that disconnection points themselves can often turn into eyespace during sabaki. A difficult thing to calculate is the existence of aji that the defender can eliminate with one move and isn't very valuable locally but where the opponent has many different possible forcing moves which help double attacks. Go is 2d not 1d.

In general, if all attacks are gote (even the killing move) and the defender can always live with one move, then standard endgame theory for corridors says the contribution factor to the size of each move is 2^(-n) for the attack that is n moves away from killing. i.e. 2^(-n) times the value of the group. Of course this should be the raw value. The potential is gradually reduced by attacks, and must be taken into account too. Of course, the largest move is expected to be played first, but this means moves largest in value on the other side of the group. Though sometimes, due to needing to take into account follow ups too, if two nearby moves work together as an attack, then such may be preferred to only one big attack move. Each attacking move has some influence extending through the weak group to all other follow ups of it.

As such weak points are the most valuable, error is most quickly reduced by accurate evaluation of them. So precision requires balancing the size of the attacking moves and their expected order.

Note that well-connected groups are required to spread influence. But weak groups spread most of all.

Influence functions would be great to take an average of such values. However, it isn't so easy to take semeai into account here. If a group that is j moves away from dead is adjacent to one that is k moves from death, then it wins if j>k. When j,k are large, this can be subtle, as reading is required far in advance. And there are many sente moves, so we cannot say that attacks are 2^(-j) of the value of the group. Because they may in fact change the status of the semeai and concern both weak groups. In particular, we must say that when j=k, the next move is actually at n=0, zero moves from a move that changes the status. Some tsumego experience is required. And unusual situations may be difficult to evaluate. However, perhaps it is possible to make a compilation of the most common semeai. See work by Richard Hunter, Robert Jasiek.

Liberties are basically the only way extra stones in go can be negative. Extra stones can bring a weak group even closer to death by reducing its space. This is particularly bad on the first line, especially when both are cutting stones since aji can lead to the opponent capturing your attack too easily. See eternal life.

What can a computer easily calculate?
1/2 for miai, 1/3 for direct ko.
count liberties of existing chains, count incremental liberties of potential stones.

importance of groups? number of eyes and their potential positions (every empty space is potential unless adjacent to solid opponent group).

20220802

definitions in go.

calm play: big and connected territory (e.g. 2 space extensions). Not trying for a tesuji to double attack to get deeper.
lighter: more space, less connected, willing to exchange, not enough for two eyes locally or painful
punish mistake: all forms: if slow, then ignore, if overreach then cut, if loose in a fight then consider saving group with more space to counterattack or living better or capturing cutting stones, or jimin probes.

conservative play: focusing on own eyespace at the cost of territory
aggressive play: focusing on territory at cost of own eyespace
play when behind: stretching at the boundary of areas despite leaving weak points, willing to fight over them.

stability vs fighting.
one's own merit points vs opp's burden

in order to invade or reduce the opponent's moyo, don't lean on the boundary to make life but rather leave them as isolated as possible so you still have lots of different aji which helps invasion, reduction (even if not biggest yet) even if opp adds a move to defend.

principles: more stones support fighting
bad shape plays too close to opp strength so they can attack.
inside for outside exchanges are always better for the outside as they gain control of more space.
qiu diao zi (ask for a flow)
take what you can get when you can't get much (such as reducing moyos).
Thickness is worthless if it attacks nothing.

during a fight, if you tenuki, all of a sudden the fight becomes very one sided (for control of that area).

They said Lee Changho gives you what you want but you still lose. What does that mean? When someone plays a move, perhaps they plan to secure the area around it. Perhaps they cut to kill one side or the other. Lee might allow that but reduce it making it gote.

20220806

If 14 points per rank in go and 361 points in total, if linear, then there is a total of 361/14~26 ranks. If 3 are top pro to AI, 9 pro, 7 ama dan, that leaves 26-19=7 kyu ranks. This is quite an underestimate of the 20-50 kyu ranks normally considered. This means that a difference of more ranks wins by less than the sum of the winning margin between each adjacent rank. This could be called a sort of convexity of the game. It implies that a conservative strategy exists which will perform against even the strongest opponents. For the endgame, miai counting holds part of this point.

ELO ratings. Consider the problem of the king racing 3 better horses than his advisor. If the advisor's best horse can beat the king's second, and so on, they have a better winning chance by messing with the matchups. Suppose each win counts for a point and each loss counts for nothing. We can get a heuristic for this problem from Lagrange multipliers. Suppose one team has A ELO rating points to allocate between players and the other has B. Given the first team's allocation, what is the optimal allocation for the second team? Assume ELO difference is translation symmetric with winning percentage (which it normally is unless tuned).

Then WLOG A=0 and the first team's ELO's are all 0. We find that if B>A, there is only one stationary point (clearly optimal as sigmoid is concave above 0), namely evenly distributing B-A among all the players. Basically marginal rating counts for less change in winning percentage the bigger the difference already is. Practically this implies that the stronger team wants their strongest player to play against the opponent's strongest and so on to minimise the chance of an upset (consider why Akira wanted to play Hikaru so much if he didn't expect to win).

If B<A, there are two solutions but the stationary points are now minima not maxima of score. Basically, all but one games can be won by sacrificing that one game. In practice, when the player's ELO's are fixed, and you can't shift points, then as sigmoid is convex below zero, then you should focus on having the advantage in as many games as possible. This tends to mean that you play a rotation. If your strongest player has the advantage against their nth best, your 2nd against their n+1th, etc, then you play them accordingly and sacrifice the rest. But even the sacrifice has technique (though less important) as your weakest should always play against their strongest and so on in order.

there are different sorts of flexibility and many translation. tan2xing4 refers to a weak group which is hard for the opponent to capture with one move (e.g. there is ko aji or sacrifice aji and local life aji). Note being heavy is a major component of flexibility.

qui2diao4zi
asking for flow. pushing opp weak group into where your weakness so that you can defend your weakness with a move that also threatens the opp weak group. Normally, your weak point is valuable, and perhaps it won't be properly defended other than with a particular move after which it is mostly defended. If you push opp into your weakness, then you may get several moves in a row forcing once close to your weak point.

kg really does seem surprisingly flawed at calculation, not focusing the effort there and making too many assumptions about averaging or intuition. It seems that it needs some hard armour to store a calculation module for semeai and life and death. However, its endgame seems near perfect, perhaps because it is more easily learnable and always important despite being boring to compute?

what are the concepts required for evaluation of empty space? balance between territory value of eyespace and the attacks on it. If a corridor required then a large pot at the end can inflate the value, but it dissipates according to security of pot one side or the other (according to number of moves away from l&d boundary).

If you put potential territory into a fixed definite place, it is easier for opp to focus their moves and bias towards it. Whoever chooses first loses from that choice. Though in Go, initiative is valuable in itself as some moves are simply bigger.

6
example 2. I'm unsure why RJ says playing the 4 is the only move. When moves are miai, they can be ignored. He means that playing in the environment to get the 3 (after the miai 4) is the only move, and that playing locally is a loss.
example 9. What is happening is that gain of follow up (due to parity) 13.5-2*0.25 (loss by T-T1 not playing largest gain) doesn't compensate for 2*X where X~T_F/2 (+/- T_F/4) where T_F is temp after 13.5. This is certainly unusual as T_F~F=13.5, but in this case, X=9-6+5-1=7. The tedomari of 9,5 is greater than 13.5.

9.2 p88
seems basic enough so far, mostly following decreasing move values and systematically considering the formula for the simplest (and hence very common) situations. The notation is well adapted to this.
Nb
if sente option moves to {S+2F|S} and F>(S+F-C) to be sente, and H=C+M_G, then we expect S<H-M_G for both options to be playable. Otherwise, the sente is likely to be better. Note the 2 C's are what we are trying to estimate and not actually the same. But this is really a case of why privilege delay can have benefits.

10.2 curious

10.5 mutual reduction. generally, the defender of a position merged from independent endgames has some sort of advantage over them being independent since they may be able to spend one move that fixes threats from two directions. In this case, something related is happening despite a corridor of endgame (only one entrance). The defender can count on playing the last move locally regardless of how many times the opponent pushes (unless they push all the way). Sometimes W can create a follow up that takes away B's defensive local tedomari too. The additional value can come from changing the parity of moves so W gets the last big move. The last move locally is big, and sometimes bigger if you can get the value of the penultimate move too.
The principle can be thus: If you have already lost the penultimate move, consider that the last move locally may not be as big as other endgames where you may get both.

11
some of these equations seem obvious to the point of being unnecessary once you get past the notation. if a sente move has been played, then the follow up can be treated as part of environment according to F?T.
table on p159 may be the first non-trivial (but still seems boring) result.

14.1
example 2
saving larger threats as they are even more forcing later is a point here. take what you can get now (as usual greedy algorithm is good in Go once gain is defined well enough).

15
problem 10. There is a true general statement something like if you can get more (all gote) in one move than two moves elsewhere (and followups are uninteresting), then the one move is always bigger. This is based on the local inequalities for count that the error is up to the largest move gain. Even estimating the error to the maximum for the move elsewhere (the maximum being the size of the gote follow up), if it remains smaller than the first move gain for the one move -G (G~1/2 being the gain of the next move locally), then the one move dominates. Once the inequality is correctly stated, such a bound is tight.

16.1
p245 typo ("reserve sente")

The author makes good points about tedomari, the relative importance of parts of theory. I like the theory as well as the thought that must have gone into creating positions for diagrams. They are certainly good exercises if you can't solve them quickly, and you should be able to find ways not in the book to slightly speed up solutions. For example, I recommend imagining fractional stones (control estimate) according to whether they are follow ups etc., in order to help estimation at a glance.

To some extent, I think the problem diagrams (i.e. every example, exercise) are more valuable than the theory which is repeating the same sort of thing in different levels of detail. But that is Go.
But I hope that such theories can be combined with life and death theory.

surprised to see so much care about the less mentioned topic of transversal.

thm55 p93

this seems to be the sort of statement that is trivial by domination, and yet the proof is so many cases. omg. unless I'm mistaken?

It is certainly an interesting result that inserting into an ideal environment with difference D can only affect the alternating sum by up to D. This follows from prop8, and is mentioned in prop54
However, the next insert probably could affect it by up to a total of 2D and so on until the general result of my prop 53. Basically the largest affects by D, the next largest independently affects by up to D and so on.

I didn't realise before reading thm55. Anyway, this means that F can be ignored up to an error of D. Otherwise the comparison is just one of simple gotes which is trivial.

thm56,58,omg again. see my paper (more like lecture note) on domination.

thm57 surely these might not be the only optimal. as in the degenerate case, it may be M, (V+1)D, VD, ...? But I agree that there exists an optimal sequence that is of the forms given.

thm62,63 these were sort of in endgame 4. Curious to make explicit the difference between t1, t, creator/preventor. Recall delta(T)+delta(T1)=T.

If delta(T1) is the smaller (normally, though we have no handle on the probability in this theory), there is a narrow window between when T1 becomes T where the creator (if they have the move) will want to play the sente before prevented.

thms 62 etc. These are the first results that I don't know by heart that I think may be worth memorising or being able to derive.

prop86 "obvious" by gain per move (efficiency).

8.5 getting to the topic I analysed. I made a bit of a mess in my paper compared to the nice notation here, but at least my thought progressed about laddertrees. ah in 8.7.

thm 130 similarly I like this result.

overall too many trivial "theorems" for my taste. Distasteful to have so much repetition of the same results (derivable from same principles) so perhaps too long, but still a good repository.

better perhaps (meta) would be to comment on when such principles apply (i.e. if follow ups are lower than temperature, the ideal environment absorbs them. RJ does mention this but then proceeds to prove special cases of this individually when the principle could be stated. e.g. thm 134.

10 section starts to get more interesting. unanswered question of how to compare two sentes. good partial order equations, but what about when ambiguous (does anyone know?)

more later. But I realise that the most efficient net starts with building the middle sections first (I mean if f:X->R and the net models f, then kinks with intermediate values of f should be built first), and leaving the most extreme kinks towards the end. a net that starts with extreme kinks will find it more difficult to build the middle kinks in later layers unless there is an earlier layer that can build that kink. It is like a factory, and bad communication and ordering can lead to blockages. This is because ReLU cutoff introduces kinks at the extreme points (ah perhaps that explains why leakyReLU can be better?)

Find large groups. For each, send probes around, perhaps simulate local ways to make eyes and their dependencies around. Goal is to check the local temperature and see if local moves are big enough. Play moves from high (temperature) to low, until local fighting cools down enough.

Efficiency improvement: Intuition/experience can be used to drastically cut down on computation by averaging (statistically or otherwise). Resources should be focused on large weak groups. Status information should be reused after a move or have a way to account for small changes.

When estimating potential, balance territory and development, focus on connected options. (e.g. if have cut centre off on one side, consider cutting on the other side too rather than focusing on territory (i.e. side eyespace). Trainees often unable to see the big picture and keep playing locally without regard to global importance.

If stones are lonely with space (like opening), then they main remain devoted to most valuable areas of eyespace/territory/development, so you as they commit, you can get stronger on other side, dominating the other direction, and hence allowing some eyespace/follow ups/moyo potential. The more stones opp has, such as 2 stones in a shimari, even if you get exchanges in sente, your local stones remain weak even if they support eyespace, so you normally just get what you can locally and don't try to develop as much there.

If less quickly alive (say approach to 3-4), then opp can lean on you even if you take their main territory. Beware that this may work well with a moyo, so delay playing there too if they threaten to expand. At the same time, consider fighting for such sides. Perhaps they have a number 1 valuable area (shimari on 3-4) but you may be too vulnerable to play immediately. Then consider reducing their number 2 area instead. Most of all, don't let them make number 2 too large because most likely, you best local move remains number 1, which they can lean on to build number 2. In part, you are less scared of them just spending a move to defend number 1 but more scared of them avoiding the need to add a move there.

Timing: If it takes opp 2 moves A,B to solidly connect at a vital point, but each damages your stones enough to be valuable, but they are weak enough that cutting through is powerful, but you are also too weak to cut right now, consider poking/probing such a weak point. If they play A/B directly, such may be miai for now so you cut through and they are too heavy. Perhaps they need to choose a different strategy. Basically if they spend one move, perhaps that is worth 1.5 as A,B in combo are valuable. But if you play first, perhaps they can't get either yet, and hence be forced to make more defensive shape. This can make such a point urgent. For example, a double cutting point in a 3-3 invasion (jump, extend variation).

This is related to probing a weak point before it disappears indirectly. It may give you a weak stone whose aji can't be activated yet, but if it doesn't work now, it is even less likely to work later.

aggression: this is taking opp's best chances for eyespace away and hope for mistakes elsewhere. e.g. start with solid shimaris and tight approach moves that work in a moyo (or 3-3 invasions if you can't build large enough). NOT invading everything and cutting everything.

intimidating: ko increases the swing but also the number of moves spent locally, good for a valuable area, but only if you can win it.

forcing moves: when defending, first check opp stones. Habit of playing forcing moves for profit but can be aji keshi other times. Forcing moves are often good when the opponent is stronger (if they exist) as they are they pure profit with valuable threat. As opp defense makes solid territory and secures potential.

severe: Is this when you don't defend your own weak points directly, but instead counter-surround from above and say that the opponent's group around will be attacked? It is when the opponent can't cut your weak point directly and needs to be clever about timing and sacrifice.

unfixable weak point: if retreating is in own territory for example, i.e. a group is too far behind secure enemy lines, then such a group may owe a move to secure it. This basically strengthens the enemies groups around.

when running out of good eye options, last remaining can be useful. For example, if the opponent has a moyo on several different sides of the board, then making a centre group can be useful for reducing the other moyo, even if it gives up territory.

if white should sacrifice centre for more strength elsewhere, and black should try to have a slight advantage everywhere, then?

Opening:

This is striking. 5-3 moves. Shimari, wedges, side extensions, all 3rd line. This can be called slow and steady development, wary of having to make eyes in the centre, wary of messing up an attack on the opponent.
They love to play on the middle point of opposing shimaris, considering it a vital point, rather than the possible no man's land today. Perhaps they think that reducing such from the centre isn't worth much.
They understand the double wing formation.
They strongly understand how to make one's own stones work efficiently together in formation, with perfect moves to kill off the opponent's potential invasions etc. They probably delved deeply into this theory, rightly viewing it as the most useful knowledge if study time was limited. But seem to get a bit more lost as to how to maximise efficiency when the opponent is near. e.g. n+1 spaces from an n stone wall.
They seem satisfied to just be alive, leaving 2 space extensions on both sides, not believing that the opponent's shimari + extension is more efficient for making territory than their lone weak stone's 2 space extension.
This seems related to how they play 5-3 moves. They judge that the 5-3 lives quite easily by leaning on the corner invasion, but perhaps don't consider that such a life isn't efficient as weak points remain in the centre. Again do they disregard the value of the centre? Is it intentionally in opposition to ancient stone scoring rules?

I suspect that the conservative play of allowing 2 space on either side comes from the top. Shusaku rarely lost as black, and such conservative play may have been why. Perhaps others then copied.

-> Middlegame
They know of the shoulder hit to the small knight's shimari, but timing and response are weird. Likewise, they play from the side to get eyes rather than attaching on the 5th line to an already secure shimari + 2 extensions. Perhaps they fear not being able to get value from the shoulder hit, because they can't see the territory, and similarly can't see the eyes. Perhaps they underestimate the development potential of shimaris, and are willing to play endgame against them from the sides? Perhaps they don't want to risk taking gote?

They don't like attacking, perhaps overvaluing connected shape (though not necessarily good). Perhaps the conservative attitude (winning a won game etc.) makes them ignore large scale attacks.

In a fight, they disrespect the value of weak points at the boundary a little, which seems to only increase the local temperature as they fight to get access to the centre. Perhaps they are too willing to fight, even when leaving valuable shape weaknesses. This can pay off if the opponent makes a mistake.

"essential to invade" in commentary was certainly not true, especially as being attacked lost a more valuable invasion point. The commentary praised an invasion that was an attack from an extension, but both got out into centre easily and the extension had a weak point. The invasion was quite deep. So they overvalued deep invasions at boundaries that led to running fights in the centre? Is this "fighting spirit" that ignores territory just for a principle they didn't understand enough?

Overfocus on securing development of own areas even at the cost of leaving weak stones at the boundary, perhaps even next to strong groups of the opponent. This is perhaps quite aggressive by modern standards.

Not sure if this is just a blunder that the commentary also didn't notice, but playing close to weak points is valuable even if they don't work to capture things. Just the sente is often valuable if it secures the opponent's development. Or is it a pun on Shusaku's name? In a fight, he seemed unwilling to use the most valuable sentes to live, instead dangling a weak group that was ko for life, trying for "clever" double attacks or tempting the opp to try to kill prematurely. But it didn't work at all. Was there any reason to think it would work other than thinking the opponent would do as asked?

Perhaps they weren't actually great at life and death in that case? Most developed seems to have been the flow of opening theory which had many good points. And not respecting territory in parts of opening is understandable as the theory was too young to have accurate principles let alone any values for evaluation. Or perhaps they wanted to experiment.