Opening problems for AI: Problem 24

Bill Spight · #1

An (almost) only move problem

Edit: White to play.

Elf's top choice got 223.7k rollouts, a humungous number, while it's second choice got 4.6k rollouts. Third place got fewer than 1.5k rollouts.

White to play

Click Here To Show Diagram Code: [go]$$Wcm22 White to play $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X . O . . . . . . . X . . . . | $$ | . . O , . . . . . , . . . . . X X . . | $$ | . . . . . . . . . . . . . . . O O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X X X . . . . . . . . . . . . . . . | $$ | . O X O X X . . . , . . . . O , . . . | $$ | . . O O O . X . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

As it appears, this is an Edo Era game. But assume area scoring with 7½ komi.

Enjoy!

Knotwilg · #2

For those who have recently been bred with Uberdude's great rendition of LZ's opening gospel, this is a no brainer.

Bill Spight · #3

Knotwilg wrote:

For those who have recently been bred with Uberdude's great rendition of LZ's opening gospel, this is a no brainer.

It's White's turn.

Shaddy · #4

Knotwilg wrote:

For those who have recently been bred with Uberdude's great rendition of LZ's opening gospel, this is a no brainer.

Shaddy · #5

Harleqin · #6

Bill Spight · #7

Shaddy · #8

who wants them

Bill Spight · #9

Shaddy wrote:

who wants them

I guess not you.

Knotwilg · **#10**

While Bill posted the solution, I was compiling this difference game to evaluate the mutual urgency.

FWIW:

RobertJasiek · **#11**

27 is first of all "returning the pincer". Extension is a secondary purpose.

HermanHiddema · **#12**

Shaddy wrote:

who wants them

Not me. I still agree with you. I'm rather surprised the AI (and the pros, apparently) would overlook such an obvious only move

Bill Spight · **#13**

Hidden for courtesy.

Bill Spight · **#14**

HermanHiddema wrote:

Shaddy wrote:

who wants them

Not me. I still agree with you. I'm rather surprised the AI (and the pros, apparently) would overlook such an obvious only move

My last post, #13, addresses that question by looking at Black's play against those two stones.

John Fairbairn · **#15**

Quote:

I'm rather surprised the AI (and the pros, apparently) would overlook such an obvious only move

I'm baffled by this. Please explain why it is the only move. The "obvious" I can understand. It makes a pretty shape, and all amateurs like pretty shapes. So much so that they play 90% of 90% of their games by making the "obvious" shape moves. In such games it is irrelevant who won or lost. It is a form of gambling, or staving off boredom, or escapism, or winding down before bed - or whatever. It certainly ain't trying to improve at go.

Which is the point of this series. So, why even join the thread at all if you don't want to be challenged?

FWIW I thought the "obvious" move was in the lower right. I can also explain to myself why, and prettiness doesn't come into it. The key word for me is equilibrium.

Knotwilg · **#16**

I think that was just herman’s way of expressing he is learning. My Sgf may shed a light on why it is indeed not as urgent as it looks.

If it were an opposition of 2 stones, either hane at the head would be “the only move”. With the extra, be it awkwardly placed, stone, white’ stretch is less powerful and the two stones are rather light. Add to that the urgency of the 2nd move in the corner by LZ’s gospel and there you go.

HermanHiddema · **#17**

It was just a joke people, an exaggeration for comedic effect which apparently didn't come over well on the internet. I'm not actually of the opinion that the AI, or the pros, are obviously wrong in their evaluation. I'm just supportive of Shaddy's gut feeling, it's the same move that caught my eye immediately and that I would've instinctively chosen if it were my game.

Uberdude · **#18**

A few years ago, I would have said p15 because of the local shape urgency. These days with AI's lessons I would see the unenclosed high corner at lower right, a class 2 on the LZ Opening Gospel, and be very tempted to play there. The gospel does allow departures for urgent areas, so then the question becomes is p15 sufficiently urgent to ignore the corner? Doesn't seem an obvious decision to me, but given Bill's clue that Elf's 2nd choice got much fewer playouts would tip me to saying it likes the corner, because I could believe it likes the corner a lot more, but not that it would like the extend a lot more and barely consider corner.

Some analysis from me and KataGo at 0 komi. Spoiler alert, closing corner is by far top choice at 10.8% winrate and white -7.3 points, p15 extend drops that to 9.2% and -7.8 points.

If white extends is it sente, and if black does answer is white's position better or worse from the exchange if then take corner? If black answers with one-point jump (kosumi another choice) then now white is 11.6% or -7.0 points, so this was an improvement to get more liberties to the stick in sente, even though black can then pincer them and you might wonder if they are heavy.

Good exchange for white

Click Here To Show Diagram Code: [go]$$Wcm22 Good exchange for white $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X . O . . . . . 2 . X . . . . | $$ | . . O , . . . . . , . . . . . X X . . | $$ | . . . . . . . . . . . . . . 1 O O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X X X . . . . . . . . . . . . . . . | $$ | . O X O X X . . . , . . . . O , 3 . . | $$ | . . O O O . X . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

So to punish extend black should tenuki and take the corner. The traditional thought is extend is sente, because it threatens attachment to seal black in and build thickness, but like the 3-4 high approach joseki bots say that speed in the opening is important, and indeed KG wants to answer black's corner move in the corner. This is to stop it reverting to the "bad" high approach to 3-4 where black can just attach under for a big happy corner.

KG agrees corners are important

Click Here To Show Diagram Code: [go]$$Wcm22 KG agrees corners are important $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X . O . . . . . . . X . . . . | $$ | . . O , . . . . . , . . . . . X X . . | $$ | . . . . . . . . . . . . . . 1 O O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X X X . . . . . . . . . . . . . . . | $$ | . O X O X X . . . , . . . . O , 2 . . | $$ | . . O O O . X . . . . . . . . . 3 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

So what if white follows up his claim of p15 being sente? Interesting KG really doesn't like 26 here (double hane or just n17 extend directly better), as that exchange makes n18 gote so black doesn't even push again and just quickly attaches at the lower right for a big corner. White doesn't fear black p16 bulge and just extends to o15 in reply and doesn't mind black cutting (support on top side helps, and black can't allow white n18 block in sente so when crawling there white can jump so cut not so severe). Interestingly white should then avalanche. White is down to 6.9% or -8.7 points, so whilst it's a loss, it's far from catastrophic (given size of middlegame fighting mistakes) as Elf's big winrate swings suggest.

My extend was sente!

Click Here To Show Diagram Code: [go]$$Wcm22 My extend was sente! $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 4 . 6 . . . | $$ | . . . . X . O . . . . . 7 3 X . . . . | $$ | . . O , . . . . . , . . . . 5 X X . . | $$ | . . . . . . . . . . . . . . 1 O O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X X X . . . . . . . . . . . . . . . | $$ | . O X O X X . . . , . . . . O 9 2 . . | $$ | . . O O O . X . . . . . . . 8 . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

So if white takes the big corner move, what is black's follow up? Hane is obvious powerful shape hane at head of 2, white wants to hane back, even though there's a cut. Is that anything to fear? No, because 26 for 27 is a wonderful useful outside stone for useless inside stone exchange for white, and the marked black stone has become an inefficient empty triangle. White can just sacrifice 2 stones and take sente.

Not worried about black cut

Click Here To Show Diagram Code: [go]$$Wcm22 Not worried about black cut $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X . O . . . . . . . B . . . . | $$ | . . O , . . . . . , . . . . 6 X X . . | $$ | . . . . . . . . . . . . . 5 2 O O . . | $$ | . . . . . . . . . . . . . . 3 4 8 . . | $$ | . . . . . . . . . . . . . . 7 . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X X X . . . . . . . . . . . . . . . | $$ | . O X O X X . . . , . . . . O , 1 . . | $$ | . . O O O . X . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

For similar reasons the double hane is not scary, white gets the nice free atari which is annoying aji to deal with: if black firmly ataris it with a white is super happy to get b in sente, if black extends at c then later white can use the aji (e.g. d), and if black keeps on pushing at b then he can avoid capturing the cutting stone, but pushing white along the 5th line helps white make the group strong and surround the right side.

Not worried about double hane

Click Here To Show Diagram Code: [go]$$Wcm22 Not worried about double hane $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X . O . . . . . . . B . . . . | $$ | . . O , . . . . . , . . . . 6 X X . . | $$ | . . . . . . . . . . d . a 5 2 O O . . | $$ | . . . . . . . . . . . . c 4 3 . . . . | $$ | . . . . . . . . . . . . . b 7 . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X X X . . . . . . . . . . . . . . . | $$ | . O X O X X . . . , . . . . O , 1 . . | $$ | . . O O O . X . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

So to prevent the lovely atari for white, black should just extend. Bots really don't like letting the opponent make beneficial exchanges in sente. Now the marked black stone is efficient / a pretty shape. Now white could extend on the right side, or tenuki. Did black really gain enough value for 2 extra moves in the local area when there are such big opening moves for the taking elsewhere?

Avoid atari to preserve good shape

Click Here To Show Diagram Code: [go]$$Wcm22 Avoid atari to preserve good shape $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X . O . . . . . . . B . . . . | $$ | . . O , c b . . . , . . . . . X X . . | $$ | . . . . . . . . . . . . . 4 2 O O . . | $$ | . . . . . . . . . . . . . . 3 . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . a . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X X X . . . . . . . . . . . . . . . | $$ | . O X O X X . . . , . . . . O , 1 . . | $$ | . . O O O . X . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Here's a sort of tewari argument that helps me appreciate why the hane is not super amazing for black. Let's rewind the right side to just the 5-3 and 5-4 points and white passes to give black sente. Black 1 closes the corner, a wonderful class 2 move from the LZOG. White 2 is likewise a class 2. These are the 2 biggest (gote) moves on this board. Next black plays 3, a very slow move to bolster his shimari towards the centre. The gospel only focuses on corner moves (ie something top left) doesn't even bother with side moves like a, so centre moves like this are even lower priority. White then plays 4 bad move splatted against the shimari and black naturally answers at 5. For sure this is a bad exchange, but is it worse than black's 3? Probably not is my feeling but I didn't check with a bot. Then white continues with 6, which is terrible and heavy, but a lot of that is because it would then be black's move next and he could play p14, but now black has to pass and white can make the 8 for 9 exchange in sente and now those 3 stones, whilst plastered against a strong black position, could also be seen as kikashi against the reinforced shimari so could be used to help the right side or just sacrificed.

Tewari

Click Here To Show Diagram Code: [go]$$Bc Tewari $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X . O . . . . . . . X . . . . | $$ | . . O , . . . . . , . . . . . 5 1 . . | $$ | . . . . . . . . . . . . . 9 3 4 6 . . | $$ | . . . . . . . . . . . . . . 8 . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , a . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X X X . . . . . . . . . . . . . . . | $$ | . O X O X X . . . , . . . . O , 2 . . | $$ | . . O O O . X . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Sides before centre!

Click Here To Show Diagram Code: [go]$$Bc Sides before centre! $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X . O . . . . . . . X . . . . | $$ | . . O , . . . . . , . . . . . , 1 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , 3 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X X X . . . . . . . . . . . . . . . | $$ | . O X O X X . . . , . . . . O , 2 . . | $$ | . . O O O . X . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

ez4u · **#19**

Bill Spight wrote:

Only move

Click Here To Show Diagram Code: [go]$$Wcm22 Only move $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X . O . . . . . . . X . . . . | $$ | . . O , . . . . . , . . . . . X X . . | $$ | . . . . . . . . . . . . . . c O O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X X X . . . . . . . . . . . . b . . | $$ | . O X O X X . . . , . . . . O , 1 . . | $$ | . . O O O . X . . . . . . . . . a . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Elf's top choice, by a huge margin in rollouts (223.7k), is enclosing the bottom right corner with :w22:

. OC, Black was threatening to play there or a. I expect that other top bots will concur.

Elf's second choice is b (4.6k rollouts). No other play got as many as 1.5k rollouts. b gets only a 1% lesser winrate estimate, so it may be playable, but :w22:

is much more certain...

I am a little slow to this conversation. But so what? :rambo:

Like Uberdude and others in this series. I wonder about the use of Elf with its hardwired komi as the basis for Bill's choice of interesting situations. We all know that Bill has meanwhile invested in a new box and powerful card. Time to get busy and step into the modern AI age, say I.

Meanwhile, I too have upgraded my equipment. I couldn't afford one of those RTX cards or the like, so I settled for a GTX 1650 super instead. :blackeye:

At least it added more bite to my overnight runs. Speaking of which...

Here is the result of running katago's 40-block on the original position with Japanese rules and komi = 0 (also with analysisWideRootNoise = 0.04 to widen the search). We see that katago calculates the same play in the bottom right as blue. However, across 4.8 million playouts, it has allocated substantial time to alternatives.

The important takeaways here:
* White's win rate is below 10% (no possible play could lose 21%) and katago estimates that under best play White is behind by ~7.3 points. It seems that the win rate "drama" in Elf's analysis may be due to being right at the tipping point if komi were 7.5 points instead of 0.
* The alternatives in the upper right and on the left side are inferior. However, they are interesting! Consider the upper right. The "standard" continuation of P15 is not as effective as the shoulder hit at O16 (win rate only 8% versus 8.7%). But wait! look more closely at the picture. Katago calculates that P15 leaves White behind by 7.5 point while O16 leaves it behind by 8.0 points. What the heck is going on here? :scratch:

Lightvector can correct me, but I like to believe that this reflects katago's calculations on the likelihood of overcoming a lead of ~7+ points. That is, O16 offers more opportunities for reversing the score that P15.
* Notice also the marked points on the left side. Extending is within katago's possible replies. The idea is inferior to enclosing the bottom right. However, if White played a high extension instead of the low version chosen in the game, the estimated score difference would only be 0.4 points.

Meanwhile, let's step back once. Before we get to the subject position a number of choices have been made. I would like to look at one, the atari at b4 in the lower left. This allows White to take sente in the lower left and gives rise to the original position in this thread. However, katago calculates that this is an error. White would be better off to descend at B3 in gote and allow Black to play first on the rest of the board. Below is katago's calculation after 1.7 million playouts. This is a fascinating result!
* Blue is the press in the top left. No surprise when we see this from a bot.
* The best score is is the 3-3 invasion in the lower right (6.5 points)
* The highest win rate is the invasion of the right side at R11 (87.6%)
Notice that all of these alternatives have been given substantial playouts ~150K or better! In addition, please also notice that the decision to descend here and accept gote has a bigger impact on the score and win rate than Elf's calculated "blunder" on the next play in the actual game.

One thing that is clear to me from this excellent series is that bots do not play fuseki and joseki. For the bots every move is a whole-board problem, nothing more and nothing less.

As a final comment in this regard, here is katago's analysis if we change the bottom right White stone from P4 in the game to the 3-4 point at Q3. This picture reflects a mere 570K playouts. :mrgreen:

However, we should note that katago now prioritizes playing in the upper right over enclosing the lower right. But wait! If we look only at the score, we notice that the best play from that point of view is actually the somewhat tighter extension on the left side at D12 (-6.7 points). Maybe those players long ago saw deeper than we imagine? :salute:

lightvector · **#20**

ez4u wrote:

The "standard" continuation of P15 is not as effective as the shoulder hit at O16 (win rate only 8% versus 8.7%). But wait! look more closely at the picture. Katago calculates that P15 leaves White behind by 7.5 point while O16 leaves it behind by 8.0 points. What the heck is going on here? :scratch:

Lightvector can correct me, but I like to believe that this reflects katago's calculations on the likelihood of overcoming a lead of ~7+ points. That is, O16 offers more opportunities for reversing the score that P15.

Bill has been posting so many of these positions that I have not kept up at all, but just reading over old posts here and there and I came across this. Yes - KataGo may sometimes prefer a move that it judges as on average putting it more behind, if it thinks that it leads to variations that escalates the complexity or swinginess of the game and gives more chances to win overall. On the flip side, it may prefer giving up some points for safety while ahead. It does care about points too - like with human pros, it's a blend of both.

In terms of points "deliberately" leaked in this way, in most cases it's pretty subtle measured in points - usually the two goals are aligned, and even when they're not, obviously blending the two goals means you favor moves that only give up a little if possible. Sometimes the two goals diverge a lot, and sometimes also it's just that the neural net is misevaluating the position, which of course still happens plenty (not in such early opening positions, but later in midgame fights).

Even if the amount of points traded for complexity/safety is mostly subtle and small, the difference in style I think is noticeable. Over the course of many moves while behind vs ahead, I think if you are mid-dan strength you can sometimes see the style difference, as being ahead/behind sometimes influences the choices between moves that are objectively probably very close but are different in aggression vs safety.

Opening problems for AI: Problem 24

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