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Subject: Endgame Puzzle rss

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Robert Bracey
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I am currently playing on Boardgame Arena. If you have not visited the site does some very nice implementations of various boardgames and has options for fun and friendly turn based tournaments, there is a Hive one starting in a week and half https://en.boardgamearena.com/#!tournament?id=8200

While doing this I have been thinking about endgame puzzles. These are very common in Chess where they test the important skill of spotting a critical move or combination (even mate in one or two puzzles can be quite challenging). Unfortunately those do not really work for Hive because the decision space is a lot smaller and surrounding the Queen is achieved by a combination of pieces not one daring move.

So here is an alternative sort of end-game puzzle based more around the peculiarities of Hive (particularly counting tempo). I have adapted it from a position in an game just played, so it is not particularly artificial. Look at the position below with White to move then answer:
Which player wins?
In how many moves?



To make this a purer puzzle I have modified the position slightly so that neither player has any defence against a properly formulated attack (both players have a win and they are both forced, as long as they get their moves in the correct sequence). I've left an option if you spot an error.

Quiz
White to move.
Who wins?
How many moves?
White 2
White 3
White 4
White 5
White 6
Black 3
Black 4
Black 5
Black 6
The puzzle has a mistake
I don't know
    18 answers
Quiz created by RobertBr

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Andrew P.
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Hmm...

Spoiler (click to reveal)
I don't see how White can stop Black from winning in 3 moves. I might be wrong, but it looks like White has no way to stop Black's two Beetles and Ant from surrounding White's Queen. Black can't stop White from freeing the Beetle from the Spider's pin, but White needs 4 moves for the win. Black also needs to be careful about the order of the pieces moved to White's queen. Bringing the Beetle down off of White's Pillbug or moving in the Ant that's pinning White's Ant first would be a mistake.


Cool puzzle! I'd love to see some more.

Can you tell me more about the tournament? I played in the unofficial World Championship on boardspace.net, but it lasted waaaaaaaaaaaaaay too long for a casual player like myself. It started in Mid May and lasted until Mid October before a champion was crowned. I was knocked out around Mid July. I kind of got burned out in the process, but I did get to play against some very talented and cool people.
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Robert Bracey
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pieforteeth wrote:
Hmm...

Cool puzzle! I'd love to see some more.

Can you tell me more about the tournament?


Thanks. If this puzzle form seems to work I will try and post a new one each week (no promises). Yes, your analysis is spot of the position agrees with mine.

Tournaments on Boardspace vary a lot in terms of format. The Hive Open is being played on five 7 day matches (its full now but this is the highest rated players) starting December so will likely last about a little over a month.

The Akrido regular which I just played in had a 10 day round robin, so you played 9 games but simultaneously over a week and a half. That felt intense at points but obviously finishes fairly quickly. The next one (this was no.2) has not been announced yet.

The one I linked to above has a Swiss format with 8 games and 3 days per game. That means you will get a full 8 games and it will take less than a month. On the downside you generally need to find a moment you are both online or run the risk you will time out.

I'm still experimenting with formats so I may post a seperate thread to ask opinions.

Robert
 
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Robert Bracey
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There is in fact a mistake in the puzzle as I laid it out, so if you answered that option see if you found the same one I did:

Spoiler (click to reveal)
Technically I said for the puzzle to be correctly formatted both players should have a forced win. In fact the player who will take longer for their win can be blocked. Admittedly it involves moving a Beetle a long winded route and ignoring the chance to win, but it is a violation of the rules I set up for the game.
For future puzzles I will alter the rubric so only the player who is winning has to have a forced win (ie. the opponent cannot change the number of moves it takes).
 
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Robert, since you gave your answer in another thread, I guess we should discuss it openly here.

I fail to see how any player can win in a few moves.

White could for instance move his Beetle and then his Grasshopper to prevent Black from surrounding his Queen with his Ant. This would slow down Black's win a lot.

Don't you think so?
 
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Robert Bracey
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LCG,

No White move can stop B-3 2. Looking at your suggestion I assume you mean White moves B-2 5, threatening to allow the grasshopper to jump to 1 3 creating a narrow gate the ant cannot get through, which forces a Black use of the Pillbug, delaying Black surround by 1 move?

Looking again I think you are right.

Robert
 
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RobertBr wrote:
I assume you mean White moves B-2 5, threatening to allow the grasshopper to jump to 1 3 creating a narrow gate the ant cannot get through, which forces a Black use of the Pillbug, delaying Black surround by 1 move?


Exactly.

And this is even worse for Black: his Pillbug cannot move the Beetle so on his next turn White could use the Beetle again to climb on Black's Ant...

I don't see a forced victory for Black in 4 moves.
 
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Andrew P.
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Great spot LCG! I didn't see that Beetle move. Hmm... it doesn't look like Black can win in 4 moves, but I think with all 3 Grasshoppers and an Ant in reserve, Black can figure out a relatively easy win. Maybe even in 5 moves.
 
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pieforteeth wrote:
I think with all 3 Grasshoppers and an Ant in reserve, Black can figure out a relatively easy win. Maybe even in 5 moves.


I did not find any victory path for Black in 5 moves or less.

If someone knows the answer to this problem please post it!
 
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Andrew P.
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I edited the original image to help with my notation.



OK here's what I'm thinking...

Spoiler (click to reveal)
1. wB2 : \bP
bA1 : \wA1 (This keeps wA1 pinned, and wS2 won’t be able to leave)
2. wG1 : -wA1 (If White wants to create a gate between bA2 and wA1)
bB1 : /wQ
3. White only has three pieces that can move. I don’t think any of them can help to stop Black’s next 3 moves.
bG1 : /bA1
4. White's move
bG1 : \wQ
5. White's move
bB2 : wQ\ for the win

White can stop bA1, but it isn’t needed to surround the queen.


If I'm missing a move for white that blows up this idea, let me know! I just watched the World Chess Championship, and I was fascinated by the commentators suggesting all kinds of moves and explaining why they do or don't work. Plus it will help me get better at Hive!

Also, if you're unfamiliar with the notation I'm using it works like this:

wb2 : \bP means White Beetle #2 moves up and to the left of Black's Pillbug.

-bP = directly to the left
/bP = down and to the left
bP\ = down and to the right and so on

This notation only makes sense if the pieces are oriented this way.
 
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I fully agree that Black seems to be in a better position, with more flexibility in the moves he can take. However, I still cannot answer the original question about the minimum number of moves required to win the game.

Now let's discuss moves...

Spoiler (click to reveal)

Indeed, wB2 \bP is the only first move for White to avoid a near death.

If Black replies with bA1 \wA1, there are better second moves for White than wG1 -wA1.

First, there is wB2 \wS2 with the Beetle threatening to either pin the Black Ant by moving onto it but also to form a gate to protect the Queen by simply going down at -wA1.

Second, there is wS1 \wG2 that frees either wB1 or wM.

In both cases, I don't see how Black can quickly win.
 
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I love these kinds of puzzles; I remember learning a lot from the ones image13 used to do back in the day, although now all the links to those images are broken, sadly. Incidentally, if anyone reading this has them saved somewhere(maybe an oldschooler like ringersoll?), or can find them somehow, that would be cool.

Regarding this puzzle:

RobertBr, you should orient your images the way pieforteeth did with the points of the hexes going up and down, not side to side, and number the bugs with multiple copies(numerals or dots). This way we can all use the standard notation in use for many years on boardspace.net, and explained in ringersoll's book, and here:

http://www.boardspace.net/english/about_hive_notation.html

I don't have a clue what the notation you are using means.

Analysis of position below:

Spoiler (click to reveal)
I think I see how black can force a win in 5 moves, including responding to the forced wB2 \bP with the ant pin bA1 \wA1 already proposed (-wA1 also works). Responding with bB1 /wQ looks to me like it will require at least 6 moves to force a win.

I'd be interested to hear if anyone thinks they can do it in 4 or less, or in 5 or less with bB1 /wQ response (or anything other than the two ant pins above, really), and if so how. Also if you think you could defend longer than 5 moves with white, I'd be interested to know how.
 
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Andrew P.
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Hmm...

Spoiler (click to reveal)
Scar murders Mufasa. cry


But THEN, after...

Spoiler (click to reveal)

1. wB2 \bP, bA1 \wA1 (or -wA1 as veme suggested)

If White moves wB2 again, Black should go bB1 /wQ. How does White stop or respond to Black adding a grasshopper at /bA2?

If white tries wS1 bS1\ to free wB1, I would still go with the bB1 /wQ plan. White needs 4 or more moves to surround Black's queen.

If White gets really daring and tries 2. wG1 wQ\, I think 2... bB1 /wQ still works. White can try 3. wG1 -bB1, but that still loses to 3... bA1 \wQ.




 
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Okay, here is what I think I had figured out. Make sure you read only the first spoiler if you would like an additional little puzzle. The answer is in the second.

Spoiler (click to reveal)
First: wB2 \bP, bA1 \wA1 or -wA1

Any other move for white leads to a faster loss, any other move for black, a more drawn out win at best (I think).

From here white has 3 approaches that can stretch the win to require 5 moves from black. Two of them force black to add a piece.

Option 1:
wG1 -wA1(or -bA1, depending on pin location), bB1 /wQ
white move, bG1 -bB1
white move, bB2 wQ\ or bG1 \wQ
white move, whichever of the last black options isn't done yet

This is the one that was described by pieforteeth.

Option 2:
wB2 wA1, bB1 /wQ
wB2 bA1

And the rest is the same as option 1. Option 3 though, is performed differently.

After the initial wB2 \bP, bA1 \wA1 or -wA1, what other sequence of moves can white use to force black to have to use at least five turns to win? Once you figure out what it is, if white uses this defense, what response(s) must black make to win in only 5 moves? I will put the explanation in a different spoiler tag after this one.


Spoiler (click to reveal)
Option 3:
wS1 wM/, bB1 /wQ
wM bP\, bA1 \wQ
wM:wA2 wM\, bP:wM wQ- or bP:wB2 wQ-
white move, bB2 wQ\

White delays here using a great defensive tactic to have in your arsenal - taking your mosquito away from an attack to serve as an emergency pillbug. Unfortunately it is too little too late.

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Andrew P.
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veme wrote:
Okay, here is what I think I had figured out. Make sure you read only the first spoiler if you would like an additional little puzzle. The answer is in the second.

Spoiler (click to reveal)
First: wB2 \bP, bA1 \wA1 or -wA1

Any other move for white leads to a faster loss, any other move for black, a more drawn out win at best (I think).

From here white has 3 approaches that can stretch the win to require 5 moves from black. Two of them force black to add a piece.

Option 1:
wG1 -wA1(or -bA1, depending on pin location), bB1 /wQ
white move, bG1 -bB1
white move, bB2 wQ\ or bG1 \wQ
white move, whichever of the last black options isn't done yet

This is the one that was described by pieforteeth.

Option 2:
wB2 wA1, bB1 /wQ
wB2 bA1

And the rest is the same as option 1 (except that if black chose the initial pin at \wA1, bA3 could optionally be placed instead of bG1).

Option 3 is performed differently.

After the initial wB2 \bP, bA1 \wA1 or -wA1, what other sequence of moves can white use to force black to have to use at least five turns to win? Once you figure out what it is, if white uses this defense, what response(s) must black make to win in only 5 moves? I will put the explanation in a different spoiler tag after this one.


Spoiler (click to reveal)
Option 3:
wS1 wM/, bB1 /wQ
wM bP\, bA1 \wQ
wM:wA2 wM\, bP:wM wQ- or bP:wB2 wQ-
white move, bB2 wQ\

White delays here using a great defensive tactic to have in your arsenal - taking your mosquito away from an attack to serve as an emergency pillbug. Unfortunately it is too little too late.



Wow what a sneaky little move! I didn't see that one at all. If I had been playing as Black and that combination of moves freed White, I would say what I always say in those situations:
Spoiler (click to reveal)
"CURSE YOU PILLBUG!!"
 
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In case this helps, here is a clean picture of the puzzle:


wB2 covers bP and bB2 covers wP.
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