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Hive» Forums » Strategy

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
    15 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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