Go here if you want to see the puzzle, first.
Answers:
Acquire
High adventure in the world of high finance
The game of corporate acquisitions
Aggravation
The classic marble race game
Alladin's Dragons
Adventures under the crescent moon
Amazonas
Explore a dangerous paradise
Amun-Re
A game for gods and other immortals
Apples to Apples
The frantic game of hilarious comparisons
Attila
From the far tundra
Axis and Allies
Control the fate of the world
Axis and Allies: Europe
The game of military strategy, courage, and cunning
Barbarossa
The classic riddle game
Battle Cry
The exciting civil war battlefield game
Battletech
No guts, no galaxy
Big City
Make your city grow...
Blokus
The cutting-edge of strategy
Boggle
The 3-minute word search game
Bohnanza
To bean or not to bean
Buy Word
A game of profit through words
By Hook or By Crook
The great bluffing game from Germany
Captain's Mistress
The game once loved by sea captains and kings
Citadels
A game of medieval cities, nobles, and intrigue
Cities and Knights of Catan
A game of culture, politics, and warfare
Cluzzle
The game of comic clay puzzles
Can't Stop
How far can you push your luck?
Carcassonne
The simple, clever tile-laying game
Clue
Classic detective game
Cosmic Encounter
The game that breaks its own rules
Descent
A game of dungeon-crawling adventure
Diplomacy
The game of international intrigue
Domaine
Land, wealth, power, prestige
Dos Rios
Valley of two rivers
Entdecker
An exciting journey of discovery and colonization
Family Business
The game of mob vengeance
Formula De
The number one motor racing game
Hera and Zeus
Divine feud for two
Hungry Hungry Hippos
The frantic marble munching game
I'm the Boss
An exciting game of deal making, negotiation, and cutthroat bargaining
Illuminati
The game of conspiracy
Ingenious
An amazing game for 1 to 4 brains
Jenga
Edge of your seat fun
Kings Table
The game of the Vikings
La Strada
Which road leads to riches?
Liar's Dice
Truth never counts when your playing
Lost Cities
Daring adventure for two
Maharaja
The game of palace building in India
Modern Art
High stakes bidding in the galleries
Monopoly
Property trading game
Nautilus
Fortunes on the ocean floor
New England
An exciting game of bidding and development
Oceania
Adventures of discovery
Odin's Ravens
Flying races for two clever ravens
Othello
A minute to learn... a lifetime to master
Parcheesi
The classic game of India
Pit
The corner the market card game
Power Grid
An energetic economic game
Princes of Florence
The strategy game of patrons, artists, and scholars
Puerto Rico
Which roles will you play in the new world?
Quo Vadis
Power and intrigue in ancient Rome
Ra
A challenging game of gods, men and their monuments
Raj
An outrageous bidding game for 2-5 players
Risk
The game of global domination
Robo Rally
A frenzied race filled with computer driven chaos
Rook
The ever-popular bidding card game
Samurai
The game of the forces
Samurai Swords
A game of high adventure
Scrabble
America's favorite word game
Seafarers of Catan
A game of seafaring, exploration, and trade
Senet
The favorite game of Egyptian pharoahs
Set
The family game of visual perception
Settlers of Catan
A game of discovery, settlement, and trade
Settlers of the Stone Age
An exciting game of migration and development
Sorry
The game of sweet revenge
Spammers
Oh God, do you have mail
Starship Catan
An adventure for two starfarers
Stratego
The classic game of battlefield strategy
Survive!
A sea full of danger and oceans of fun
Taj Mahal
The game of power and majesty in India
Ticket to Ride
The cross-country train adventure game
Tigris and Euphrates
A game of culture, crisis, conflict, and civilization
Time's Up
The fast paced game of multiple personalities
Titan the Arena
A fierce game of deadly combat...
Too Many Cooks
The crazy cookin' card game
Through the Desert
A game of caravans and desert oases
Traders of Genoa
The exciting game of wares, messages, and traders
TransAmerica
One step ahead
Trouble
There's trouble in the bubble
Twilight Imperium III
An epic boardgame of galactic conquest, politics, and trade
Twister
The game that ties you up in knots
Wizard
The ultimate game of trump
Wyatt Earp
A thrilling game of outlaws, sheriffs, and fast guns
Technorati tags: board game, board games, game puzzle, puzzle, taglines
Sunday, May 07, 2006
Game tournaments links
Sign up in time for the following championships:
Rock Paper Scissors
Marbles
Tiddlywinks
Snakes and Ladders
Lots of others, such as Gin Rummy, Twister, ...
Yehuda
P.S. Cute Zits (on blogging).
Technorati tags: board games, board game
Rock Paper Scissors
Marbles
Tiddlywinks
Snakes and Ladders
Lots of others, such as Gin Rummy, Twister, ...
Yehuda
P.S. Cute Zits (on blogging).
Technorati tags: board games, board game
Saturday, May 06, 2006
3 Player Puerto Rico, in detail
A Puerto Rico game with Rachel and Nadine.
We played with the standard game, with the following changes:
Since I had played 3rd (corn) the last two times, we decided that I would not be able to play 3rd again this time. I played 2nd.
Many games have standard opening moves, such as chess and go, so it doesn't bother me that the opening moves in PR are also pretty standardized, albeit they leave perhaps even less room for experimentation than the other games.
However, even following the standard moves, the second player is in a slightly weaker position, which is a bit of a problem. I have wondered several times if perhaps this could be addressed, by giving 2nd player corn or sugar, or by giving the 3rd player indigo or sugar, and so on. I haven't gotten around to trying these out, yet.
Anyway, here is how our game went (no notes, since we played on shabbat):
1st round: Nadine takes Settler/quarry, I get a corn, Rachel takes a sugar. I take Builder/Sm Market. I briefly considered trying something new by taking Mayor, until I remembered that giving Nadine her quarry manned before building would be a boon for her. In our games, 3rd player often takes Sm Sugar rather than Sm Market on first build if they got a sugar plantation, and that's what Rachel did. Nadine then passed, rather than buy either Sm Market or Sm Indigo without the quarry reduction.
2nd round: I take Trader, Rachel takes Craftsman, Nadine takes Captain. So ends the scripted opening.
3rd round, Rachel buys Sm Market, Nadine buys Sm Indigo, I pass, hoping to get a trade good going soon. Nadine takes Mayor, and Rachel mans her corn. I then diverged from what would be the most normative play of Settler with a bonus, and instead took Craftsman, since Rachel hadn't manned her Sm Market. Meanwhile, Nadine will likely take Trader, leaving me with Settler with a double bonus.
4th round: Which she does. Nadine trades indigo for 3 (bonus), I trade corn for 1, and Rachel trades sugar for 2. I take Settler with 2 and take a coffee. Rachel takes another corn, and Nadine takes Tobacco. Rachel now has 2 corns and a sugar, Nadine had a quarry, indigo, and tobacco, and I have coffee, indigo, and corn. Rachel takes captain. She has 5 vp, I have 2, and Nadine has none.
5th round: I get builder with a bonus and build coffee with 2 left over. Rachel builds Hospice. You may snort, but Hospice can sometimes quickly pay for itself with quarries and corns; in this game, however, it never did. Nadine buys Tobacco. Rachel takes Mayor, and Nadine takes Craftsman. Nadine was hoping to trade tobacco, but she wasn't also producing an indigo that would have ensured that my lone coffee would have to ship first. Nadine also didn't mind starting a tobacco boat at this point, although it ended up being hard to trade her tobacco later.
6th round: Rachel takes Captain with the bonus, and Nadine is forced to ship her tobacco. I still have my coffee. Rachel is now at 8 vp, while both Nadine and I have only 2 each. That's a hefty gap to start with, but without a trade good she is going to find herself in trouble, soon. Nadine takes Settler, I believe. I trade my coffee for a total of 7.
7th round: From here on it gets a little hazy. Nadine and I both buy a Harbor at this point. Nadine wanted to buy Factory, but was only now reminded that it cost 8 rather than 7, and seeing as she was not yet producing sugar, decided that Harbor was more worthwhile for the cost at this point. I would have liked to buy a Factory at 7 cost, but since I had a coffee monopoly for the foreseeable future, I didn't think that I needed it. What I needed was to start closing the VP gap with Rachel, however. I took Mayor, and Rachel took Craftsman.
8th round: At this point, another lovely coffee trade looked tempting, but not half as tempting as starting a coffee boat. The coffee boat I started now essentially lasted until the end of the game, and ended up being a huge swing in victory points for me. A tobacco boat was also going, if you remember, which meant that Rachel's shipping opportunities were limited to the small boat until she bought the Discretionary Hold or a Wharf. She ends up buying the Discretionary Hold soon after.
On my next opportunity to trade, I trade an indigo, rather than a coffee again. I was still holding a coffee monopoly, which meant the only way to clear out the trading house other than with coffee was with corn, and I didn't want to sacrifice the 2 vp I was getting with shipping coffee with a Harbor. I figured that I would get the money soon enough.
However, I ended up letting Nadine get Guild Hall first, which was a loss for me. Guild Hall is just 2-3 VP better than any other building, most of the time. I'm so glad that I don't play with it anymore when we are at my house. Cathedral is just so much better.
Rachel decided to play a strange strategy by adding University to her Hospice. Under the right conditions, you can use the University to end the game in the last round, by buying a large building and having it come prefilled, while your opponents are stuck with unmanned buildings. Under ideal conditions, it can also do a lot of good with other buildings, too. However, even at a cost of 7 and prefilled, it is not a bargain.
On the second to last round of the game, we hit a strange little bump with this, in fact. I had purposely left 2 colonists in the supply, rather than only 1, for reasons that I can't remember. It turns out that if I had left only 1, I could have taken Mayor before Rachel took Builder as her last move. There would then have been no colonists left in the supply or boat with which to fill her building! But it never came to that, since I had foolishly left 2 colonists in the supply.
On my first opportunity to buy a big building, after Nadine took Guild Hall, I decided to take Wharf, which proved to be very fruitful, as I was producing 2 natural corns and often 3 when I took Craftsman. My coffee boat, and Nadine's tobacco boat, were filling up slowly, which meant no extra points for Rachel's Discretionary Hold.
And my big building, when I got around to it, was Custom's House. So all was well with the world, for me.
Nadine ended with 28 shipping vps and a complete Guild Hall, for 57 points. Rachel had 30 shipping vps and Fortress for 56 points. My Custom's House and 33 shipping vps totaled 62 points. So 2nd place can win sometimes, after all. But only if he gets a coffee monopoly and a coffee boat.
Yehuda
Technorati tags: board game, board games
We played with the standard game, with the following changes:
- Hospice: you can move one of our colonists onto Hospice immediately after buying it.
- Large Warehouse: Unused, instead we played with Discretionary Hold (a: can store any 3 barrels, and b: can place one barrel of any type onto each full boat at end of captain phase for 1 vp each).
- Factory: cost 8
- University: cost 7, and comes with a colonist from the supply.
Since I had played 3rd (corn) the last two times, we decided that I would not be able to play 3rd again this time. I played 2nd.
Many games have standard opening moves, such as chess and go, so it doesn't bother me that the opening moves in PR are also pretty standardized, albeit they leave perhaps even less room for experimentation than the other games.
However, even following the standard moves, the second player is in a slightly weaker position, which is a bit of a problem. I have wondered several times if perhaps this could be addressed, by giving 2nd player corn or sugar, or by giving the 3rd player indigo or sugar, and so on. I haven't gotten around to trying these out, yet.
Anyway, here is how our game went (no notes, since we played on shabbat):
1st round: Nadine takes Settler/quarry, I get a corn, Rachel takes a sugar. I take Builder/Sm Market. I briefly considered trying something new by taking Mayor, until I remembered that giving Nadine her quarry manned before building would be a boon for her. In our games, 3rd player often takes Sm Sugar rather than Sm Market on first build if they got a sugar plantation, and that's what Rachel did. Nadine then passed, rather than buy either Sm Market or Sm Indigo without the quarry reduction.
2nd round: I take Trader, Rachel takes Craftsman, Nadine takes Captain. So ends the scripted opening.
3rd round, Rachel buys Sm Market, Nadine buys Sm Indigo, I pass, hoping to get a trade good going soon. Nadine takes Mayor, and Rachel mans her corn. I then diverged from what would be the most normative play of Settler with a bonus, and instead took Craftsman, since Rachel hadn't manned her Sm Market. Meanwhile, Nadine will likely take Trader, leaving me with Settler with a double bonus.
4th round: Which she does. Nadine trades indigo for 3 (bonus), I trade corn for 1, and Rachel trades sugar for 2. I take Settler with 2 and take a coffee. Rachel takes another corn, and Nadine takes Tobacco. Rachel now has 2 corns and a sugar, Nadine had a quarry, indigo, and tobacco, and I have coffee, indigo, and corn. Rachel takes captain. She has 5 vp, I have 2, and Nadine has none.
5th round: I get builder with a bonus and build coffee with 2 left over. Rachel builds Hospice. You may snort, but Hospice can sometimes quickly pay for itself with quarries and corns; in this game, however, it never did. Nadine buys Tobacco. Rachel takes Mayor, and Nadine takes Craftsman. Nadine was hoping to trade tobacco, but she wasn't also producing an indigo that would have ensured that my lone coffee would have to ship first. Nadine also didn't mind starting a tobacco boat at this point, although it ended up being hard to trade her tobacco later.
6th round: Rachel takes Captain with the bonus, and Nadine is forced to ship her tobacco. I still have my coffee. Rachel is now at 8 vp, while both Nadine and I have only 2 each. That's a hefty gap to start with, but without a trade good she is going to find herself in trouble, soon. Nadine takes Settler, I believe. I trade my coffee for a total of 7.
7th round: From here on it gets a little hazy. Nadine and I both buy a Harbor at this point. Nadine wanted to buy Factory, but was only now reminded that it cost 8 rather than 7, and seeing as she was not yet producing sugar, decided that Harbor was more worthwhile for the cost at this point. I would have liked to buy a Factory at 7 cost, but since I had a coffee monopoly for the foreseeable future, I didn't think that I needed it. What I needed was to start closing the VP gap with Rachel, however. I took Mayor, and Rachel took Craftsman.
8th round: At this point, another lovely coffee trade looked tempting, but not half as tempting as starting a coffee boat. The coffee boat I started now essentially lasted until the end of the game, and ended up being a huge swing in victory points for me. A tobacco boat was also going, if you remember, which meant that Rachel's shipping opportunities were limited to the small boat until she bought the Discretionary Hold or a Wharf. She ends up buying the Discretionary Hold soon after.
On my next opportunity to trade, I trade an indigo, rather than a coffee again. I was still holding a coffee monopoly, which meant the only way to clear out the trading house other than with coffee was with corn, and I didn't want to sacrifice the 2 vp I was getting with shipping coffee with a Harbor. I figured that I would get the money soon enough.
However, I ended up letting Nadine get Guild Hall first, which was a loss for me. Guild Hall is just 2-3 VP better than any other building, most of the time. I'm so glad that I don't play with it anymore when we are at my house. Cathedral is just so much better.
Rachel decided to play a strange strategy by adding University to her Hospice. Under the right conditions, you can use the University to end the game in the last round, by buying a large building and having it come prefilled, while your opponents are stuck with unmanned buildings. Under ideal conditions, it can also do a lot of good with other buildings, too. However, even at a cost of 7 and prefilled, it is not a bargain.
On the second to last round of the game, we hit a strange little bump with this, in fact. I had purposely left 2 colonists in the supply, rather than only 1, for reasons that I can't remember. It turns out that if I had left only 1, I could have taken Mayor before Rachel took Builder as her last move. There would then have been no colonists left in the supply or boat with which to fill her building! But it never came to that, since I had foolishly left 2 colonists in the supply.
On my first opportunity to buy a big building, after Nadine took Guild Hall, I decided to take Wharf, which proved to be very fruitful, as I was producing 2 natural corns and often 3 when I took Craftsman. My coffee boat, and Nadine's tobacco boat, were filling up slowly, which meant no extra points for Rachel's Discretionary Hold.
And my big building, when I got around to it, was Custom's House. So all was well with the world, for me.
Nadine ended with 28 shipping vps and a complete Guild Hall, for 57 points. Rachel had 30 shipping vps and Fortress for 56 points. My Custom's House and 33 shipping vps totaled 62 points. So 2nd place can win sometimes, after all. But only if he gets a coffee monopoly and a coffee boat.
Yehuda
Technorati tags: board game, board games
Friday, May 05, 2006
Ads and Blogger
I'm biting the hand that feeds me, but is there anything that Blogger does well that other free blog sites don't do?
So far, all I can see are the deficiencies: no tags, lots of outages, no scripting other than JavaScript, no easy access to pictures, unformatted comment pages, limited captcha, ... I opened a Wordpress account just to see what I was missing, and boy did it look better.
To add insult to injury, I was finally approached by an ad company willing to pay me to put some ads on my site (baby steps, but steps!), but the ads only work if I have access to: PHP, ASP, Perl, Coldfusion, Wordpress plugin, vBulletin, Movable Type, Drupal, or Postnuke. In other words, on any site other than Blogger.
Blogger is a Google company and works just fine with Google Adsense, but that seems to be about it.
Yehuda
Articles I'm working on: Web 3.0, and Games that are Art
Technorati tags: Blogger
So far, all I can see are the deficiencies: no tags, lots of outages, no scripting other than JavaScript, no easy access to pictures, unformatted comment pages, limited captcha, ... I opened a Wordpress account just to see what I was missing, and boy did it look better.
To add insult to injury, I was finally approached by an ad company willing to pay me to put some ads on my site (baby steps, but steps!), but the ads only work if I have access to: PHP, ASP, Perl, Coldfusion, Wordpress plugin, vBulletin, Movable Type, Drupal, or Postnuke. In other words, on any site other than Blogger.
Blogger is a Google company and works just fine with Google Adsense, but that seems to be about it.
Yehuda
Articles I'm working on: Web 3.0, and Games that are Art
Technorati tags: Blogger
Clans, 2-Player
Saarya and I were alone last night, as Rachel went to bed early, and Saarya asked to play a game. I wanted it to be of reasonable length, and Binyamin from the game group had left me Clans in order to try out. I hadn't thought that I would be able to get to it, but here was an opportunity.
Clans has a theme the way that Through the Desert has a theme; in other words, none discernible.
The game is essentially a board with around 70 spaces in five types. 60 (four types) of the spaces are playable, while the spaces of the one remaining type (lakes) are impassable. Some of the spaces connect to only three other spaces, while others connect to as many as eight other spaces. Five colors of meeples are distributed roughly evenly around the board to start.
Each round, you pick up all meeples in a space and move them to an occupied adjoining space. You can't move into an unoccupied space. So already you can see that this limits the number of movements to no more than 60/(number of players) each.
A region with seven meeples cannot be moved, and adjacent regions with seven meeples are combined.
Whenever your movement creates an isolated occupied space (surrounded only by unoccupied spaces), each color of meeple in that space scores equal to the total number of meeples in the space. For instance, if the space contains three green meeples, one blue meeple, and one black meeple, then green, blue, and black all score five points.
It doesn't matter how many meeples of a color are in the space; all colors in the space score the same. As the game progresses, specific region types also offer an increasing bonus for each color scoring in them, while others produce no score at all; each region type gets a turn for either category.
If the isolated space has meeples from all five colors, then all meeples of colors with only one meeple in that space are first removed before scoring. So an isolated space with two black meeples and one of each other color meeple will score only two points for black only.
In addition, the player who caused the scoring gets a bonus token for each space scored.
The game ends when there are no more moves or no more bonus tokens. Each player has a secret color, and at the end of the game, your score is your color's score plus your bonus tokens. So in the beginning of the game, people don't necessarily know what color you are. It becomes obvious as the game progresses, however. I couldn't really see the point of this, although I am assuming that it is supposed to add some sort of bluffing or hidden scoring element. With competent players, neither of these appear to apply.
The rules are mostly ok, but a little deficient. For instance, it mentions what happens when you form two isolated spaces at once, but not if you form three of four isolated regions at once. This is pretty easy to extrapolate. Harder to extrapolate, however, is what happens if the isolated region contains exactly one meeple of each color. According to the rules, you remove all meeples from colors with only one meeple before scoring. That leaves you with nothing. Does that count as scoring for purposes of taking the bonus token? Probably, but not clear and not discussed in the rules.
A two-player game is probably best, because the person sitting to the left of a weak player will have a decided advantage. Your basic object in the game is to be the one making the scoring moves. Not only does it give you the bonus token, but it also lets you determine, usually, on which region to score, and therefore whether it will be a bonus, regular, or non-scoring space, as well as which meeples will be constituent in the space. Of course, your choices are very limited, but you can often swing a small advantage one way or the other.
Some things become painfully obvious:
Any space cannot be scored until the number of connections to that space drop to none. Therefore, your opponent will not be able to score so long as you can leave him on his turn all spaces still connected to two other spaces. Triangular patterns work well here, as do circular chains.
You want to use up as many as you can of other meeple colors and only one of yours, thereby leaving you more scoring opportunities. However, you have to be careful that the space doesn't include all five colors and only one of your color's meeples (which will be removed before scoring). The converse to that is to use two of your meeples and only one each of all other meeples. It doesn't leave you with a big score, but it prevents other colors from scoring, at least.
Scoring with a lot of meeples that aren't your color on a non-scoring space is a fine move, since you get the bonus token and no one else gets anything.
And so on.
Like Dvonn, the number of legal moves shrinks as the game goes on, so it has a similar feel. Unlike Dvonn, however, the game can be maneuvered into something akin to Dots and Boxes, where one player leaves the other player with only a series of bad moves left, while the first player then just collects the point. I think this can be mostly avoided, if you know what you are doing.
So it's interesting at first glance. And I would be happy to try it again. It remains to be seen if it has any sort of longevity. And it would have been a better game without the confusing tacked on theme and illustrated board which only serves to make the connections between the spaces less visible.
By the way, I won, which doesn't happen often against Saarya. I expect that he will win any future games.
Yehuda
Link: Baby Blues is doing board games again, and it looks like it may be the first in a series.
Technorati tags: board game, board games, Clans
Clans has a theme the way that Through the Desert has a theme; in other words, none discernible.
The game is essentially a board with around 70 spaces in five types. 60 (four types) of the spaces are playable, while the spaces of the one remaining type (lakes) are impassable. Some of the spaces connect to only three other spaces, while others connect to as many as eight other spaces. Five colors of meeples are distributed roughly evenly around the board to start.
Each round, you pick up all meeples in a space and move them to an occupied adjoining space. You can't move into an unoccupied space. So already you can see that this limits the number of movements to no more than 60/(number of players) each.
A region with seven meeples cannot be moved, and adjacent regions with seven meeples are combined.
Whenever your movement creates an isolated occupied space (surrounded only by unoccupied spaces), each color of meeple in that space scores equal to the total number of meeples in the space. For instance, if the space contains three green meeples, one blue meeple, and one black meeple, then green, blue, and black all score five points.
It doesn't matter how many meeples of a color are in the space; all colors in the space score the same. As the game progresses, specific region types also offer an increasing bonus for each color scoring in them, while others produce no score at all; each region type gets a turn for either category.
If the isolated space has meeples from all five colors, then all meeples of colors with only one meeple in that space are first removed before scoring. So an isolated space with two black meeples and one of each other color meeple will score only two points for black only.
In addition, the player who caused the scoring gets a bonus token for each space scored.
The game ends when there are no more moves or no more bonus tokens. Each player has a secret color, and at the end of the game, your score is your color's score plus your bonus tokens. So in the beginning of the game, people don't necessarily know what color you are. It becomes obvious as the game progresses, however. I couldn't really see the point of this, although I am assuming that it is supposed to add some sort of bluffing or hidden scoring element. With competent players, neither of these appear to apply.
The rules are mostly ok, but a little deficient. For instance, it mentions what happens when you form two isolated spaces at once, but not if you form three of four isolated regions at once. This is pretty easy to extrapolate. Harder to extrapolate, however, is what happens if the isolated region contains exactly one meeple of each color. According to the rules, you remove all meeples from colors with only one meeple before scoring. That leaves you with nothing. Does that count as scoring for purposes of taking the bonus token? Probably, but not clear and not discussed in the rules.
A two-player game is probably best, because the person sitting to the left of a weak player will have a decided advantage. Your basic object in the game is to be the one making the scoring moves. Not only does it give you the bonus token, but it also lets you determine, usually, on which region to score, and therefore whether it will be a bonus, regular, or non-scoring space, as well as which meeples will be constituent in the space. Of course, your choices are very limited, but you can often swing a small advantage one way or the other.
Some things become painfully obvious:
Any space cannot be scored until the number of connections to that space drop to none. Therefore, your opponent will not be able to score so long as you can leave him on his turn all spaces still connected to two other spaces. Triangular patterns work well here, as do circular chains.
You want to use up as many as you can of other meeple colors and only one of yours, thereby leaving you more scoring opportunities. However, you have to be careful that the space doesn't include all five colors and only one of your color's meeples (which will be removed before scoring). The converse to that is to use two of your meeples and only one each of all other meeples. It doesn't leave you with a big score, but it prevents other colors from scoring, at least.
Scoring with a lot of meeples that aren't your color on a non-scoring space is a fine move, since you get the bonus token and no one else gets anything.
And so on.
Like Dvonn, the number of legal moves shrinks as the game goes on, so it has a similar feel. Unlike Dvonn, however, the game can be maneuvered into something akin to Dots and Boxes, where one player leaves the other player with only a series of bad moves left, while the first player then just collects the point. I think this can be mostly avoided, if you know what you are doing.
So it's interesting at first glance. And I would be happy to try it again. It remains to be seen if it has any sort of longevity. And it would have been a better game without the confusing tacked on theme and illustrated board which only serves to make the connections between the spaces less visible.
By the way, I won, which doesn't happen often against Saarya. I expect that he will win any future games.
Yehuda
Link: Baby Blues is doing board games again, and it looks like it may be the first in a series.
Technorati tags: board game, board games, Clans
Thursday, May 04, 2006
Solving the Flipping Game
My friend David Klein has the following to say about the flipping game that I mentioned in the Monkey post (my comments in italics):
Assume the game is laid out as follows:
ABC
DEF
GHI
JKL
Each location is either flipped up or down. Each move consists of selecting a location (e.g. B) and flipping both that location as well as all orthogonally adjacent locations (for B, this would mean locations B as well as A, C, and E). Your job is to flip them all up (or down) in the least number of moves.
The game is always solvable. Indeed, working from the bottom row upwards, it is trivial to bring all of them face up, except for the top row, which leaves only 2^3 possible "games". There are 12 "operators" corresponding to selecting one of the 12 positions to flip. It is trivial to see that these operators are commutative and idempotent (i.e. doing an operator twice is the identity and has no effect). Thus any sequence of moves is equivalent to choosing for each of the 12 operators to apply it either zero or one times, i.e. there are 2^12 different move sequences. If none of them repeat, then we can reach all 2^12 different board positions. If one board position repeats, then applying the two sequences one after another gives the identity position. I.e. there is a non-trivial sequence which is the identity. Performing Gaussian elimination on the transformation matrix shows that this can't occur. Indeed, the sequence to flip only A is
ABDFHIL
only B is
ABCGHIK
and only C is
BCDFGHJ
In other words, In any sequence of flips to solve the game, no piece ever has to be chosen twice, because a twice-chosen piece simply undoes what the first flip series did. You will never have ...B....B... to solve this puzzle. That means that any board can be completely solved in 12 moves or less!
To understand why you only need to know how to solve A, B, and C, consider the following:
To solve the bottom three pieces J, K, and L, you only have to flip some from the third row of pieces G, H, and I. To solve the third row, flip the second row. To solve the second row, flip the first row. That means that you will always be left with some combination of A, B, and C to finish up. Add the corresponding sequences to the flips, and you finish the puzzle.
Now, to get the smallest number of steps, add all of these flips together in a row, sort, cancel all even pairs, and the result is your solution.
Let me show you how to solve the case where only L is flipped and I think the rest will be clear:
ABC
DEF
GHI
JKl
On the bottom (4th) row, only L is flipped. Flip I to get it right:
ABC
DEf
Ghi
JKL
On the 3rd row, H&I are flipped. Flip E&F to get them right.
Abc
dEf
GHI
JKL
On the 2nd row D&F are flipped, flip A&C to get them right
abC
DEF
GHI
JKL
The sequence so far is IEFAC
That leaves only A&B flipped. The sequences to fix them were given previously as
ABDFHIL and ABCGHIK
The full sequence is then
IEFACABDFHILABCGHIK
sorting and cancelling even pairs we get
ADEGIKL
I also asked about the solution for an NxM board:
As to an NxM board: The matrix is (NxM) on (NxM) and solving the matrix equation for any right hand side (i.e. original configuration) takes about (NxM)^3/3 operations (This can probably be done much more efficiently as the matrix is sparse). Note: I haven't proved yet that the matrix is non-singular for all N and M. In any case, if it is singular, the Gaussian elimination process will detect it and generate the configuration which is not solvable.
Yehuda
Update: fixed math logic. I originally wrote that you should apply "uniq" after sorting moves, but the correct function is to include a move once if there are an odd number of those moves in the sequence and not include it at all if there are an even number.
Technorati tags: board games, board game, abstract game, abstract games
Assume the game is laid out as follows:
ABC
DEF
GHI
JKL
Each location is either flipped up or down. Each move consists of selecting a location (e.g. B) and flipping both that location as well as all orthogonally adjacent locations (for B, this would mean locations B as well as A, C, and E). Your job is to flip them all up (or down) in the least number of moves.
The game is always solvable. Indeed, working from the bottom row upwards, it is trivial to bring all of them face up, except for the top row, which leaves only 2^3 possible "games". There are 12 "operators" corresponding to selecting one of the 12 positions to flip. It is trivial to see that these operators are commutative and idempotent (i.e. doing an operator twice is the identity and has no effect). Thus any sequence of moves is equivalent to choosing for each of the 12 operators to apply it either zero or one times, i.e. there are 2^12 different move sequences. If none of them repeat, then we can reach all 2^12 different board positions. If one board position repeats, then applying the two sequences one after another gives the identity position. I.e. there is a non-trivial sequence which is the identity. Performing Gaussian elimination on the transformation matrix shows that this can't occur. Indeed, the sequence to flip only A is
ABDFHIL
only B is
ABCGHIK
and only C is
BCDFGHJ
In other words, In any sequence of flips to solve the game, no piece ever has to be chosen twice, because a twice-chosen piece simply undoes what the first flip series did. You will never have ...B....B... to solve this puzzle. That means that any board can be completely solved in 12 moves or less!
To understand why you only need to know how to solve A, B, and C, consider the following:
To solve the bottom three pieces J, K, and L, you only have to flip some from the third row of pieces G, H, and I. To solve the third row, flip the second row. To solve the second row, flip the first row. That means that you will always be left with some combination of A, B, and C to finish up. Add the corresponding sequences to the flips, and you finish the puzzle.
Now, to get the smallest number of steps, add all of these flips together in a row, sort, cancel all even pairs, and the result is your solution.
Let me show you how to solve the case where only L is flipped and I think the rest will be clear:
ABC
DEF
GHI
JKl
On the bottom (4th) row, only L is flipped. Flip I to get it right:
ABC
DEf
Ghi
JKL
On the 3rd row, H&I are flipped. Flip E&F to get them right.
Abc
dEf
GHI
JKL
On the 2nd row D&F are flipped, flip A&C to get them right
abC
DEF
GHI
JKL
The sequence so far is IEFAC
That leaves only A&B flipped. The sequences to fix them were given previously as
ABDFHIL and ABCGHIK
The full sequence is then
IEFACABDFHILABCGHIK
sorting and cancelling even pairs we get
ADEGIKL
I also asked about the solution for an NxM board:
As to an NxM board: The matrix is (NxM) on (NxM) and solving the matrix equation for any right hand side (i.e. original configuration) takes about (NxM)^3/3 operations (This can probably be done much more efficiently as the matrix is sparse). Note: I haven't proved yet that the matrix is non-singular for all N and M. In any case, if it is singular, the Gaussian elimination process will detect it and generate the configuration which is not solvable.
Yehuda
Update: fixed math logic. I originally wrote that you should apply "uniq" after sorting moves, but the correct function is to include a move once if there are an odd number of those moves in the sequence and not include it at all if there are an even number.
Technorati tags: board games, board game, abstract game, abstract games
Session Report Up
The latest session report from the JSGC is here. Games played: AD&D 2nd ed., Shadows Over Camelot.
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