CyberKev and I have been discussing the Friendless metric. You see, the problem is that he's got his above zero, which is a great thing... but let us recap for those of you who don't know what a Friendless metric is. The problem with a large games collection is that you spent a lot of money on a lot of games, and some of them don't get played. In fact, many of them don't get played. You, the non-gamer, may be chortling to yourself thinking "hah, I knew he didn't really buy those games to play - he's just a spendthrift / show-off / wanker / (d) all of the above"... but common wisdom is that 50% of board games never get played. Many are bought as gifts for nephews and nieces who never bother to read the rules. So even though I have 50 games I've never played, that's only 14% of my collection, and I'm doing very well.
A lot of boardgamegeeks keep track of when they play what game on boardgamegeek.com. This satisfies a primal geek instinct to gather statistics about ourselves, and will one day provide an anthropologist with awesome data for a Ph.D. thesis on collecting, leisure and obsession. One of the purposes to which I put this data is to answer the question "do I really need all these games?" It's geek angst.
Now if I had only a copy of Scrabble, and I'd played it 173 times, I could safely answer "yes". If I had 10,000 games and had still only played Scrabble, I could safely answer "no" (though collecting games is a totally different matter and I don't address that here). So the point is to compare the games you have to the games you play to provide some measure of how much you're really using all those games. That's what the Friendless metric attempts to do.
To calculate the Friendless metric, make a list of all of your games in descending order of how many times you've played them. Scrabble with 173 plays comes first, Triominos with 0 plays comes last. For each game at the beginning with 10 or more plays, we consider that game to have earned its keep. Even better, having played one game that many times, you're forgiven one at the other end which you haven't played so much. So for playing Scrabble so many times we'll forgive you for never playing Triominos. People who play games tend to accumulate them, so we'll assume that was a gift. Then, we look at how many times you've played the last game remaining on the list... and that's your Friendless metric. The higher the better. Most bggeeks have a value of zero, so I extended the definition to go into negatives. A value of -x tells you that to get to a Friendless metric of 1 you need to play x more of your games that you've never played. Mine has been between -8 and -2 for most of the year, and just today reached 1 for the first time! Woohoo!
Now, as mentioned above, CyberKev reached positive numbers a few months ago. This is a great piece of news - it means that he's utilising his game collection. However, when his Friendless metric reached 3, CyberKev noticed that there was no longer any reward in playing his unplayed games. By playing an unplayed game he moves that game from 0 plays to 1 play... but his Friendless metric is 3, so that game is still one of the ones which is forgiven anyway. In fact, that game has to get to 4 plays before it has any chance of affecting the Friendless metric. And NO WAY is CyberKev going to play Triominos 4 times (of course, he could just get rid of it - that works very nicely). So the problem with the Friendless metric is that once it gets to 1 it fails in one of its primary aims - to encourage you to play all of your games.
What we need then is a continuous Friendless metric - one which rewards all plays, rather than just a few games you've played 9 times and a few games you've played a number of times equal to your Friendless metric. I've been thinking about this since CyberKev explained the problem to me, but just this evening I think I've come up with a nice solution. The design goal is to reward you (i.e. make your number higher) for playing ALL of your games. Also, to reward you for playing those infrequently played games more than for playing the frequently played ones. That may not make much sense at first, but consider that it actually encourages you to dispose of infrequently played games so that your collection more closely resembles what you actually will play - if you're not going to play this game, you can benefit by not even having it! And finally, a minor goal was to reward even plays of frequently played games, just a little bit.
Consideration of the shape of the reward curve I wanted led me to the exponential distribution. Basically there's a big reward for a first play, and smaller rewards for subsequent plays. The distribution has a parameter called lambda which controls how quickly the rewards drop off (and how long they last). I experimented, and it felt right to me to set lambda to 0.3. Don't worry, I'll explain.
Consider it like this. If you play a game 0 times, you get 0% of the possible reward for it. If you play a game an infinite number of times, you get 100% of the possible reward for it. With lambda set at 0.3, if you play a game once you get 26% of the possible reward for it. And as you get more plays you proceed to 45%, 59%, 70%, 78%, 83%, 88%, 91%, 93%, 95%, and so on with diminishing returns for each play. (This is the cumulative distribution function.) Those numbers feel vaguely right to me.
So, for each game I calculate what percentage of the possible reward you've achieved. I then averaged those numbers, and displayed the percentage. But then I realised, in one of the AHA! moments, that I could turn that percentage back into a number of plays, to a number that was like an average number of plays, but wasn't really. So I coded up the inverse of the CDF and the magic numbers started coming out.
My CFM is (currently) 2.45. My average number of plays per game owned is 4.5 Those numbers are comparable. In fact, if I'd played every game in my collection the same number of times, they would be the same. So the difference is the penalty for owning games I don't play.
I have 350 games of which I've never played 51. My other test subject has 198 games, which he has played an average of 11.6 times each, but he has a CFM of 1.18. Why is that? Well, it turns out that the gentleman is a Magic: the Gathering player who plays LOTS and LOTS of Magic. So his mean plays per game is very much distorted by that. Of his 198 games, he hasn't ever played 113 of them. So my collection much more accurately matches what I play.
I like this number. It feels beautiful. Comments?
BTW, the stats with these numbers in are hosted at http://friendless.servegame.org/stats/. More on that tomorrow.
Saturday, October 27, 2007
Thursday, October 25, 2007
Playing Super Scrabble With Myself
With Scrabblette allegedly studying this evening, I set myself a project of playing Super Scrabble Solitaire. Super Scrabble is just like normal Scrabble with but a 21x21 board and 200 tiles, so roughly twice as large. Also, the tile mix is slightly friendlier - proportionally there are fewer Js and Vs and more Ts and Ss.
I thought about the assessment rules on the train on the way home. It would be possible to attempt to set myself up for a really big score through careful planning... get the Q on the quadruple letter score, and the Z on the triple word score, and so on, but that would be really boring and not at all like the real game. So to compare games of solitaire Super Scrabble I will compare average points per turn. Hence I'm usually motivated to play the best word for any move. I did find myself not wanting to waste spaces that I thought I could get a good score on. The 7 spaces where BENEFITS ended up was an example - I knew it would be easy to play a 7 letter bingo ending in S on a triple word score, so I left the spot available until I had one.
The game lasted 2.5 hours and I found myself tiring about halfway through. The board is so big and there are so many places to play (though not as many as you'd expect) that you get worn out trying to consider all of the possibilities. Sometimes I just played a word because I liked the word and wanted to remember it later - BIOTA, VATIC, ZORI, ARIEL. And sometimes I played a poor word to get rid of some letters to try to get something decent on my rack.
Here are the words and what they scored:
DICING 22
SPLINTS 36
JILT 27
MOAN 22
JEANS 24
TORNADO 66 (bingo #1)
VANE 38 - if there had been an L I could have played HEAVENLY!
YAWNED 30
AXON 40
PACE 44
COW 21
BENEFITS 77 (bingo #2)
DOCTOR 27
FUSED 23
GRUBS 38
BIOTA 24
CUE 10
SQUAT 77
PIXIES 69
DAMN 37
MOW 32
UNSATING 58 (bingo #3)
WONTS 40
WHY 30
ZEE 41
VATIC 20
HULK 38
PORGY 46
DIMMER 42
WEDGE 20
QI 21
EVER 16
KNEEL 18
ZITS 69
MANY 42
USHER 51
FIB 33
LARCH 44
ZORI 57
RAJ 28
IDLE 15
OVER 20
FORGED 39
HEAD 49
RAFTER 36
TUP 16
ARIEL 20
OFTEN 20
KNOT 28
TOE 17
ZIT 12
PI 6
for a total score of 1776 in 52 turns = 34.2 points per turn.
My impression is that rack management is more important in this game than in the small game. If you think 3 Us on your rack is bad, consider the possibility of having 7! Also, although scores were slightly higher than the original game, they weren't dramatically so. The quadruple letter tiles and quadruple word tiles are way out in the boondocks, and a word like WONTS on a DWS and QLS is worth 40, when in the original if you got it on a DWS and a TLS it would still be worth 32. If I average about 340 points per game, and this counts as 4 games, then that's about 30% higher. High yes, but not silly.
Anyway, this game was hard work. I allow myself to look in the dictionary (because I'm here to learn, not to compete fairly) and 2.5 hours of anagramming, considering possibilities and looking up words that don't exist (e.g. BIOTECH and FUNCTOR) sucks the energy out of you. That's why I have to go to bed now.
By the way, here is a photo of my niece, just because she's cute.
I thought about the assessment rules on the train on the way home. It would be possible to attempt to set myself up for a really big score through careful planning... get the Q on the quadruple letter score, and the Z on the triple word score, and so on, but that would be really boring and not at all like the real game. So to compare games of solitaire Super Scrabble I will compare average points per turn. Hence I'm usually motivated to play the best word for any move. I did find myself not wanting to waste spaces that I thought I could get a good score on. The 7 spaces where BENEFITS ended up was an example - I knew it would be easy to play a 7 letter bingo ending in S on a triple word score, so I left the spot available until I had one.
The game lasted 2.5 hours and I found myself tiring about halfway through. The board is so big and there are so many places to play (though not as many as you'd expect) that you get worn out trying to consider all of the possibilities. Sometimes I just played a word because I liked the word and wanted to remember it later - BIOTA, VATIC, ZORI, ARIEL. And sometimes I played a poor word to get rid of some letters to try to get something decent on my rack.
Here are the words and what they scored:DICING 22
SPLINTS 36
JILT 27
MOAN 22
JEANS 24
TORNADO 66 (bingo #1)
VANE 38 - if there had been an L I could have played HEAVENLY!
YAWNED 30
AXON 40
PACE 44
COW 21
BENEFITS 77 (bingo #2)
DOCTOR 27
FUSED 23
GRUBS 38
BIOTA 24
CUE 10
SQUAT 77
PIXIES 69
DAMN 37
MOW 32
UNSATING 58 (bingo #3)
WONTS 40
WHY 30
ZEE 41
VATIC 20
HULK 38
PORGY 46
DIMMER 42
WEDGE 20
QI 21
EVER 16
KNEEL 18
ZITS 69
MANY 42
USHER 51
FIB 33
LARCH 44
ZORI 57
RAJ 28
IDLE 15
OVER 20
FORGED 39
HEAD 49
RAFTER 36
TUP 16
ARIEL 20
OFTEN 20
KNOT 28
TOE 17
ZIT 12
PI 6
for a total score of 1776 in 52 turns = 34.2 points per turn.
My impression is that rack management is more important in this game than in the small game. If you think 3 Us on your rack is bad, consider the possibility of having 7! Also, although scores were slightly higher than the original game, they weren't dramatically so. The quadruple letter tiles and quadruple word tiles are way out in the boondocks, and a word like WONTS on a DWS and QLS is worth 40, when in the original if you got it on a DWS and a TLS it would still be worth 32. If I average about 340 points per game, and this counts as 4 games, then that's about 30% higher. High yes, but not silly.
Anyway, this game was hard work. I allow myself to look in the dictionary (because I'm here to learn, not to compete fairly) and 2.5 hours of anagramming, considering possibilities and looking up words that don't exist (e.g. BIOTECH and FUNCTOR) sucks the energy out of you. That's why I have to go to bed now.
By the way, here is a photo of my niece, just because she's cute.
Tuesday, October 16, 2007
SPONSORED BY FUNATICAL GAMES
During the week before the last Gathering of Friendless I realised my mate from Funatical Games had said "if there are any games you want to try out, just let me know". Funatical distributes Z-Man games (and others) in Australia, so there's lots of interesting stuff. Z-Man's quality varies, but they publish a lot of games. So my mate came over with a big pile of games which I had to quickly read the rules of in time for the Gathering.
This time, to avoid having 7 guests I invited 15 people, and still only 5 showed up. And Jane was late. So the 4 of us started with Ubongo because it's very pretty. CyberKev and I did very well, and it was very close at the end. In fact, if CyberKev hadn't accidentally played the easy side of the card, it might have been even closer. I don't know if I really go for the puzzle component, but for a puzzle game it's OK. I'll have to try it with the kids.
We then played Escalation where I suffered from having CyberKev sit to my right. That meant he could play bad cards at me, and I got badly hurt in several brawls. That meant I couldn't do much to hurt Scrabblette to my left, and she won easily. She also got very good cards, which didn't help. It's a silly game which is best played by kids. Still, it's better than Loot.
Still waiting for Jane, we tried a new word game, My Word. Note the lack of exclamation mark - it's not Reiner's game, it's one where you have to make a lattice of four letter words. We found this to be very good Scrabble training, which is OK if you want that sort of game (I do). We all learned some new four letter words, and looked strangely at some common words which just seemed wrong. CyberKev managed to set himself up for massive points a couple of times, and won easily.
Finally Jane arrived and we played Unspeakable Words to welcome her. Most of us already knew the rules (well, some of them), and it was nice to get into a game without any teaching. Ashley probably should have had some, but we figured he was a big boy who could look after himself. I like Unspeakable Words a lot. Scrabblette completely kicked our butts.
We then went on to Dragon Parade. I didn't have a lot of hope for this game, until we realised it was like Members Only, which I do like. Once I could see the strategy of it, and how nicely it was balanced, I decided I did quite like it. Scrabblette said afterwards she felt she couldn't control the dragon and didn't like it so much. I felt the dragon went where I told it to, and did like it. One complaint though - we ran out of scoring tokens after 4 rounds. We each gave 5 points back to the bank to complet the game. I pulled off a narrow win by foiling Ashley's evil plan to run the dragon out of town.
Jane then had to leave but Scrabblette was fired up and we played Midgard. I love the Norse theme, more than I like vikings really, so I was positively disposed towards it to start. When I read the rules I realised it was like El Grande light, which was not such a good thing. And playing a pissing war game against CyberKev is always dangerous. True to form, CyberKev rushed to the lead. True to form, no matter what I wanted someone else wanted it more. "I think I'll just grovel in this mud in last place"... "NO, THAT'S MY MUD! 20 VICTORY POINTS FOR MOST MUD!" Coming into the third era Scrabblette was one point behind CyberKev, though all I saw was CyberKev in front. I figured my best option was to hit him hard, and played a card which cost him maybe 20 points. However I hadn't noticed how strong Scrabblette's position was, and she went on to beat him by 23. Great... now she can kick my butt at pissing wars as well.
Anpther successful evening. We tried out 4 new games from Funatical, and crossed off another of my unplayed games. The kid says "climbed arc de trioumph and sacrificed my legs, 284 steps just to go up! luckily the eiffel tour as the locals call it has a lift!"
This time, to avoid having 7 guests I invited 15 people, and still only 5 showed up. And Jane was late. So the 4 of us started with Ubongo because it's very pretty. CyberKev and I did very well, and it was very close at the end. In fact, if CyberKev hadn't accidentally played the easy side of the card, it might have been even closer. I don't know if I really go for the puzzle component, but for a puzzle game it's OK. I'll have to try it with the kids.
We then played Escalation where I suffered from having CyberKev sit to my right. That meant he could play bad cards at me, and I got badly hurt in several brawls. That meant I couldn't do much to hurt Scrabblette to my left, and she won easily. She also got very good cards, which didn't help. It's a silly game which is best played by kids. Still, it's better than Loot.
Still waiting for Jane, we tried a new word game, My Word. Note the lack of exclamation mark - it's not Reiner's game, it's one where you have to make a lattice of four letter words. We found this to be very good Scrabble training, which is OK if you want that sort of game (I do). We all learned some new four letter words, and looked strangely at some common words which just seemed wrong. CyberKev managed to set himself up for massive points a couple of times, and won easily.
Finally Jane arrived and we played Unspeakable Words to welcome her. Most of us already knew the rules (well, some of them), and it was nice to get into a game without any teaching. Ashley probably should have had some, but we figured he was a big boy who could look after himself. I like Unspeakable Words a lot. Scrabblette completely kicked our butts.
We then went on to Dragon Parade. I didn't have a lot of hope for this game, until we realised it was like Members Only, which I do like. Once I could see the strategy of it, and how nicely it was balanced, I decided I did quite like it. Scrabblette said afterwards she felt she couldn't control the dragon and didn't like it so much. I felt the dragon went where I told it to, and did like it. One complaint though - we ran out of scoring tokens after 4 rounds. We each gave 5 points back to the bank to complet the game. I pulled off a narrow win by foiling Ashley's evil plan to run the dragon out of town.
Jane then had to leave but Scrabblette was fired up and we played Midgard. I love the Norse theme, more than I like vikings really, so I was positively disposed towards it to start. When I read the rules I realised it was like El Grande light, which was not such a good thing. And playing a pissing war game against CyberKev is always dangerous. True to form, CyberKev rushed to the lead. True to form, no matter what I wanted someone else wanted it more. "I think I'll just grovel in this mud in last place"... "NO, THAT'S MY MUD! 20 VICTORY POINTS FOR MOST MUD!" Coming into the third era Scrabblette was one point behind CyberKev, though all I saw was CyberKev in front. I figured my best option was to hit him hard, and played a card which cost him maybe 20 points. However I hadn't noticed how strong Scrabblette's position was, and she went on to beat him by 23. Great... now she can kick my butt at pissing wars as well.
Anpther successful evening. We tried out 4 new games from Funatical, and crossed off another of my unplayed games. The kid says "climbed arc de trioumph and sacrificed my legs, 284 steps just to go up! luckily the eiffel tour as the locals call it has a lift!"
THE SEVENTH GUEST
I just realised I'm a long way behind on session reports for The Gathering of Friendless. It's because I've been playing squash... of course... I play on Saturday morning, and I'm a useless lump of whining lard until Tuesday at least.
Anyway, Episode 3 of The Gathering of Friendless occurred a couple of weeks ago. The title of the episode was chosen because I was desperately trying to avoid having exactly 7 guests. Seven is the crappiest number for board-gaming. After you've played Shadows Over Camelot you're down to party-style games like Saboteur and The Great Dalmuti. They're fine games, but I prefer 3 or 4 player games on average. Sadly, 7 is a small enough number that it *seems* like there should be some better games to play, so people are reluctant to split into 2 tables. My theory is that with 6 players we could play, with 8 players I could convince people to split into 2 tables, but 7 is just very difficult so it's better avoided.
I took the approach of inviting 9 people and warning all of them that exactly 2 people not coming was unacceptable. They took me seriously, and 4 people didn't come along, leaving us with ... you do the maths... which is a fine number for games.
We started with Carcassonne in honour of the kid who'd visited the real place during the week. I realised that the game is much cleverer than I'd thought, and despite being flogged by CyberKev I increased my rating for it on BGG. All the tile types work together to contribute to the tension, and it's just such a clever game. I can't wait for the collectors' 3D edition (no, I haven't heard of such a thing. I made that up).
We then went on to Word Tower, because the ladies at the table like word games. For whatever reason, the ladies at the table were all at sea with this game, and it was a battle between CyberKev and I to rush to the win. CyberKev scored 4, I scored 5, Hubertus scored 1, and the ladies scored nothing at all. I believe male and female brains are different, and it seems this was a male-brain game.
We then tried out Tsuro, a very useful game which takes from 2 to 8 players. I've tried it with 2 and 5 and it was fine with both of those numbers. Scrabblette made the mistake of coming to attack me while sitting on my right. The second she approached I ran her off the board. A combination of experience and luck allowed me to see off the others well.
It was getting late, but we still had the stamina for Cartagena II. Actually, Jane didn't have the stamina. Jane had a nap. But the rest of us guessed what the rules were from the German and some discussion on BGG, and at least agreed on some rules to use in the absence of anything better. I figured out how to control the boat between the islands, and had 6 of my pirates in town before anyone else had 4.
I enjoyed the evening a lot. I played two games I'd bought but hadn't got to the table before, and we didn't have to play Shadows Over Camelot over and over and over.
Anyway, Episode 3 of The Gathering of Friendless occurred a couple of weeks ago. The title of the episode was chosen because I was desperately trying to avoid having exactly 7 guests. Seven is the crappiest number for board-gaming. After you've played Shadows Over Camelot you're down to party-style games like Saboteur and The Great Dalmuti. They're fine games, but I prefer 3 or 4 player games on average. Sadly, 7 is a small enough number that it *seems* like there should be some better games to play, so people are reluctant to split into 2 tables. My theory is that with 6 players we could play, with 8 players I could convince people to split into 2 tables, but 7 is just very difficult so it's better avoided.
I took the approach of inviting 9 people and warning all of them that exactly 2 people not coming was unacceptable. They took me seriously, and 4 people didn't come along, leaving us with ... you do the maths... which is a fine number for games.
We started with Carcassonne in honour of the kid who'd visited the real place during the week. I realised that the game is much cleverer than I'd thought, and despite being flogged by CyberKev I increased my rating for it on BGG. All the tile types work together to contribute to the tension, and it's just such a clever game. I can't wait for the collectors' 3D edition (no, I haven't heard of such a thing. I made that up).
We then went on to Word Tower, because the ladies at the table like word games. For whatever reason, the ladies at the table were all at sea with this game, and it was a battle between CyberKev and I to rush to the win. CyberKev scored 4, I scored 5, Hubertus scored 1, and the ladies scored nothing at all. I believe male and female brains are different, and it seems this was a male-brain game.
We then tried out Tsuro, a very useful game which takes from 2 to 8 players. I've tried it with 2 and 5 and it was fine with both of those numbers. Scrabblette made the mistake of coming to attack me while sitting on my right. The second she approached I ran her off the board. A combination of experience and luck allowed me to see off the others well.
It was getting late, but we still had the stamina for Cartagena II. Actually, Jane didn't have the stamina. Jane had a nap. But the rest of us guessed what the rules were from the German and some discussion on BGG, and at least agreed on some rules to use in the absence of anything better. I figured out how to control the boat between the islands, and had 6 of my pirates in town before anyone else had 4.
I enjoyed the evening a lot. I played two games I'd bought but hadn't got to the table before, and we didn't have to play Shadows Over Camelot over and over and over.
Sunday, October 07, 2007
Am I Getting Any Better at Scrabble?
I've been playing Scrabble on-line using the Scrabulous Facebook application, and Scrabble will become my most-played game for the year. I'd like to think I'm playing better even though I'm regularly losing to Scrabblette and Ashfallen, who are both very fine players. My scores for completed 2 player games on Facebook are: 382, 295, 304, 360, 389, 339, 336, 316, 289, 343 which is an average of 335.
My scores at Scrabble club last year were: 353, 367, 309, 435, 344, 381, 299, 358, 316, 236 which is an average of 340. Well that's a bit depressing. I'm finding fewer bingos at the moment, and that makes a big difference to scores. I hope it's just a run of bad luck.
Postscript: in the 10 Scrabble club games I made 8 bingos. In the 10 Scrabulous games I made 6 bingos. That more than accounts for the difference in scores.
My scores at Scrabble club last year were: 353, 367, 309, 435, 344, 381, 299, 358, 316, 236 which is an average of 340. Well that's a bit depressing. I'm finding fewer bingos at the moment, and that makes a big difference to scores. I hope it's just a run of bad luck.
Postscript: in the 10 Scrabble club games I made 8 bingos. In the 10 Scrabulous games I made 6 bingos. That more than accounts for the difference in scores.
Balanced Incomplete Block Designs and Steiner Triple Systems
When I was playing Take It Easy today I realised that the tiles formed a block design. So the thought immediately came to mind: "is there a Steiner Triple System in this game?" At this point you're thinking, "well duh, didn't you know that?" I guess I'm just slow.
A block design is a set of b subsets (called blocks) of a set X, each of size k. Set X has v elements, each of which appears in r blocks. In an incomplete block design, not all k-element subsets of of X are in the list of blocks. In a balanced incomplete block design (BIBD) there is a number λ such that any two elements of X appear in λ blocks together. This is called a (v, b, r, k, λ) BIBD.
Let me clarify. X = {1, 2, 3, 4, 5, 6, 7, 8, 9} so v=9. Each tile is a subset of size 3 of those numbers, so k=3. There are 27 tiles, so b=27. From this we can determine r... there are 27 tiles with 3 numbers each, so there are 81 numbers in all - and each can be one of 9 values, so each must appear 9 times, so r=9. It's true in a block design that v*r = k*b.
What about λ? 7 and 8 appear together on 3 tiles - with 1, 5, and 9. But how many times do 1 and 5 appear together on a tile? Never! So there is no value for λ and the block design is not balanced. That's a pity because I can't show you how λ*(v − 1) = r*(k − 1).
A Steiner triple system is a set of m elements with 3-element subsets such that for any two elements they appear together in exactly one 3-element subset.
Set contains a Steiner triple system - the subsets of size 3 are the sets, and for any two cards there is a unique third card which forms a set. For any two numbers which appear together on a tile, there are 3 such tiles on which they appear (e.g. 178, 578, 978). However it's not the case that on any two tiles there's a unique third tile which makes up the triple... e.g. 123 and 178. Unless we do something really cunning...
Take any two tiles. If they have two numbers in common, the third tile in the triple is the other tile with those two numbers on it. If the tiles have zero numbers in common, e.g. 123 and 578, the third tile is the tile with exactly the numbers that don't appear on either tile, so 946 in this case. That tile is unique. If the tiles have one number in common, then the third tile is the tile with that number and two completely different numbers, e.g. the third tile for 123 and 178 is 146. So now, given any two tiles there's a unique third tile forming the triple (or set). That's a Steiner triple system! Woohoo!
In fact, the simpler rule is that in each of the 3 positions on the tile the numbers must be all the same or all different. There are only 3 dimensions rather than 4, and Take It Easy has only 27 tiles instead of 81.
I decided long ago to collect games with Steiner triple systems so I guess I have to get Take It Easy now and I could use it to play Set. Hmm... could I use Set cards to play Take It Easy?
A block design is a set of b subsets (called blocks) of a set X, each of size k. Set X has v elements, each of which appears in r blocks. In an incomplete block design, not all k-element subsets of of X are in the list of blocks. In a balanced incomplete block design (BIBD) there is a number λ such that any two elements of X appear in λ blocks together. This is called a (v, b, r, k, λ) BIBD.
Let me clarify. X = {1, 2, 3, 4, 5, 6, 7, 8, 9} so v=9. Each tile is a subset of size 3 of those numbers, so k=3. There are 27 tiles, so b=27. From this we can determine r... there are 27 tiles with 3 numbers each, so there are 81 numbers in all - and each can be one of 9 values, so each must appear 9 times, so r=9. It's true in a block design that v*r = k*b.What about λ? 7 and 8 appear together on 3 tiles - with 1, 5, and 9. But how many times do 1 and 5 appear together on a tile? Never! So there is no value for λ and the block design is not balanced. That's a pity because I can't show you how λ*(v − 1) = r*(k − 1).
A Steiner triple system is a set of m elements with 3-element subsets such that for any two elements they appear together in exactly one 3-element subset.
Set contains a Steiner triple system - the subsets of size 3 are the sets, and for any two cards there is a unique third card which forms a set. For any two numbers which appear together on a tile, there are 3 such tiles on which they appear (e.g. 178, 578, 978). However it's not the case that on any two tiles there's a unique third tile which makes up the triple... e.g. 123 and 178. Unless we do something really cunning...Take any two tiles. If they have two numbers in common, the third tile in the triple is the other tile with those two numbers on it. If the tiles have zero numbers in common, e.g. 123 and 578, the third tile is the tile with exactly the numbers that don't appear on either tile, so 946 in this case. That tile is unique. If the tiles have one number in common, then the third tile is the tile with that number and two completely different numbers, e.g. the third tile for 123 and 178 is 146. So now, given any two tiles there's a unique third tile forming the triple (or set). That's a Steiner triple system! Woohoo!
In fact, the simpler rule is that in each of the 3 positions on the tile the numbers must be all the same or all different. There are only 3 dimensions rather than 4, and Take It Easy has only 27 tiles instead of 81.
I decided long ago to collect games with Steiner triple systems so I guess I have to get Take It Easy now and I could use it to play Set. Hmm... could I use Set cards to play Take It Easy?
Friday, October 05, 2007
Tsuro is the secret game of Metro
Once upon a time, CyberKev and I were discussing how I had won three games of Metro in a row and hence for the fourth game I was viciously targeted and completely annihilated. I don't know whether I really was good at Metro, but it felt like it to me - I knew what I was doing and played with confidence. I also remarked that apart from the obvious techniques of keeping your own tracks alive and screwing other players there was some sort of area control element to the game that I hadn't quite sorted out yet.
For example - your track is in the 2x2 area in the corner of the board. Say I can't (or choose not to) play a tile to terminate your track earning you only 3 points, but I may be able to play a tile such that there are no paths out of that area. (Note that there still may be paths in - in Metro, paths in (INs) and paths out (OUTs) are separate.) If I do that, you're as good as screwed. Inevitably your track will wander around that 2x2 area no matter what you do. The best bit is unless you understand the secret game of Metro you won't even know that I did that, and you'll think later it was just bad luck :-).
It's extremely hard to do this in Metro, because you only get one tile at a time, can't rotate it and you have so many things you need to achieve. However it's nice when you pull it off. Also, I'm not yet experienced enough to easily recognise the IN and OUT tracks.
Tsuro is an abstract game which is similar to Metro in some ways - you lay tiles with tracks on and your track terminating is bad. However in Tsuro you can turn the tiles any way you like, you only get one life and when you lose it you lose the game, and there are no INs and OUTs - a tile can switch INs and OUTs which can result in players colliding with each other (and that's bad for both of them). Also, you get 3 tiles to choose from, but only one place to play them, which is where you're going next.
The goal of the game in Tsuro is to stay alive, or alternatively, to make your opponents dead. You can achieve this by squeezing them for room in a Tron light-cycle like fashion, so there's nowhere for their track to go, or by simply avoiding them and hoping they crash first. In my experience, the two player game rewards aggression, and there's a slight resemblance to Hey! That's My Fish! where you're trying to claim territory. However, unlike Fish! and light cycles there are paths to escape from a blocked off territory. As your opponent, I want to minimise your escape paths if I can.
The two player game is strategic, as players compete for space to move in. The game takes up to 8 players, and as you add more players there are more interferences between players. If I place a tile that will determine where you go next you'll almost certainly be eliminated (sorry Scrabblette), so if you must be near someone try to make it a player on your left! I found that with more players the game was more chaotic as lots of players get forced into small spaces.
Tsuro is indeed the game I was thinking of when I hypothesized there was more to Metro than meets the eye. Surely with this extra experience I truly will become the Metro Master!
P.S. the kid says "um goin back 2 france tomorrow, colleseum wasnt that amazing roof that michealagelo painted wasnt that cool either. I think i like france better! (except the damn Keyboard!) Oh byea and wats Tsuru? How is Cartehgana 2?"
For example - your track is in the 2x2 area in the corner of the board. Say I can't (or choose not to) play a tile to terminate your track earning you only 3 points, but I may be able to play a tile such that there are no paths out of that area. (Note that there still may be paths in - in Metro, paths in (INs) and paths out (OUTs) are separate.) If I do that, you're as good as screwed. Inevitably your track will wander around that 2x2 area no matter what you do. The best bit is unless you understand the secret game of Metro you won't even know that I did that, and you'll think later it was just bad luck :-).
It's extremely hard to do this in Metro, because you only get one tile at a time, can't rotate it and you have so many things you need to achieve. However it's nice when you pull it off. Also, I'm not yet experienced enough to easily recognise the IN and OUT tracks.
Tsuro is an abstract game which is similar to Metro in some ways - you lay tiles with tracks on and your track terminating is bad. However in Tsuro you can turn the tiles any way you like, you only get one life and when you lose it you lose the game, and there are no INs and OUTs - a tile can switch INs and OUTs which can result in players colliding with each other (and that's bad for both of them). Also, you get 3 tiles to choose from, but only one place to play them, which is where you're going next.
The goal of the game in Tsuro is to stay alive, or alternatively, to make your opponents dead. You can achieve this by squeezing them for room in a Tron light-cycle like fashion, so there's nowhere for their track to go, or by simply avoiding them and hoping they crash first. In my experience, the two player game rewards aggression, and there's a slight resemblance to Hey! That's My Fish! where you're trying to claim territory. However, unlike Fish! and light cycles there are paths to escape from a blocked off territory. As your opponent, I want to minimise your escape paths if I can.
The two player game is strategic, as players compete for space to move in. The game takes up to 8 players, and as you add more players there are more interferences between players. If I place a tile that will determine where you go next you'll almost certainly be eliminated (sorry Scrabblette), so if you must be near someone try to make it a player on your left! I found that with more players the game was more chaotic as lots of players get forced into small spaces.
Tsuro is indeed the game I was thinking of when I hypothesized there was more to Metro than meets the eye. Surely with this extra experience I truly will become the Metro Master!
P.S. the kid says "um goin back 2 france tomorrow, colleseum wasnt that amazing roof that michealagelo painted wasnt that cool either. I think i like france better! (except the damn Keyboard!) Oh byea and wats Tsuru? How is Cartehgana 2?"
Tuesday, October 02, 2007
500 Games Rated!
I've reached 500 games rated at boardgamegeek.com! I registered there just under 3 years ago, so it's been a massive sustained and expensive effort since then. I own 348 games, so I guess the bulk of what I've played and rated has been paid for by my own wallet. Goodness. I could have invested in shares or something... if only I liked stock market games.
My extended stats say that I played 139 new games in 2005, 187 in 2006, and 112 so far this year. I guess those numbers don't include expansions. I've recorded 1809 plays in total, so about 1 in 4 times I play a game it's a new one.
My 10s are Trias, Scrabble, Mystery of the Abbey, Lord of the Rings: The Confrontation and a book (Connection Games by Cameron Browne). If I was to add another it might be a mathematically beautiful game like Hex or Twixt, but I don't get to play those often enough to be sure I really like them.
There are a lot of games that I rate a 1 or a 2, but they're mostly kids' games, party games, or just stupid things that shouldn't have been published in the first place. I save the real vitriol for the 3s - games that are obviously real games that I just detest. Here are some of my lowest rated "real games".
Maginor (2) - it's just Rock Paper Scissors. But without all the excitement.
Andromeda (3) - took way too long and wasn't very exciting for the second half.
Australia (3) - might go up a couple of rating points if it was rethemed. The theming is just so unlike the real Australia it annoys me.
Dante's Inferno (3) - when we played this the kid started cooperating with me just so we could finish the game. Interfering with another player costs too many resources to be worth it.
Niagara (3) - why does this game have gems? It's all about not falling off the waterfall. It's too annoying.
Railway Rivals (3) - one of the sorts of train games that I hate. Takes way too long.
Timbuktu (3) - it looks like a brain-burner, but it's completely random. A shame really, because it comes close to being a good game - nice bits, nice mechanics. But in the end, it's just not worth the time invested.
Dungeoneer (3) - lovely art work, but the rules were awful. I've decided that building a map out of playing cards just isn't pretty - tiles always work better. Some good ideas held together badly.
My extended stats say that I played 139 new games in 2005, 187 in 2006, and 112 so far this year. I guess those numbers don't include expansions. I've recorded 1809 plays in total, so about 1 in 4 times I play a game it's a new one.
My 10s are Trias, Scrabble, Mystery of the Abbey, Lord of the Rings: The Confrontation and a book (Connection Games by Cameron Browne). If I was to add another it might be a mathematically beautiful game like Hex or Twixt, but I don't get to play those often enough to be sure I really like them.
There are a lot of games that I rate a 1 or a 2, but they're mostly kids' games, party games, or just stupid things that shouldn't have been published in the first place. I save the real vitriol for the 3s - games that are obviously real games that I just detest. Here are some of my lowest rated "real games".
Maginor (2) - it's just Rock Paper Scissors. But without all the excitement.
Andromeda (3) - took way too long and wasn't very exciting for the second half.
Australia (3) - might go up a couple of rating points if it was rethemed. The theming is just so unlike the real Australia it annoys me.
Dante's Inferno (3) - when we played this the kid started cooperating with me just so we could finish the game. Interfering with another player costs too many resources to be worth it.
Niagara (3) - why does this game have gems? It's all about not falling off the waterfall. It's too annoying.
Railway Rivals (3) - one of the sorts of train games that I hate. Takes way too long.
Timbuktu (3) - it looks like a brain-burner, but it's completely random. A shame really, because it comes close to being a good game - nice bits, nice mechanics. But in the end, it's just not worth the time invested.
Dungeoneer (3) - lovely art work, but the rules were awful. I've decided that building a map out of playing cards just isn't pretty - tiles always work better. Some good ideas held together badly.
Sunday, September 23, 2007
The Big Magnus Spiele Order
Following my series of articles earlier this year (last year?) "They Have Some Really Good German Games in Germany", I rounded up some of Brisbane's most spendthrift gamers and made a big order from Magnus Spiele. The first box arrived on Friday so I carefully took photos so you could all share in the excitement.
As you can see, the box was wrapped in brown paper and sealed with wax, as well, so it was obvious customs / quarantine / drug lords hadn't opened it. Feeling like Howard Carter, I removed the outer layer of wrapping.
A perfectly preserved box! Wondering what treasures lay inside, I carefully cut the tape with the knife previously used on hundreds of IKEA flat packs.
Inside I found newspaper (German, I presume, though I didn't look) and plastic bags full of authentic German air. The very air that Einstein breathed! Hundreds of German air-borne viruses! If a butterfly's wings can cause a tornado, what disasters will result from this disruption of the natural order?
Nestled inside, the treasures themselves! Also, some German games catalogues and a Ticket to Ride Lite edition software CD. Should I play it myself or share it with the guys?
With trembling fingers I extracted the games themselves. Then I applied name stickers to each of them, while Scrabblette told me I was going to be late if I didn't have dinner the VERY INSTANT. I bet Howard Carter didn't get that.
Anyway, more news soon. Because the order was so big Magnus Spiele had to split it into two boxes. This is the small box.
BTW, the kid says "nothing happenin here. at shatoe manshion thing love u 2 bye!"
As you can see, the box was wrapped in brown paper and sealed with wax, as well, so it was obvious customs / quarantine / drug lords hadn't opened it. Feeling like Howard Carter, I removed the outer layer of wrapping.
A perfectly preserved box! Wondering what treasures lay inside, I carefully cut the tape with the knife previously used on hundreds of IKEA flat packs.
Inside I found newspaper (German, I presume, though I didn't look) and plastic bags full of authentic German air. The very air that Einstein breathed! Hundreds of German air-borne viruses! If a butterfly's wings can cause a tornado, what disasters will result from this disruption of the natural order?
Nestled inside, the treasures themselves! Also, some German games catalogues and a Ticket to Ride Lite edition software CD. Should I play it myself or share it with the guys?
With trembling fingers I extracted the games themselves. Then I applied name stickers to each of them, while Scrabblette told me I was going to be late if I didn't have dinner the VERY INSTANT. I bet Howard Carter didn't get that.Anyway, more news soon. Because the order was so big Magnus Spiele had to split it into two boxes. This is the small box.
BTW, the kid says "nothing happenin here. at shatoe manshion thing love u 2 bye!"
Thursday, September 20, 2007
TAKE ME AWAY TO MARSEILLES
The Gathering of Friendless Episode 2, "TAKE ME AWAY TO MARSEILLES", occurred last Friday. The kid was off to the south of France with his mum the next day so he visited me for one last gaming session before he went. (He'll be back next month.) All of the ladies invited declined their invitations for various reasons, e.g. Scrabblette had to study, so there were just five boys.
We started with Hamsterrolle while we were waiting for CyberKev to arrive. Some careless play by the kid and I saw our side get beaten badly by Ashley and Hubertus.
We then took advantage of Scrabblette's absence to play a game she hates - Ca$h'n'Gun$. It seems some female people have a real problem with a game where you points guns at people. I don't like guns at all (guns don't kill people, Americans kill people) but I can see the cleverness in the design. In the first game I was killed very quickly - obviously I should have chickened out a bit more but I couldn't believe how vindictive my opponents were - and Ashley won with $130K. In the second game we used special powers and I was the super-coward (+$5K for each chicken-out) so I was able to play defensively enough to survive and aggressively enough to win with $130K.
We then went on to the flagship game for the evening - Urland. I bought this from the U.S. when Scrabblette was there in April and hadn't played it yet, so I was itching for it. We eventually figured out why there were too many gene cards when CyberKev asked "John, did you buy the expansion?". Oh yeah, I remember there was an erweiterung in there somewhere. So I gave a fairly poor rules explanation - i.e. I read the rule book out - because although I'd read the rules they hadn't made enough sense to stick. The dummy player is a strange concept to me, and although it seemed to work OK I still don't really get it. The way the game progressed was that Ashley, Hubertus and the kid bid very high for gene cards, and CyberKev and I were much more conservative. CyberKev got no genes throughout the game, and I only got one. Mine was a good one though - FEET. Soon I was running all over the board and had an ictho in every area. It turned out that CyberKev and I had played right, as we were contending for the win coming into the final scoring. Luckily the rules favoured me, and I won with 35 points compared to CyberKev's 33.
Careful not to look at the clock, we gamed on. I suggested Cartagena which I think is a great simple game, easy to teach and intriguing for new players at least a couple of times. CyberKev said he never wins, so I thought I probably would. However he did win, by maybe 6 cards, over me. As expected, the newbies weren't competitive. The game rewards experience, but I think there might be a plateau where all players play at roughly the same level of ability.
It was then midnight but we were going strong. I suggested The Battle of Lanka, a card game which Scrabblette brought back from India. Don't you wish you had an international games courier :-) ? CyberKev and I and our lady partners had played this game 4 times earlier in the year, so CyberKev and I needed another play to get it onto our nickel lists. In the first game CyberKev won narrowly over me, and in the second game I won by a fair way over everyone else. In the second game I had a card CyberKev desperately needed but I discarded it for the kid instead. It's not a brilliant card game, but it's easy and asuras and rakshasas make a change from dwarves and elves occasionally.
Anyway, the next day the kid went to Dubai (Hey at Dubai goin 2 London now say hi 2 every 1 4 me by!) and London (Hey y'all how u goin? Goin 2 france 2morrow. london i amazin. tower sweet, lords huge, madam 2sards scary (4 me!) (is he alive?!) lol! bye!) and will be in France soon. "Gimme the sound of the rollin' dice, gimme a whiskey don't think twice, deal me the cards that take my blues away... TAKE ME AWAY TO MARSEILLES!"
We started with Hamsterrolle while we were waiting for CyberKev to arrive. Some careless play by the kid and I saw our side get beaten badly by Ashley and Hubertus.
We then took advantage of Scrabblette's absence to play a game she hates - Ca$h'n'Gun$. It seems some female people have a real problem with a game where you points guns at people. I don't like guns at all (guns don't kill people, Americans kill people) but I can see the cleverness in the design. In the first game I was killed very quickly - obviously I should have chickened out a bit more but I couldn't believe how vindictive my opponents were - and Ashley won with $130K. In the second game we used special powers and I was the super-coward (+$5K for each chicken-out) so I was able to play defensively enough to survive and aggressively enough to win with $130K.
We then went on to the flagship game for the evening - Urland. I bought this from the U.S. when Scrabblette was there in April and hadn't played it yet, so I was itching for it. We eventually figured out why there were too many gene cards when CyberKev asked "John, did you buy the expansion?". Oh yeah, I remember there was an erweiterung in there somewhere. So I gave a fairly poor rules explanation - i.e. I read the rule book out - because although I'd read the rules they hadn't made enough sense to stick. The dummy player is a strange concept to me, and although it seemed to work OK I still don't really get it. The way the game progressed was that Ashley, Hubertus and the kid bid very high for gene cards, and CyberKev and I were much more conservative. CyberKev got no genes throughout the game, and I only got one. Mine was a good one though - FEET. Soon I was running all over the board and had an ictho in every area. It turned out that CyberKev and I had played right, as we were contending for the win coming into the final scoring. Luckily the rules favoured me, and I won with 35 points compared to CyberKev's 33.
Careful not to look at the clock, we gamed on. I suggested Cartagena which I think is a great simple game, easy to teach and intriguing for new players at least a couple of times. CyberKev said he never wins, so I thought I probably would. However he did win, by maybe 6 cards, over me. As expected, the newbies weren't competitive. The game rewards experience, but I think there might be a plateau where all players play at roughly the same level of ability.
It was then midnight but we were going strong. I suggested The Battle of Lanka, a card game which Scrabblette brought back from India. Don't you wish you had an international games courier :-) ? CyberKev and I and our lady partners had played this game 4 times earlier in the year, so CyberKev and I needed another play to get it onto our nickel lists. In the first game CyberKev won narrowly over me, and in the second game I won by a fair way over everyone else. In the second game I had a card CyberKev desperately needed but I discarded it for the kid instead. It's not a brilliant card game, but it's easy and asuras and rakshasas make a change from dwarves and elves occasionally.
Anyway, the next day the kid went to Dubai (Hey at Dubai goin 2 London now say hi 2 every 1 4 me by!) and London (Hey y'all how u goin? Goin 2 france 2morrow. london i amazin. tower sweet, lords huge, madam 2sards scary (4 me!) (is he alive?!) lol! bye!) and will be in France soon. "Gimme the sound of the rollin' dice, gimme a whiskey don't think twice, deal me the cards that take my blues away... TAKE ME AWAY TO MARSEILLES!"
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