A Continuous Friendless Metric

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.

A Cosmic Encounter

We played Cosmic Encounter on Wednesday night at Book Realm. Cosmic is not really my kinda game, but forces conspired against me. You see Trevor had managed to buy the ancient 2nd edition complete with all expansions in useable condition for $A5, when it's worth up to $US300. We know this because Cyberkev is a Cosmic guru, so when Trevor and Cyberkev and RealmKeeper and Ozvortex and I sat down to play, I thought it only fair that we try out Trevor's treasure.

First discovery was that although the cards and special powers were present, the tokens and "who you have to attack" counters were not all there, so we cannibalised some bits from other games. We took the pirates from Cartagena and put them in the draw string bag from Ingenious to decide who should be attacked. I used influence markers from Go West as my tokens, and RealmKeeper and Trevor used pretty glass stones from Magic as their tokens.

I won't go through the specifics of the game, because I can't remember them, so I'll tell you about the special powers. I was Boomerang. This meant when you attack me, I get to attack you first. That seemed like a quicker way to die, to me, but as Cyberkev pointed out, it means you get lots more opportunities to capture bases which is how you win the game. Trevor was Skeptic, which meant that he was constantly telling people "I don't think you can win", and on several occasions they agreed with him and backed off. Cyberkev was Vulch, meaning that he picked up all of the used Edicts. So if you wanted to use something against him, you had to give it to him. Andrew was Delegator, meaning that he could change the primary player in conflicts. I found that so annoying that I didn't call him as an ally very much. Ozvortex was the Will, meaning he could choose the opponent and planet he wanted to attack. It didn't seem to help though.

So the Delegator was by far the most annoying. Realmkeeper got somewhat shafted because he had bad cards and after a couple of times where he switched someone's attack out from under them he didn't get invited back and wasn't able to use them up to get new ones. Ozvortex had a fist full of cards, and once I managed to take 4 of them as consolation. Shortly after, I compromised with him, and as giving me a base would have won the game for me, I convinced him to give me his whole hand instead. Both times, I got a heap of Edict cards, and had to spend time thinking about how I could use them to my advantage.

Eventually, as will happen with sort of game where it is so easy to pick on the leader, we had 4 bases each. I attacked Trevor on my turn, and he called for all allies. The Delegator joined in, and made Cyberkev the primary opponent rather than Trevor. We played our cards, and I was well and truly defeated, which I had expected because I had such bad attack cards. But I did have an Edict that said both of those attack cards were Compromises. That meant Cyberkev and I had to make a deal, so we traded a base for a base and shared the win.

I was pleased that it was Cyberkev I had dealt with there, as I thought he would take the win. Trevor might have refused, because he likes to fight. Ozvortex probably would have agreed, Realmkeeper could have gone either way depending on his whim. But I thought Cyberkev would find it very hard to refuse a chance to share a win. As it was, I think he considered his chances of winning some other way, and decided that sharing a win with me was his best outcome, on average.

So that was my second game of Cosmic, what do I think? Well my 6.5 rating at BGG remains unchanged. It's an alright game, but I just can't get into the negotiation of allies. Sure, I could try to be charming or friendly or loyal or intimidating or whatever to try to gain support, but I know that most people I play with will ally with me based on their best interests, not my personal skill. So it was no surprise to me when all 5 of us had 4 bases, because nobody was stupid enough to let someone else win. We might as well shorten the game and play for 1 base each. I definitely prefer analytical games, where I can harness the resources of my massive brain to crush my opponents... or not.

Coincidentally, on Thursday night we played Mall of Horror which requires much the same negotation skills as Cosmic. Sadly I was so tired on Thursday night because I couldn't sleep Wednesday night because Cosmic Encounter had pumped me up so much, that I was flat all through the game. I made a bad mistake to get my gunman killed, and fell out of contention 2/3 of the way through the game. Mall of Horror is another game that I would play again, but wouldn't rush to.

Probably my favourite of this genre of game is Ca$h'n Gun$, maybe because you can always chicken out when you've got guns pointed at you, and that means you only die if you're not careful, and the game becomes a struggle to balance caution and greed. Also it's a bit quicker, so there's less time spent negotiating, and it's funny to shoot kids.