Monday, January 09, 2012

Beyond Maths Trades

The maths traders in Australia were discussing whether it was possible in a maths trade to offer multiple items in exchange for one in a maths trade. No it's not, it doesn't even nearly work for reasons which are obvious to mathematicians. However I thought about it for a bit, and realised that with the introduction of a pricing mechanism, there can be such a trade. So I borrowed some symbols from the Z Notation (in which I was trained as an undergrad) and wrote this spec:

Let I be the set of items in the trade.
Let U be the set of users in the trade.
Let P be the set of prices, objects that can be summed and are totally ordered.

# every item has an owner, "\fun" means total function
owns : I \fun U

 # if you don't own anything you're not in trade
ran(owns) = U

# some people assign values to some things, "\pfun" means partial function
values : U \cross I \pfun P

# For each user u, there is a function vu, which is the values that user places on items
vu = { (i,p) | (u,i) \mapsto p \in values }

# and that user at least values the things they own
\forallu:U @ owns~\limg{u}\rimg \subseteq dom(vu)

# Then a valid solution to the trade is an assignment of items to users
s : I \pfun U

# the items received by u are
ru = s~\limg{u}\rimg

# the items sent by u are
su = owns~\limg{u}\rimg \cat ran(s)

# such that nothing is assigned to the person it came from
s \cap owns = \emptyset

# and everyone gets a bargain, by their own personal pricing rules
\forallu:ran(s) @ Σ (i \in ru) vu(i) \geq Σ (i \in su) vu(i)

# For a solution to be useful, it must be non-trivial:
\neq \emptyset

# and furthermore, we would like to restrict ourselves to minimal solutions so as to not make offered trades incomprehensibly complex, so if t is a solution, then t is not a subset of s (can't find the right symbols to write that!)

It occurs to me that blogspot is maybe not the ideal medium for writing specifications.

Thursday, January 05, 2012

The Numbers for 2011

Wow, I am really crap at blogging these days! When I started blogging, Facebook hadn't been invented, so if I wanted to say something I had to say it here. These days there are too many distractions.

2007 article
2008 article
2009 article
2010 article

There are 448 games in this collection (last year 424).

The BGG average rating for this collection is 6.43 (last year 6.4).

Your average rating for this collection is 7.04 (last year 7.07).

On average you have played each of these games 7.75 times (last year 7.11). 

Your Friendless Metric is 1 (102 games played 10+ times, 46 games never played.) (last year 1, 89, 46) 

Your Continuous Friendless Metric is 3.49 which corresponds to an average utilisation of 55.24%. (last year 3.39, 55.24%)

So I had a bit of a blowout in the collection in 2011. Apart from the bonus influx from the Cochabamba competition, I added a few (notably, Thunderstone and a lot of expansions), and got rid of hardly any. That's about to change, but it hasn't yet. Also in 2011 I set up Scrabblette with her own games shelf so she can see how many games she's responsible for us owning (and not playing).

I didn't do a whole lot of face-to-face gaming in 2011, but I did join up at, and played a great many good games many times. I also played a great many mediocre games many times. Luckily Yucata keeps adding new stuff and I keep changing what I play. Also relevantly, I acquired Yspahan, Oregon, Famiglia and Thunderstone after playing them on Yucata. Each of those got a lot of plays, and so didn't affect my stats too much. I do feel kinda dodgy that I have played the physical copy a couple of times, and the on-line game 50 times, and it counts as 50 plays for me, but that's a dodginess I can live with. There are also some games I own that I play on Yucata but will remove from my collection, and some that I will continue to enjoy to play on-line and in real life.

During the year I *did* manage to achieve my goal of 55% utilisation, after trying for several years. I'm fairly impressed that I managed to maintain that even with the Cochabamba influx.

For 2012, my goal is to decrease the number of games I own. Since I have games lying all over the game room bench, that's pretty much necessary now. However I enoyed the Cochabamba gamefest so much that I intend to do a similar thing this year, i.e. acquire a bunch of games I know nothing about and figure them out and play them. Of course Tom won't be around to send them to me, so I'll have to pay for them myself... which is why I hope to sell a truckload of games from my collection. Trading *would* be an option if there were lots of new cool games up for trade in Australia, but there is not, so I'll just have to take money for them. If Scrabblette asks, that's why all those games are lying all over the game room bench.