Sunday, February 15, 2009

The Physics of Candyland

Candyland is something of an enigma to me. It has been a lurking frustration for many months now – it is simply confounding in nature. I do not refer to why parents continue relentlessly torturing their children with such a device, that is easily solved (they do not know any better, much as the teacher yelling at her Linux-using disciple does not know of the world outside the Windows).
No, here I refer to something much more intricate, something that didn't occur to me until I needed a frame of reference. I have written the occasional review over at Board Game Geek (http://www.boardgamegeek.com), and in doing so have attempted to come to a more precise definition of what I like and do not like about the game I am reviewing. One aspect of games I generally tend to dislike heavily is the random one. It bothers me, and almost always feels lazy at lack of a more precise solution to a mechanical problem. There are notable exceptions, and impressive instances of mitigating such luck. That is not the point here. I decided to utilize a randomness scale, from 1-5 stars, in each review. While only an estimate in each case, this scale would depend upon how much random luck the game featured, and would be subsequently reduced by the amount it is mitigated or confined to the game opening solely.
This led me to another thought: what are the extrema here? What is the maximum amount of luck possible in a game, I asked myself. The answer turned directly to Candyland. What is the minimum amount of luck possible in a game? One which is entirely predetermined, where a player cannot even use a random method to make a decision. A labyrinth, in other words.
The astute reader will see where this is headed. Candyland *is* an entirely predetermined game from the onset. Assuming no extra shuffles are necessary, or that three decks are used in the initial shuffle, once you pull that first card, there is nothing you can do to change things. Your fate is sealed, you just don't know where it will lead. This differentiates itself from a game in which one rolls dice or shuffles cards several times during play, which is certainly random, and subject to completely random effects as the game progresses.
So now we see the confusion. How can the most random game possible also be the least random game possible?
A potential answer, perhaps, lies in quantum mechanics, specifically in the infamous Schroedinger's cat analogy.
For the uninitiated, here is the analogy: a cat exists with a cyanide capsule inside a sealed box. Every second the cat remains in there, there is a certain probability (p) the capsule will open, killing the cat instantly. When you open the safe, will you find a dead cat or an alive cat? Was the cat dead or alive *before* you opened the safe? The obvious answer upon opening the safe is that there is a certain probability (P) that the cat has died in the given time, and a certain probability (1 – P) that the cat is still alive. Once you open the safe, you know for certain one way or another, for sure (this is called “collapsing the wavefunction”).
The interesting part comes from the state of the cat before opening the safe. While no observers are around, the cat is *both* dead and alive at the same time. This is of course a silly result, and it is often refuted with an easy claim that the quantum universe does not apply to a macroscopic one (half of all quantum effects cancel out once you are dealing with just 2 particles – a single mole is composed of 10^23 atoms) (hence, the cat is never both dead and alive). But at the quantum level, this sort of thing does happen, this does exist.
The question here is, can we consider a theoretical random color spectrum with a given probability of turning up each turn as not macroscopic in nature and therefore applicable to quantum effects, or is each card a macroscopic entity with the information imprinted upon it being dependent upon the card itself, leading to a nullification of any and all quantum effects? Is any possible quantum effect here largely canceled due to the number of cards necessary to play a complete game?
In the meantime, Candyland will remain something of an enigma to me.

1 comment:

Kimberly said...

I wasn't sure if you are active on another game site, but I liked your top 10 of 2009 article and that you've played Samarkand: Routes to Riches recently.

I would like you to know that the owner of Queen Games, Rajive Gupta, will be at the large Queen Games booth (701) at Origins on Thursday and Friday. Please stop by and say hello. If you want to schedule a specific time to meet with Rajive, please let me know and I can schedule that for you as well. We value your opinion.

P.S. We will be at GenCon as well if you are going to miss Origins this year.

my regards,

Kimberly Tolson
Manager of North American Operations
Queen Games
k.tolson@queen-games.de
405.334.9538