October 15, 2012

Horse 1378 - Boardo

I played a game of Monopoly at the weekend; not surprisingly it resulted in unhappiness (I won). The reason I won is purely down to knowing one of the basic mechanisms of the game; this is where we begin the story.

Monopoly is played with two six-sided dice. There are 36 ways to roll two dice but there are 16/36 ways to roll numbers between 6-8; that is almost one half of the total possible dice rolls.
The most commonly landed on space is "jail". There are Community Chest and Chance cards which direct you to go there, a square on the board which sends you there and if you roll three doubles, you also go there. The next commonly landed on space is Go because of operation of the Community Chest and Chance cards.
It therefore follows that the most profitable squares to own on the Monopoly board are the ones 6-8 spaces away from Jail and Go. These spaces fall in the brown set (Bow St, Marlborough St, Vine St) and the light blue set (The Angel Islington, Euston Rd, Pentonville Rd).
I weaseled my way to owning the brown set.

If you think about other games, they provide interesting mathematical thought puzzles.
The game Candyland which is usually only played by anyone over the age of 8 because they want to play with someone younger, requires zero decision making because quite literally every move is directed by the cards. Candyland is a classic zero player game because the player can make no difference to the outcome of the game and although the result is unknown before the start, it has a predetermined outcome.

A game like Sorry which also is directed by cards, has decision making but not the chance element as directed by dice. The order of movement is directed from the outset. If the unturned card is a 5, it will always be a five.
Snakes & Ladders on the other hand has chance but no decision making. If you roll a 3, you move three spaces and are directed to move upwards or downwards by the directions on the board; that's it.

I like card games but again we find something interesting. There is usually quite a complex decision making process but either the order of the cards in s central stockpile is fixed or in the case of trick taking games, once a card has been played, it is gone. If I have in my hand the King of Hearts, then unless you are playing with multiple decks, no-one else does. A lot of card games including those at casinos can have elements of card counting to them.
I've found Bridge players to be exceptionally excellent at tracking each and every one of 52 cards in a deck. Of the group whom I usually play Bridge with, there are two ladies who on the surface have lovely conversations about their family and like to gossip, however we suspect that secretly, they have named every card in the deck. If for example "Maria and Todd aren't getting along" we can infer that the person holds the Queen and Ace of Spades (Black Maria being the queen, and the German word for death is Tod which described the "death card" or the Ace of Spades).
Games like Poker which is shown on television almost as a sport, is more about a psychological showdown of players than about the cards which they happen to possess.

Recently on this blog I have spoken of the game Risk. The board itself is a largish network of unevenly joined spaces, the reward system is uneven, there is a high element of decision making and there is an element of chance. As far as fixed square board games go, it is very complex and is only really matched in terms of complexity by tabletop war games.
Tabletop war games are possibly the ultimate expression of complexity if you include them as board games. In most cases, different troops have different movement rates, they aren't restricted in terms of direction that they can move, different games have inbuilt reward and punishment structures and in a lot of cases even the size of the dice are unequal (D4 up to D100 and beyond).
This is when describing a game mathematically starts to become useless and instead of looking at fixed positions we start to look at general trends. Taken to its most complex, game theory itself is sometimes used in applications far beyond mere board games and is applied to such things as behavioral psychology, economics, epidemiology etc. all of which are a far far cry from a game like Monopoly.

Then there are quiz type games like Trivial Pursuit which I happen to hate. These games generally reward so called "knowledge". My problem with quizzes is that they tend to act like Sorry or Snakes and Ladders in that you either do or don't know the answer to the question. There is no skill or decision making involved other than rolling a die and moving a piece.
Games like Taboo, Balderdash and Pictionary which are based on Victorian era parlour games tend to be much more enjoyable because even if you possess no skill whatsoever, you can still find fun in the inherent comedy of the game.

Aside: I should explain the title to this post.
Boardo is the second most complex game in the world. It ranks only behind Mornington Crescent in terms of unfathomability.
Boardo is a board game with its origins a tangled fusion of snakes and ladders, Monopoly, chess, Trivial Pursuit and Scrabble, in some versions with optional card games thrown in as well. Players take it in turns to roll the dice (although not always) and make a move, in the logical direction, to their destination. Once there, they have to obey the rules that pertain to that location. Play must not go against the grain, nor can anyone farkle three times in a row without immediate suspension from the game.
Link: http://kevan.org/morningtonia.pl?Boardo

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