Let's take a
look at one of the oldest board games to be played by two players: Backgammon.
It's a game that involves strategy and a bit of luck from the roll of the dice
to determine who wins. Backgammon is played by two people, where the board
itself consists of twenty four triangles called "points" divided up
into four quadrants of six triangles in each. The quadrants are the player's
home board and outer board, and the opponent's home board and outer board. The
home and outer boards are divided by a bar in the center, splitting it into a
left and right side as you can see here:
The objective of
the game is to move all your pieces, whichever color you are, to your home board and then take them off the
board in the process called "bearing off". The image above is the
standard setup for every Backgammon game. You each have fifteen pieces placed
in specific locations to start in every game and it's always those same spots.
To win, you have to move all of them into your home board as indicated above.
So if you are red, you have to move your pieces to the area labeled your
color's home board and your opponent is doing the same as well. The direction
you move the pieces depends on where your two pieces are on the board. In the
above image, red has the two pieces on the bottom right, so you would move the
red pieces clockwise, going through each quadrant to reach the color red's home
board. For white, the pieces would be moving the opposite direction as
indicated here:
To start, each person rolls one die and whoever rolls
higher goes first with the move from the two dice rolled. For example, if I
roll a 6 while my opponent rolls a 2, then I go first and make my move of 6 and 2. Moving around the board is simple: you
move one piece per each die you rolled or combine the roll to move a piece. If you choose to combine the roll,
let's say you rolled a 2 and a 5 so you would move a piece 7 spaces ahead, you
would move the piece by each die you rolled. In other words, you can't jump
ahead 7 spaces without moving 2 spaces first and then 5 or vice versa as well
as the condition that your opponent doesn't occupy either space ahead. If you
rolled doubles, then it's twice the rolls. If I roll two 5s, I can move four of
my pieces five spaces ahead or combine. You can move any piece ahead unless the
space is blocked by your opponent. A space on the board is blocked when your
opponent has at least two pieces on the space. However, if your opponent has
only one piece on the space, then you can attack their piece. Attacking results
in your opponent's piece being knocked onto the bar of the board where it has
to start from the beginning while your piece takes its spot. This is the part where strategy comes into
play. Leaving a piece alone by itself makes it vulnerable from being attacked
by your opponent.
If you get your piece attacked and
knocked onto the bar, then when it's your turn you must roll that piece back
onto the board before moving any other pieces. It would sound simple getting
the piece back onto the board but there's a problem with that: the quadrant
where you bring the piece back in is also your opponent's home board. This can
play as a strategy by your opponent when he gathers his pieces in the area
later on in the game. There could be some spaces occupied by your opponent
which would result in you having to roll a specific number to get the piece
back in. Even worse, it's possible to be unable to move your piece back onto
the board if all the six spaces are occupied by your opponent's pieces which
result in you wasting turns until one of the points becomes available.
Bearing off can only happen once all of
your pieces are in your home board. When it's your turn, you roll the dice to
bear off each piece. In your home board, the furthest triangle is 6 spaces away
to bear off, then the next is five spaces away, and so on. You can only bear
off pieces that are in that space that matches the dice roll. For instance, if
I roll a 4 and a 3, then I move a piece from the point that's four spaces away
to bear off and a piece from a point that's three spaces away. You win when you
get all of your pieces off the board first.
The math behind this game is more on the
lines of probability since you are using the dice to move around the board. In
an opening move there are certain moves that you can a make based on the roll
you get whether you went first or second. It also comes down to the probability
of getting a certain number you want to try to get ahead in the game. In a
scenario where your opponent occupies four points and you're trying to get a
piece onto the board, it would be simple to calculate it. You would multiply
the chance of not entering for each die as they are independent of one another,
then subtract that result from 1 as doing that would give you the probability
of entering. You would do this for each scenario and end up getting all of the
probabilities for each one. The example where your opponent has four points
occupied can be illustrated here to figure out the chances of entering your
piece back in:
p(not entering) = 4/6 x 4/6 =
16/36, p(entering) =1 - 16/36 = 20/36
There are different strategies you can
use to win Backgammon. The Running strategy involves moving your pieces as fast
as possible based on the roll of the dice and is ideal if you start out with
high numbers in the beginning. The Blitz involves attacking and sending their
pieces onto the bar which would slow them down as they would have to try to
roll them back in. Holding involves blocking points to make it difficult for
your opponent to bring them back in due to a lesser chance they would have
based on those probabilities discussed earlier. This is the basic game to play
without getting too technical as it would take more than 1,200 words to
completely explain the concept of the doubling cube and preferred opening moves.
From experience playing this game, I'd highly recommend it as something new to
try out.
Bibliography
Brown, Seth. "5
Simple Strategies to Win Backgammon." About.
About, 2014. Web. 20 Nov. 2014. <http://boardgames.about.com/od/backgammon/a/Basic-Backgammon-Strategy.htm>.
Keith, Tom.
"Backgammon Rules." Backgammon
Rules. Backgammon Galore, 2012. Web. 20 Nov. 2014.
<http://www.bkgm.com/rules.html>.
Packel, Edward. The Mathematics of Games and
Gambling. Washington: Math. Assoc. of America, 1977. Print.
I have never played backgammon before but it does seem like a fun game to play. At first look, this game seemed to be based on luck since you only roll dice, something you can't control, but it seems to be a little more complex than that. although the game doesn't look to be heavily based in math in order to win, it does appear to help if you want to know your probabilities.
ReplyDeleteI think this is a really fun and cool game, although I feel like it seems harder than it is. It seems like it's very fun playing on the probability chances and thinking of the different strategies to move your piece. The different strategies to winning were very interesting to read about, I really liked the Blitz strategy and the Holding strategy most of all. They seem very effective and involve a lot of strategizing, obviously.
ReplyDeleteI've heard of the game before but I have never played it. Your post was well written and helped me comprehend the game more! I did not know that this game was related to math. It's crazy to think of all the places that math actually shows up! Also all the different strategies were cool to read about!
ReplyDeleteI used to be really into the game of backgammon. I haven't played it in a bunch of years however. It was good to be able to read this and be reminded how to play. I'm curious if it would work best to stick to one strategy the entire game, or to switch up strategies? Maybe it would be good to start off by using the holding technique, then switch to a more aggressive tactic? I never got this far into it so i don't really have an idea though. However I thought this was well written and because of this post I may consider playing again in the future.
ReplyDeletebackgammon seems like a very interesting game and despite the necessity of there being some amount of luck from rolling the dice there is some skill involved in playing. i had never completely understood how to play until i read this post but now i somewhat understand how to play and i might start playing the game.
ReplyDeleteI have never played backgammon or any game similar to it. Grasping the rules and movements of the pieces was difficult at first but after watching a match on YouTube, I believe I would like to try and play the game. I believe all the rules of the game is what makes it so interesting to me and the math behind the game is very basic which makes the game more predictable.
ReplyDeleteI have never played backgammon or heard of it. You did a good job explaining how to play the game. It sounds like a fun game to play. You also did a good job explaining how the probabilities influences weather you win or not. I also liked how you explained what the different strategies are for winning the game.
ReplyDeleteI have never played backgammon but I've heard of it. I never really understood how to play the game, but you made it easy for me to get the gist of it. I really liked the strategies that you included as well!
ReplyDeleteI never really thought that there was a strategy to backgammon, I always just made moves more or less randomly. It's cool to now know of these strategies as well as the probabilities associated with them. It would definitely be cool to play and calculate the probabilities to try and chose the best option.
ReplyDeleteI haven't played this game yet but I always wondered how and what the purpose behind it was. Really well explained in the summary. I found it fascinating how the players need a strategy and a little bit of luck to win. It does stink though, how the players can end up starting all over when the pieces come into contact with the others.
ReplyDeleteThis game is seemingly a game of chance, even the strategies explained depend highly on the player getting lucky with the numbers he needs. It is highly similar to some travel board games I used to play when growing up. I like them because there is no better player at the game, assuming all fair players and non cheat in the rolling of the dice.
ReplyDeleteI never knew how to play backgammon before. I even had the game when I was younger but I never understood it. This summary of the game really helped me understand the game a lot more. I knew what game it was right when I saw the pictures so I thought it was nice that you had the pictures. This was a good blog and hopefully now I can find the game and try to play it.
ReplyDeleteBackgammon was a very interesting topic. Although I have never played the game before and never knew the rules or point of the game, I found your blog very interesting. You did a great job at explaining the rules and point of the game. I feel like something that you could have gone into a little more was strategy, for instance, is there any strategy in sacrificing a piece? But I did like the probabilities. They were really thought provoking, especially in that I think it would be amazing if someone could calculate every single probability and play the game solely based off of them.
ReplyDelete