Contents -> Rambling Mind Blasts -> Blokus Strategy
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I'm fascinated by a relatively new game called Blokus. There are some strategy tips provided on the instruction sheet and on the Blokus web site (where you can also play online), but I've been thinking about it so much I thought I'd take a shot at an approach of my own.
Wikipedia, of course, has a good article on the game too.
The Game
The object of Blokus is to place 21 pieces onto a 20 by 20 board (400 positions) such that one is left with as few piece squares as possible. Each piece is comprised of one to five squares in various geometries. There are four sets of pieces and two to four players play at a time, but all four sets of pieces are always used, e.g. if two players are playing each player plays two colors at a time. The catch is that the pieces you lay down on the board can only touch at the corners as opposed to on an edge. Also, the first move a player makes must cover one of the boards four corners. One gains extra points for playing all their pieces and an extra bonus if the last piece played is the piece with only one square.
I've played several games so far and it much more complex than it seems on the surface. You can play it online or pick up a physical game. Either way I would encourage you to check it out. I took it into The Daily Dose and played with John Flowers and some other patrons. It generated interest in all that played.
Observations
Obviously, not all pieces are equal. Area is a major factor since one wants to minimize the piece squares not placed by the end of the game. However, another factor that needs to be considered are the number of corners. Since connections can only be made at the useable corners, pieces with many corners create more opportunities to lay out down other pieces.
If I take a look at the ratio of useable corners to area, I end up with the following piece order: 1, 2, 4, 21, 7, 9, 18, 20, 3, 6, 12, 15, 16, 19, 5, 8, 11, 17, 14, 13 and 10. Interestingly enough, the piece that gains bonus points if played last, and tends to "open up" areas of the board when boxed in, turns out to have the "best" corner to area ratio.
Another factor is edge space. Edge space is bad but in a different way than area. An edge represents lost opportunity since it blocks adjacent board space from play by other pieces of the same color. Pieces with small edge to area take up a maximum amount of space while blocking a minimal number of adjacent spaces. In some cases, two edges block the same adjacent space thus reducing the "edge penalty."
Dividing the corners by the edge (blocked space) to area ratio, results in what I'll call the CEA score (Corner-Edge-Area Score). The larger the CEA, the more corners I gain and I use the maximum amount of area while minimizing the amount of blocked adjacent space. Ranking the pieces by CEA, I end up with: 1, 21, 18, 2, 7, 9, 12, 15, 16, 19, 4, 6, 20, 11, 17, 3, 5, 14, 10, 13 and 8.
This yields four clusters of pieces whose area is 5: 21-18, 12-15-16-19, 20-11-17, and 14-10-13. Note that piece 21 actually cannot be played first because the rules require that the first move cover one of the four far corners of the board.
Next Game Approach
Given these observations, the next game I play I will:
Proof in the Pudding
That's the idea at least. Can't wait until next time I have an opportunity to play and try it out. You can download the piece reference card and piece analysis matrix I put together to support this post. Let me know if you have an opportunity to try these observations.
P. Todd
None
March 17, 2006
This was an interesting read. I'm anxious to try this strategy. Thanks for the analysis. --Don Bradford
October 18, 2006
Nice little write-up. You probably know you can try these out right away at Blokus.com, where they host games for free.
I like your analysis, and much of it matches the strategies that I've developed just using intuition. However, I would never use 10 or 14 as forays into enemy territory. They are too easy to blok out. 10 is a great edge piece (to "sneak past" an encroaching opponent) and 14 is the ultimate, lockdown bloker, which I usually use the first time is within striking distance in the board's center.
Happy blokusing. --Tom
January 9, 2007
I LOVE BLOKUS. You are my hero. Thanks to you I was able to beat my 5 year old son's "W" strategy in Blokus and even create some pretties along the way. Thanks for everything. If my email doesn't work try tami_jammi@hotmail.com!
BLOCKUS YEA BABY. --Tami Eshleman
January 10, 2007
Very intriguing. Look forward to trying this out. Thanks. --Greg
