“RISKy Business: An In-Depth Look at the Game RISK” marks a helpful
correction in the details provided by an earlier paper. The paper recalculates transition
state probabilities in a correct manner and explores a new direction in allowing a variable
number of sides on the dice rolled.
The earlier paper by Baris Tan: “Markov Chains and the RISK Board Game” does
have a number of mistakes this manuscript corrects. One of those is the miscalculation of
probabilities due to the lack of independence in the comparison of dice rolls. The correct
treatment of the probabilities involved is given by Sharon Blatt.
Another error in the original paper that Blatt claims is present is the fact that one
army can attack. This is not entirely an error, and depends on ones interpretation of
“attacking army.” Baris Tan states on his second page (page 150 of that issue of
Mathematics Magazine): “a territory may be attacked by a player who at least two armies
(one to keep on the territory and one to attack) on a neighbor territory.” This seems to
imply that the number of armies present in the territory from which a player attacks are
not the number of attacking armies to Baris Tan. Thus his allowance of the number of
attacking armies to go to zero fits his implied definition of an attacking army, since at
least one army must be left in the territory and this army is not included in the number of
attacking armies. Despite the fact that Baris Tan seems to be following the actual rules of
the game of RISK here, this allowance on the part of his definition, forces players to
subtract one from the number of armies present in a territory they are attacking from to be
able to use his results. This change is confusing and Blatt’s treatment is more clear.
On the other hand, Baris Tan has linked together various portions of his paper
better, for instance between the first and second sentences, where a reader feels that the
author will expand upon or lead from the first sentence to more. Instead though the
article goes off without another mention of this, relying completely on Tan’s treatment of
the topic. A couple of similar transitions rather than relying on Tan’s earlier treatment to
cover the wholes would be helpful.
Tan also comes up with charts and exams how the mathematics can effect strategy
while Blatt leaves this out. Inclusion of the charts and a short discussion of the resulting
strategy would increase make Blatt’s paper quite a bit better. Also in the second section,
Blatt makes the claim that the game must be won by conquering all the territories, but
this is not true if the game is played with missions. This was addressed in the prior paper
by Tan but not here by Blatt.
Finally, a couple of small grammatical mistakes should be fixed up. For instance,
in the second to last paragraph of section 5, the period at the end of the 4th sentence has a
space before it and should be moved adjacent to the word that precedes it. In section 6
immediately above the S matrix the portion should read: “...the resultant matrix, S, is
calculated....” where a comma is placed after S. The last grammatical correction that
should be made that I noticed was in the 2nd paragraph of section 7, the middle of the
second sentence has “....an continent...” and should read “...a continent...”
All in all with a couple of small corrections this is a nice correction to a prior
mistake dealing with how mathematics can be used to help strategy development in a
game such as RISK.