Lecture Notes in Computer Science- P59 pptx

5.3 Game Progress In the new edition of Ticket to Ride, we fixed some rules based on original rules be-cause of our ideal – combining the board game and three minimum spanning tree theo

(4) All the players have to learn the related knowledge about the shortest path algo-rithm and minimum spanning tree

5.3 Game Progress

In the new edition of Ticket to Ride, we fixed some rules based on original rules be-cause of our ideal – combining the board game and three minimum spanning tree theories The progress is likely the original game The difference between new and old edition games is that we gave the new game an additional element The element is the concept of start location and minimum spanning tree theories cards First, players should cast a start point and knowledge card Then, they should choose if they want them After casting start point and knowledge cards, players begin to a single turn

In the single turn, players can do three actions:

(1) Draw two of the railway cards or choose one which is opened directly

(2) Draw three of the 3 ticket cards, and reserve the selected ticket

(3) Re-cast new start point card and knowledge cards

(4) Put the railway carriages on the map to establish the route Players also can skip the step if there is no available condition

In principle, the game will repeat these four steps until a player rich the end condi-tions of single round game The game progress graph is shown in Fig.2

5.4 Game Regulations

There are the descriptions of the game regulations

(1) The station recorded in the starting point card has to match the stations in the knowledge card else the player cannot play the game (example is shown in Table 1)

(2) Regulations of drawing the railway card:

a Railway card color: white、black、red、yellow、orange、blue、purple、 green、full-color

b In the beginning of each round, the railway cards are divided into two piles One is composed of five opened cards and the other one is covered pile of cards

c When drawing the cards, each player can select two cards from the covered pile of cards else select the card from five opened cards It means player can get the wanted card which is opened

(3) Players can give up the knowledge card in hands, and player’s score will be detected according to the card Then the player proceeds game from pick up the starting point

(4) After the player completed one knowledge card, player can decide if he/she will continue draw next knowledge card or not

(5) Establish the player’s railway routes:

a The color of the railway card and spaces of the map routes are matched, then the railway cards can occupy the routes of the railway map The full-color card can occupy any color routes on the map For example, there are three white

280 W.-C Chang, Y.-D Chiu, and M.-F Li

spaces on the route [BRAGANCA-BENAVENTE], the player can occupy the route with three railway cards combination First one is three white railway cards; Second is two white and one full-color railway cards; Third is one white and two full-color railway cards; Fourth, three full-color railway cards The other card combinations are useless

b Grey route is available for all the colors For example, there are three grey spaces on the route [BRAGANCA-SALAMANCA], any kinds color of rail-way cards are acceptable, such as two orange and one red railrail-way cards

c The quantity of the railway cards and spaces of the map routes are matched, then the railway cards can occupy the routes of the railway map

d If the route of the map is occupied by other players, this route cannot be used

by others

5.5 Score Rules

The score rules of this game are listed in the following:

(1) The player will gain 10 score if the player used the most railway carriages (2) If the ticket card is completed, the player will get the score on the card On the country, the player did not complete the ticket card will deduct the score (3) The score of ticket card is calculated by the shortest path from starting point to destination For instance, the route For instance, the route, [VALENCA-VERIN] shortest path is 3 and the route [VALENCA-BRAGA] shortest path is 2, others are following the rules

(4) Knowledge card score consists of two parts; first one is partial score when the player completed part of the answer route, second is completed score when the player completed all the answer routes (example is shown in Table 2)

In order to encourage the player follow the correct algorithm, we give high scores for players We give a sample of Dijkstra’s algorithm in Table 2 When the player com-pleted one edge of the answer route and the railway carriages establish order is exactly the same as the Dijkstra’s algorithm, the player will get the score with three times of the spaces number of the edge The edge from VALENCA to VERIN has 3 spaces of railway carriage; the gaining score is 3*3=9

The completed score is based on the railway stations in the knowledge card After players completed the correct order of the algorithm, then players get the completed score

Table 1 Example of choosing start point card and knowledge card

The starting

point card player

owned

The recorded linked stations on the

knowledge card

Result

VILA REAL, BRAGANCA

Useless knowledge card

VERIN, BRAGANCA

Usable knowledge card

Fig 2 Single round for each player

282 W.-C Chang, Y.-D Chiu, and M.-F Li

Table 2 Example of accomplish Knowledge cards and ticket cards

Connected Railway

Stations Knowledge Partial Score Completed Score VALENCA,VERIN,BENAV

ENTE,BRAGANCA,CHAV

ES,BRAGA, PORTO

Dijkstra’s algorithm spaces number

of the route*3 14 VALENCA,VERIN,BENAV

ENTE,BRAGANCA,CHAV

ES,BRAGA, PORTO

Prim’s algorithm spaces number

of the route *2 14 VALENCA,VERIN,BENAV

ENTE,BRAGANCA,CHAV

ES,BRAGA

Prim’s algorithm spaces number

of the route *2 12

Table 3 Comparison with traditional Education and Teaching combining board game

Traditional Education Teaching minimum spanning tree theories combining

board game

Darren Lim ’s theory

Efficiency in

learning Teachers’ ability effect the level of

efficiency in learning.

Students can clarify their learning problem with game Students can clarify their learning

problem with game Interest in

learning Hard to let student interested in

learning.

Easier to make students interested in learning Easier to make students interested

in learning

Students’

feeling in

learning

spanning

three

theories.

Abstract Easier to catch the theories Easier to catch the

theories

Prepare

before

learning

None Students have to contact this

kind of knowledge before Students have to contact this kind of

knowledge before

Usable

computer

science

All computer sciences Graph theory Programming, Data Structure, Graph

Theory

6 Comparison

In this section, we compare this kind of teaching combining board game with tradi-tional education and Darren Lim’s theory [1] in several points of view in Table 3

After the comparison, we can clearly find the advantage in teaching minimum spanning tree theories combining board game These advantages are:

(1) Efficiently in learning: Students can use an existence to help them to learn, the minimum spanning tree theories are not abstracts, again

(2) Interest in learning: Because of this tool is game, so students can learn knowledge with playing game Anyway, playing is always funnier than sitting in the class-room

On the other hand, teaching minimum spanning tree theories combining board game also have a weak point Students have to know this kind knowledge first, then, they can use the game help learning, and Darren Lim’s theory is, too

Compare with Darren Lim’s theory, we can find Darren Lim’s theory can use in more computer science, but depth of implement, we have concreteness ideas

We made an additional comparison table shown in Table 4 In Table 4, we compare our ideal with Darren Lim’s theory in the points of view “how to implement”, “usable range”, and “if the ideal be computerized” We can dig out a characteristic in Darren Lim’s theory The characteristic is the theory can be use in widen range In the other hand, our ideal is better in having a clear and definite way to implement it

Table 4 Comparison with Darren Lim’s theory

Teaching minimum spanning tree theories combining board game

Darren Lim’s theory

If the ideal be

computerized?

How to teach these

concepts?

Have clear and definite rules to express concepts

Abstract ideal and no de-tailed description

Usable range in

computer science

Only in graph theory Not only in graph theory, but

also in data structure and programming

7 Conclusion

How to teach and learn the theories of graph is an important to teachers and students And, how to express some abstract knowledge concepts is difficult But there, we use game to express and help students to learn minimum spanning tree theories

By this way, we believe that these minimum spanning tree concepts can be learned much more efficiently If the idea – combining board game Ticket to Ride with minimum spanning tree theories can be cybernated, the speed of learning must be shorter and the efficiency would be higher

Acknowledgements

We would like to thank National Science Council and Chung Hua University This research was supported in part by a grant from NSC 96-2520-S-216-001 and CHU 96-2520-S-216-001, Taiwan, Republic of China This paper owes much to the thoughtful and helpful comments of the reviewers