On three French web sites I discovered three different designs for pasang board.
2 Tours de Jeu, a site documenting rules for strategy games, exhibits a simple makeshift pasang board. The pieces are placed inside squares (just like checkers and chess), a departure from the conventional placement on grid intersections. This is not really unusual; an early non-libre version of Pasang Emas included a theme which departed similarly from the convention. What is really unusual is the set of rules for the game. It is totally different from what Pasang Emas implements. This unusual version of pasang is described by R C Bell in his book "Discovering Old Board Games".
Some people dispute the accuracy of Bell's account. But I do not currently wish to go into that debate. I wouldn't be surprised either way.
Association pour Vivre l'AutoGestion, a social club for family entertainment, has this catalogue of rental games. Page 25 of this catalogue shows an ornamented pasang board. You have got to see it to believe it. The French are adding a dash of their own art to the Brunei game. That's truly multi-cultural.
Geoludie has an online catalogue of world games for sale. It includes what appears to be a modern looking pasang board with small plastic marbles as pieces (unless my discernment has failed me and those are actually computer generated). Geoludie's pasang has 2 sets of rules: the one described by Bell and the one implemented by Pasang Emas. (Geoludie actually contacted me in 2006 regarding the irreconcilable differences between the two versions. So, they are in business of selling pasang for a long time already). The unusual use of marbles (placed presumably inside shallow cups on the board) is based on Bell's description of the game. Having played Chinese checkers using marbles on a holey board, I can attest the practicality of that design.
17 March 2018: Edited to replace broken links with Wayback Machine
November 16, 2010
November 11, 2010
Game complexity
I instrumented Pasang Emas to collect statistics on its games. I set the demo mode to play weak against weak, weak against strong, and strong against strong. The following results were gathered from observing more than 3,000 games and more than 170,000 board positions. The results are not sensitive to the strength of the players.
Branching factors
In the opening stage, exactly 11 possible moves are available for the first player and 10 for the second.
In the kas selection stage, an average of 31 possible moves are available. The number will be less if we "merge" different moves that result in identical situations. Theoretically, the maximum branching factor during this stage is 50. This was indeed witnessed during the experiment.
In the rest of the game, a player has an average of 6 possible moves to choose from at each turn. This is very much less than the theoretical maximum of 40. Indeed, the maximum seen during the experiment was only 26.
Overall, the average branching factor is 7.
Game length
Since there are 118 pieces to capture, and each move is a capture move, the game obviously cannot exceed 118 plies. The longest game seen was 94 plies.
On average, a game takes 56 plies.
Complexity
The mode (12%) of the branching factors is 5. So, we can estimate the size of the game tree (ignoring the "zeroth" move, that of choosing a pattern to start the game) as 556, which is approximately 1039.
If we use the mean value 7 for the branching factor, the estimated tree size is 756, or approximately 2 x 1047.
A better estimate is to use the distribution of the branching factors. Here is a breakdown:
The above distribution is used in the following Ruby code to estimate the tree size:
The above code gives an estimated game tree size of 6 x 1042. (Using a more accurate breakdown from the raw data does not significantly change the result).
Average capture
Since there are 118 pieces to capture and the average game length is 56 plies, the average number of pieces captured by a move might be mistakenly taken as 118/56 = 2.1. But this is not the case. About 50% of the games observed during the experiment ended up in suntuk. The average number of pieces captured per move was only 1.9.
Branching factors
In the opening stage, exactly 11 possible moves are available for the first player and 10 for the second.
In the kas selection stage, an average of 31 possible moves are available. The number will be less if we "merge" different moves that result in identical situations. Theoretically, the maximum branching factor during this stage is 50. This was indeed witnessed during the experiment.
In the rest of the game, a player has an average of 6 possible moves to choose from at each turn. This is very much less than the theoretical maximum of 40. Indeed, the maximum seen during the experiment was only 26.
Overall, the average branching factor is 7.
Game length
Since there are 118 pieces to capture, and each move is a capture move, the game obviously cannot exceed 118 plies. The longest game seen was 94 plies.
On average, a game takes 56 plies.
Complexity
The mode (12%) of the branching factors is 5. So, we can estimate the size of the game tree (ignoring the "zeroth" move, that of choosing a pattern to start the game) as 556, which is approximately 1039.
If we use the mean value 7 for the branching factor, the estimated tree size is 756, or approximately 2 x 1047.
A better estimate is to use the distribution of the branching factors. Here is a breakdown:
| branches | frequency | ||
|---|---|---|---|
| 1 | 3% | ||
| 2 | 7% | ||
| 3 | 9% | ||
| 4 | 11% | ||
| 5 | 12% | ||
| 6 | 11% | ||
| 7 | 10% | ||
| 8 | 8% | ||
| 9 | 6% | ||
| 10 | 6% | ||
| 11 | 5% | ||
| 12 | 2% | ||
| 13 | 1% | ||
| 14 | 1% | ||
| 15 or more | 8% |
The above distribution is used in the following Ruby code to estimate the tree size:
f = [3, 7, 9, 11, 12, 11, 10, 8, 6, 6, 5, 2, 1, 1, 8]
s = 1
f.each_with_index { |n, i| s = s * (i+1) ** (n/100.0 * 56) }
puts s
The above code gives an estimated game tree size of 6 x 1042. (Using a more accurate breakdown from the raw data does not significantly change the result).
Average capture
Since there are 118 pieces to capture and the average game length is 56 plies, the average number of pieces captured by a move might be mistakenly taken as 118/56 = 2.1. But this is not the case. About 50% of the games observed during the experiment ended up in suntuk. The average number of pieces captured per move was only 1.9.
August 11, 2010
Pasang Emas won awards
Pasang Emas won the following BICTA 2010 awards:
- third place in the "industry" category, and
- the Made-in-Brunei Award.
July 31, 2010
Official boost for Pasang Emas
The Authority for Info-communication Technology Industry of Brunei Darussalam (AITI) hosted a ceremony to hand over copies of Pasang Emas to the Ministry of Education.
Media coverage of the ceremony:
Our photographer was unusually negligent during the ceremony. After the ceremony, we had this photo taken of the three people who made Pasang Emas a reality: the initiator, the developer and the mentor.
Media coverage of the ceremony:
Our photographer was unusually negligent during the ceremony. After the ceremony, we had this photo taken of the three people who made Pasang Emas a reality: the initiator, the developer and the mentor.
July 27, 2010
Lilliputians play pasang too!
"Majlis Ilmu" is an annual event to commemorate the birthday of His Majesty the Sultan of Brunei.
This year, pasang was featured rather prominently in the exhibition gallery of Majlis Ilmu. Three different renditions of the game were exhibited. There were the usual,
the giant,
and the electronic.
There was also a luxurious board, placed high on an exhibition rack, away from naughty hands that might tarnish its beauty.
Another traditional game, congkak, was also exhibited.
On a pasang board, there is usually a square cup in the middle called "gadong".
The "gadong" is not really significant to the game. It is used to keep pieces, or, if you make it large, to restrain playful kids!
After successfully testing that unorthodox feature, the kids were released unharmed. By then they were subdued enough to give a good demonstration of the game.
They were playing against a pair of formidable opponents.
Visitors witnessed a fierce battle. Capture! Capture! No mercy!
After the throng of visitors subsided, two key people in the development of Pasang Emas posed in front of their baby.
And the four fighting kids were friends again.
This year, pasang was featured rather prominently in the exhibition gallery of Majlis Ilmu. Three different renditions of the game were exhibited. There were the usual,
the giant,
and the electronic.
There was also a luxurious board, placed high on an exhibition rack, away from naughty hands that might tarnish its beauty.
Another traditional game, congkak, was also exhibited.
On a pasang board, there is usually a square cup in the middle called "gadong".
The "gadong" is not really significant to the game. It is used to keep pieces, or, if you make it large, to restrain playful kids!
After successfully testing that unorthodox feature, the kids were released unharmed. By then they were subdued enough to give a good demonstration of the game.
They were playing against a pair of formidable opponents.
Visitors witnessed a fierce battle. Capture! Capture! No mercy!
After the throng of visitors subsided, two key people in the development of Pasang Emas posed in front of their baby.
And the four fighting kids were friends again.
July 8, 2010
Network play
Pasang Emas version 3.0.0 comes with a new feature. It is now possible to play against your friends across the network. Here is a screen shot of the network dialog:
The game server was running in the same computer from which I took the screen shot, thus the name "localhost" for the server. The server currently does not perform authentication, thus the missing entry box for password.
Five other players were already logged in. The three players with status "Waiting" were really netcat session. I used netcat to debug the game protocol and preserve my sanity. The two players with status "Playing" were actual Pasang Emas sessions running on separate computers in a lab.
The game server was running in the same computer from which I took the screen shot, thus the name "localhost" for the server. The server currently does not perform authentication, thus the missing entry box for password.
Five other players were already logged in. The three players with status "Waiting" were really netcat session. I used netcat to debug the game protocol and preserve my sanity. The two players with status "Playing" were actual Pasang Emas sessions running on separate computers in a lab.
May 24, 2010
How it really looks like
A primary school teacher posted this blog entry containing many pictures showing pasang boards the way they are traditionally made. Notice the "cup" in the middle of each board. This cup, called "gadong", plays no part in the game. The first player is supposed to accumulate her bounties in there, while the second player puts hers on the table. The game is in no way affected if this purely ornamental rule is not observed. In fact this cup actually blocks from view pieces near the centre.
When I learnt pasang, my mentor lent me a set with wooden pieces. I think that's the way they were traditionally made. But the bulky wooden pieces, which must have been a hassle to make, gave way to the more convenient and cute coat buttons, conveniently available at the nearest supermarket at a very affordable price. Two themes in an early version of Pasang Emas parodied this button-using trend. Notice in some of the pictures the use of red and bluish buttons for the kas. Red and blue combination is a convention introduced by Pasang Emas.
Jabatan Muzium-Muzium (Department of Museums) published reference cards showing traditional opening arrangements. You can see these cards in some of the pictures.
A secondary school posted this blog entry showing pictures of students learning pasang. Here again we can see the unmistakable traditional board dotted with tailor buttons. The man with the white cap must be the instructor. Indeed he must be. He is my pasang mentor.
When I learnt pasang, my mentor lent me a set with wooden pieces. I think that's the way they were traditionally made. But the bulky wooden pieces, which must have been a hassle to make, gave way to the more convenient and cute coat buttons, conveniently available at the nearest supermarket at a very affordable price. Two themes in an early version of Pasang Emas parodied this button-using trend. Notice in some of the pictures the use of red and bluish buttons for the kas. Red and blue combination is a convention introduced by Pasang Emas.
Jabatan Muzium-Muzium (Department of Museums) published reference cards showing traditional opening arrangements. You can see these cards in some of the pictures.
A secondary school posted this blog entry showing pictures of students learning pasang. Here again we can see the unmistakable traditional board dotted with tailor buttons. The man with the white cap must be the instructor. Indeed he must be. He is my pasang mentor.
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