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Subject: Dummy player for 2 player games rss

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Thomas Franke
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There has been a discussion about the 2 player suitability of Automobile (http://www.boardgamegeek.com/thread/414372/) and also a session report about playing with 2p without changing too much in the game (http://www.boardgamegeek.com/thread/417959), which seems to have worked relatively well.

However, one opinion in the first thread was, that a dummy player might be needed to simulate a 3p game, in order to generate more tension.

Having read this, I became interested and tried to devise a simple AI for such a Dummy. At the moment, it is not playtested, but simply based on some calculations, as I do not possess the game myself, just played at the local gaming group.

But if you are interested, feel free to add your thoughts or test it at home and add your experiences.

The Dummy is not meant to be a "real" player, but simply a means of creating multi-player tension in a 2p game. As he cheats substantially, he s not scored to compare to the human players results.

The rules and routines of the Dummy AI are laid out according to the game phases, with some general rules at the beginning.

Dummy player for 2 player Automobile

You need a D6 for determining some of the dummy player’s actions.

General rules:
The dummy player (called Dummy) needs no money for his actions and does never collect loss cubes.

Therefore, Dummy needs no parts factory.

Factory building
Whenever Dummy builds one or more factories, he tries to build ahead of the most advanced occupied model space.

a. If his R&D cubes allow for a choice, the actual model space is determined with the die:

Example for different numbers of R&D in Dummy’s supply:
1-2 R&D cubes: build just ahead of most advanced model space

3-5 R&D cubes:
--> Roll die:
1-3 on D6: build in next model space and pay 1 cube
4-6 on D6: skip one model space and pay 3 cubes

6-9 R&D cubes:
--> Roll die:
1-2 on D6: build in next model space and pay 1 cube
3-4 on D6: skip one model space and pay 3 cubes
5-6 on D6: skip two model spaces and pay 6 cubes

In the improbable case that he has more than ten cubes, Dummy proceeds respectively - just using single die results - and rerolling, if he rolls too high (e.g. reroll a 4-6 with 10-14 cubes as you could skip at most 3 spaces).

b. If Dummy does not have any R&D cubes at all, he upgrades his most advanced non-level-3 factory.

Phases:

1. Draw demand tiles
No difference to human player.

2. Select characters
a. In the first round Dummy always selects first
b. The character is selected by rolling the D6 (1=Ford ... 6=Chrysler)
c. Reroll, if the rolled character is already occupied by a human player or Durant is rolled and the Dummy has no un-built factories.
d. With Durant: Build one factory in a model space as described under General rules.

3. Player actions - 3 rounds
a. Dummy’s general action pattern is the following:
i. Build two factories (see General rules) if available, else just one
ii. Place three Distributors on the mid-price box if available, else the rest remaining. If none, take R&D cubes.
iii. Produce cars: Dummy produces in all of his factories. The number of produced cars is always just above or below the average production capacity of each model space and is determined by a 50:50 D6 roll.

Examples:
Luxury cars:
1 factory: 1-3 on D6: 1 car, 4-6 on D6: 2 cars (average: 1,5)
2 factories: 1-3 on D6: 3 cars, 4-6 on D6: 4 cars (average: 3,5)
3 factories: 1-3 on D6: 5 cars, 4-6 on D6: 6 cars (average: 5,5)

Mid-priced cars:
1 factory: 1-3 on D6: 1 car, 4-6 on D6: 3 cars (average: 2)
2 factories: 1-3 on D6: 5 cars, 4-6 on D6: 6 cars (average: 5,5)
3 factories: 1-3 on D6: 9 cars, 4-6 on D6: 10 cars (average: 9,5)

Low-priced cars:
1 factory: 1-3 on D6: 2 car, 4-6 on D6: 3 cars (average: 2,5)
2 factories: 1-3 on D6: 6 cars, 4-6 on D6: 8 cars (average: 7)
3 factories: 1-3 on D6: 11 cars, 4-6 on D6: 13 cars (average: 12)

b. If Dummy has no un-built factories at the beginning of the Player action phase, the action pattern is changed:
i. Close down the factory/factories on the most dated model space
ii. Build two factories (see General rules) if available, else just one
iii. Produce cars: see above

c. If Dummy has selected Ford and has 3 un-built factories, he will build three factories with his build action.
Otherwise, the building of new, more advanced factories takes precedence over upgrading an existing one with the Ford action.

4. Sell cars via Howard (individual decision for each car)
a. If Dummy has produced cars for which there are no demand tiles (e.g. luxury or low-priced on turn one), he sells this type of cars.

b. In the first round, if Dummy produced low-priced as well as luxury cars, the latter have a higher priority.

c. If Dummy has only produced car types with demand tiles, he tries to estimate the ratio of supply vs. demand, and will sell those cars with the highest expected over-supply or lowest under-supply.

To do so, he calculates the expected supply averages with:
i. 3,5 per tile in the first turn (and for the single tiles in turn 3 and 4)
ii. 3 per tile for the lower demand type in turns 2-4
iii. 4 per tile for the higher demand type in turns 2-4

Examples:
Turn 1 mid-price demand: 3,5 * 3 = 10,5
Turn 2 low-price demand: 3 * 3 = 9
Turn 2 mid-price demand: 3 * 4 = 12
Turn 3 luxury demand: 3,5
Turn 4 low-price demand: 3 * 4 + 3,5 = 15,5

So in Turn 2, Dummy would sell 2 mid-priced cars via Howard, if there are e.g. 11 low-price cars and 16 mid-priced cars produced (11-9=2 < 16-12=4).
On the other hand he would have sold two low-priced cars, if the production would have been low-priced 8 and mid-priced 9 (8-9=-1 > 9-12=-3).

In case of a tie, the higher priced cars take precedence.

d. If there is a choice, cars are taken from the model space with the most cars and in case of a tie from the most outdated one.

5. Sell cars via distributors
a. If Dummy still has produced cars for which there are no demand tiles (e.g. luxury or low-priced on turn one), he sells these first using distributors on the luxury/low-priced-boxes first, if possible.

b. In the first round, if Dummy produced low-priced as well as luxury cars, the latter have a higher priority.

c. For car types with demand tiles, if there is a choice, Dummy proceeds as described in 4c., using distributors on the luxury/low-priced boxes first, if possible.

d. If there is a choice, cars are taken from the model space with the most cars and in case of a tie from the most outdated one (individual decision for each car).

6.Executive decisions
a. If Dummy has no more un-built factories in his supply, he chooses the Close factory action - if available - as his first Executive decision (with the exception of Turn 4).

b. Else (or in later rounds of executive decisions), if the calculation described in 4c. (taking into consideration only cars still unsold) results in an estimated over-supply of 3 or more for a type of car, that Dummy and at least one other player still have to sell, Dummy chooses the leftmost executive action he can afford (R&D cube wise).

c. If there is more than one type of car, for which the condition in 6b. is true, Dummy tries to take an executive action for each of these types.

d. In this case, the priority of the types is determined by the size of the estimated oversupply (first executive action for higher over-supply). In case of a tie, the higher priced cars take precedence.

e. The gained bonus sale or price reduction tokens are placed in the model space with the most cars and in case of a tie on the most outdated one (individual decision for each car).

7. Sell cars via demand tiles
No difference to human player.
8. Losses
Dummy never takes loss cubes
9. End of turn
No difference to human player.


As I said above, I tried to do a really simple AI (and I think it is simpler than it initially looks like, as there is some redundancy and a lot of examples of and some general principles are true for several game situations. These relatively simple rules, however could only be achieved, by letting the Dummy cheat substantially, i.e. he needs no money at all. I wouldn't say he plays like a real player at all, but I think he could pose kind of a challenge in a two player game.

Feedback welcome!
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Corin A. Friesen
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The one problem I see (and I have only read half of this good article for lack of time, I'll come back for more) is with the demand tiles. I'm not saying it's a problem with the actual system, but the dummy player is an AUI (Artificial UnIntelligence) which will make random moves. This means you cannot try to figure out what tile he is holding based on his moves, which would detract from the gameplay, though might lead to some dynamic games!

Otherwise, great in theory.
 
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Thomas Franke
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That's right. But judging from my limited play experience, it is not exactly easy to guess the other players demand tiles from their moves (perhaps easier once they know what they do). Therefore, I try to stick with average values modified by the knowledge of my own tiles.

Regarding numbers of production, the amounts do not change too much randomly with the Dummy, so they can be taken into consideration for ones own production decisions.
And even when the Dummy totally specializes in one type of car, he should usually be able to sell most of them due to high distributor use and only around average production per factory. Only with third turn low price models and luxury cars he tends to overproduce a bit.

However, the human players would be wise to stay out of this market then (depending on the position of the model psaces of course).

P.S.: I like the term AUI. blush

I do think however, that some random element has to be included for a Dummy player in any case. Otherwise, the human player who knows and executes the AI would always know exactly how it acts in advance, whereas the other player (who is probably not as well informed about the Dummy's programming) would have less information.
 
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