capabilities) as possible.” Surprisingly, it has turned out that it is not possible to use the features of PLACA because its definition [32] is not available (c.f. the footnote to the entry of [32] in the list of references for an explanation). Hence system requirement 10 is actually fulfilled#10, although not in the way it originally was intended.
21.3 Interpretation of System Test Results
Some insteresting statistics have been gathered during the system test described in chapter 20; these findings are summarised in table 20.1 on page 159.
The results show certain subtle points about the Haplomacy game and test bed, and about the playerACMEs. The points are not obvious from the data, but the statistics do however fit nicely with the general trends which were observed during a closer inspection of a series of simulated games.
21.3.1 Undecided Games
As many as 36.1% of the simulated games did not have a winner after 250 turns. It is quite possible that some of these would have declared a winner if they were allowed to run a bit longer, but it is not likely that a large fraction of the prematurely terminated games would do so. The reason is that stalemate situations occur, i.e. situations where no progress is made because the players, due to their simple order giving strategies18.5.21 and limited negotiation skills, fail to advance their positions due to standoffs.
It has been seen multiple times, however, that the game does not come to a standstill, but that the game state will cycle with a period of 2–4.
21.3.2 Winning Strategies
What the statistics do not show is the strength (percentage of the units) with which each player attacks. With the simple order giving scheme
1Actually the order giving routines use explicitly randomises the data from which an arbitrary choice is made, in order to minimise the possibility of a stalemate situation, there are times when the strategy will not have more than one possible outcome
used18.5.2, it generally pays to use a strong attack, since that will max-imise the probability of gaining a new unit, for two reasons:
• The chance of succeeding in an attack is better when more units participate in the attack. This increases chances that a new unit can be gained, which can be used in a new attack, etc.
• The chance of gaining a new unit is higher if the support centres of the player’s home country are left vacant — which is more likely if more of the player’s units participate in the attack. It can be fatal, however, to lose one of these support centre, since this will severely reduce chances of gaining new units.
The attack strengths used by the four players are slightly randomised in order to result in less predictable behaviour. Their individual values were hand-tuned to provide a reasonable equal distribution of winners, among the four players2, while still being consistent with the ‘personality’ of the player. The possible ranges of values are defined below (the values are drawn from a uniform distribution in the given range):
Red [0.50,0.70) Blue [0.60,0.75) Green [0.40,0.60) Yellow [0.50,0.65)
Part of the explanation why the vindictive player (Blue) wins consistently more games than the rest of the players is therefore that the player has the highest average attack strength.
21.3.3 Analysis of the Ruthless Player
The ruthless player is eliminated far more often than any other player. This is not surprising, since the player readily makes new enemies. In the cases where the enemies are friendly towards each other the ruthless player will quickly be eliminated. However, if the enemies of the ruthless player are at war with each other, the ruthless player may actually benefit from the situation because it will have the shortest distance to its next target.
2The statistics show that the distribution is somewhat skewed, but this was not realised until after the system test was analysed.
21.3 Interpretation of System Test Results 169
21.3.4 Analysis of the Vindictive Player
The vindictive player clearly wins the most games, and is very seldomly eliminated. Three factors count to the advantage of the vindictive player:
1. The player does not make enemies with anyone unless it has been attacked. This reduces the number of enemies of the player, which makes it all the more effective when striking back.
2. The player asks its friends to attack its enemies. While the ruthless player ignores the request and the cowardly players only accepts it when the vindictive player is the strongest, the cautious player will accept it if relations are friendly; and they usually are, because the cautious player is — well,cautious.
3. The customary friendly relations between the vindictive and cautions players counts to the advantage of the vindictive player if the ruth-less player is eliminated early in the game — the vindictive player will then quite likely be on a crusade against the yellow player, even-tually eliminating it because the cautious player does not attack any player unprovoked, and because the vindictive player attacks with more strength.
21.3.5 Analysis of the Cautious Player
The cautious player has the sad record of winning the fewest games; it is simply too nice — it readily improves relations if an enemy requests it — which the cowardly player does all the time. But the low attack strength also plays a role here. The cautious player does not make new enemies on its own, which may explain why it manages to avoid elimination in many cases.
21.3.6 Analysis of the Cowardly Player
The cowardly player obtains fairly average results. The reasons are — as already mentioned, that it can exploit the gullible cautious player. And the cowardly player happily attacks the weakest player, which can pay off in certain situations.