As a statistician and analyst I intend to offer a suggestion or two regarding Alliance war.
"
Game Theory is the study of mathematical models of conflict and cooperation between intelligent rational decision-makers."
In Game Theory all complex decisions can be reduced to a series of Choices within a given Environment in order to achieve desired Outcomes.
I won't bore you with descriptive analogies.
As this applies to Alliance War:
Desired Outcomes = defeat opposing alliance.
Environment = Alliance War map with 9 necessary routes + a given Point Rubric
Choices = Constrained by the environment such that an Alliance has exactly 1 strategic option.
The third item (Constrained Choices) is the
visible complaint that you have with Alliance War 2.0, and is seemingly why everyone is upset.
The second item (Environment) is the root cause of the of the Constrained Choices problem.
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The Alliance War map allows the for the placement of 50 defenders across a map with 92 tiles, 54 of which are capable of containing a defender.
The Alliance War map can be traversed entirely by an alliance moving on as few as 9 paths.
Due to the relative high-value of Boss kills (20,000 each) and Exploration (300 per tile), there are no viable strategies that do not include full exploration.
Therefore, those values (totaling 150,000)can be canceled and removed from the victory calculation.
Victory Calculation
= placement * (X1 - Y1) + diversity * (X2 -Y2) + kills (Y1 - X1) + rating * (X3 - Y3)
Where,
placement = 50
diversity = 125
kills = 50
uniquechamps = 106 (at the time of writing)*
rating = 0.02
X1 = Alliance A # defenders
X2 = Alliance A # unique defenders
X3 = Alliance A total defender rating (avg defender rating * X1)
Y1 = Alliance B # defenders
Y2 = Alliance B # unique defenders
Y3 = Alliance B # defender ratings (avg defender rating * X1)
* side-note this calculation is written with respect to the scoring system as presented within the Forums, not as presented within the game itself. I.E. this calculation is consistent with Alliance-Wide diversity.
With the above Victory Calculation in mind, there are now (2) potential strategic options, and only (1) viable option.
Option 1) Strong Defense, attempt to prevent Opposition from 100% Exploration
Option 2) 100% Exploration, Maximize Diversity, Maximize Defense Rating.
The Alliance War Map can be traversed and fully explored by 9 people on 9 routes. An Average Alliance with 10 members will have 1 member out of 10 reserved entirely as backup. So the Map environment does not prohibit 100% exploration.
There is no penalty for an attacker Knock Out so a given determined attacker could revive his entire team for 40% hp 15 times. More than enough to make it through any given path, albeit expensively.
The Alliance War node buffs are regarded as being weak and insufficient from prohibiting a determined assault.
Best possible outcome = Opposition is unable to take 1 or more boss tiles.
Most likely outcome = Opposition will 100% explore map.
Scenario 1 = Max Diversity, High Quality
Let's assume that two imaginary Alliances are able to field 150 defenders totaling 750,000 defense rating (avg defender = 5000). Both are able to provide 106/150 unique champions, both are able to 100% all three BGs.
The score for both teams would be 193,250
Scenario 2 = Minor Diversity, High Defense Quality
Let's assume that Alliance A executes strategic Option 2, while Alliance B forgoes diversity for maximum defender quality, fielding 3 identical battlegroups of 50 unique champions. Both alliance can field champs avg defender rating = 5000
Alliance A = 193,250
Alliance B = 186,250
Alliance B loses by a 7,000 spread, all Diversity points.
Scenario 3 = Minimum Diversity, Highest Defense Quality
Let's now assume that Alliance A executes strategic Option 2, while Alliance B miraculously is able to field the 30 teams of the exact same 5 strongest quality defenders. (probably full mystic teams). Both alliance can field champs avg defender rating = 5000
Alliance A = 193,250
Alliance B = 180,625
Alliance B loses by a 12,625 spread, all Diversity points.
Scenario 4 = Maximum Diversity, No Duplicates
Ok, let's say Alliance B thinks there is some advantage to ONLY fielding the 106 unique defenders. Both alliance can field champs avg defender rating = 5000
Alliance A = 191,050 (can only kill 106 defenders, but larger defense rating)
Alliance B = 186,650 (can kill 150 defenders, but smaller defense rating)
Alliance B loses by 4,400 points, all Defense Rating & Placement overcomes Kills.
When you chart those 4 strategies:
Only 2 Strategies actually have a viable outcome.
Max Diversity, High Quality can outmatch 3 of 4 potential opponent strategies, and tie against a matching strategy.
Max Diversity, No dupes has an opportunity to win against Min Diversity, High Quality.
GAME THEORY HAPPENING NOW
So, if you are to consider your own potential strategies, Min Diversity, High Quality has no chance of winning against any of the four opponent strategies.
When that happens in Game you discard that as a viable strategy, and you discard that strategy as a viable strategy for your opponent since they will arrive at the same conclusion. This effectively reduces the choice table.
Now you have 3 potential strategies rather than 4, as does your opponent.
Since we do not know in advance what the opponent will decide, we will assume that each potential strategy is equally likely for the opponent.
Max Diversity, High Quality has 1 chance to tie, and 2 chances to win, a 66% probability of success and a 33% probability to tie.
Minor Diversity, High Quality has 1 chance to lose, 1 chance to tie, and 1 chance to win, a 33% probability of success, and a 33% probability to fail.
Max Diversity, No Dupes has 2 chances to lose and 1 chance to win, a 33% probability of success, and 66% probability to fail.
ANOTHER REDUCTION
Since the Max Diversity, No Dupes strategy has a better chance to reward the opposition than me, I will remove that from my choice of viable strategies. Since I remove that choice for myself, I will assume that my opponent has come to the same conclusion:
And now we have arrived at the root of the problem.
Under the environment and conditions of Alliance War 2.0, there is only (1) viable strategy any rational Alliance can pursue.
If the only way you could play chess was Torre Attack Wagner Gambit, then you would probably not want to play chess.
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So what can be done?
Change the Environment such that more than 1 strategem is viable:
Potential options include
- More PATHS than 10, such that no Alliance can possibly 100% exploration.
- Introduce COSTS to the equation. Defense kills was a sufficient Cost in AW 1.0, but is not necessarily the only cost that could be introduced.
- Restructure the points Rubric such that the rewards for Exploration (90,000) and Boss kills (60,000) are not so disproportionate to Diversity (13,250) & Rating (< 2000)
