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четверг, 12 сентября 2013 г.

Team tourney theory – Counter-champion


The game of pairings without champion’s game is a game with full information and can be calculated throughout. But when we have a champion’s game everything becomes much-much different. We have to take into account the unpredictable factor – enemy champion.

How can we choose our own champion?

1 – Defender as a champion. Most popular strategy is to play an allcomers army as a champion. So, we just stabilize the champion’s game and can focus on the game of pairings. The minus of this method – our powerful army is away and plays with some opponent’s army that can be not the best choice for the team and can decrease the outcome.

2 – Army without good matchups as a champion. If we have an army that we are not possible to use effectively – we can drop it from hand into a champion’s game. Possibly, it will be the best possibility to find average pairing for that army. It can be an attacker that has no targets or defender with 1 very-very bad matchup.

3 – The weakest army as a champion. Just to drop the weakest army from hand before the game of pairings main part.

4 – Counter-champion. We can try to predict enemy champion and set the best army to counter enemy champion. It’s the method to maximize the result, but if you fail to predict the campion – you can loose by much.


Let’s look again at a pairings evaluation table (evaluations range from 0 to 20):




Opponent's team
GK
CSM
Eld
Tyr
BA
DE
Our team
Eld
5
13
10
15
11
6
IG
13
13
16
2
4
16
Dae
15
5
3
2
14
3
GK
9
14
13
14
8
13
SM
6
5
6
9
16
4
SW
6
14
17
16
10
14


The average value for the table is 10 pts, so it’s the game with equal composition strength. So, the opponent’s team is as strong as our team. Let’s assume that we play the final round of the tourney and we need to get a win at all costs! It’s the situation, when we can try to risk! It’s the right time to follow the point 4 – choosing the counter-champion. If we guessed opponent’s champion – the game of pairings for us is a game with full information! So, we can calculate it throughout and find the optimal strategy!

I’ll show you the example based on the pairings evaluations table given above.

1 – First of all I have to guess the opponent’s champion. I think that opponent can put only IG, SM or Nidz as their champ. I assume that the best variant for opponent will be to set Tyranids as a champion – I go all-in and take it as a fact (but, actually, It may be a mistake… dramatic mistake).  In this example I was so lucky that I guessed opponent’s champion right.

2 – We set our champion, according to minimax strategy. Its SW!
3 – We was not lucky and lost the roll-off. But it’s of no help for our opponent, cause we already pre-calculated the outcome and we can take minimum 66 points in this game = victory! (Even with lost roll-off!!!).
4 – We set SM as our first defender. If you spend some time, toying with minimax strategy – you’ll find the weakest player to be the best first defender for your team most of the time!
5 – Our opponent will make the best attaker-best defender strategy. So, opponent attacks with DE. Cause we have already played SM, opponent defends with BA. Actually, it’s a mistake.
6 – Our Daemons realize their potential in attack on BA and we defend with GK. No surprises here.
7 – Opponent has no other variant as to attack our GK with his GK.
8 - The last two pairs is almost automatic and the game table will look like this:

champ
SW
16
Tyr
champ
1
SM
4
DE
2
4
Dae
14
BA
3
5
GK
9
GK
6
8
IG
16
Eld
7
9
Eld
13
CSM
10
72


So, I showed you, how to win the game of pairings with a lucky shot with champion’s game, besides we’ve lost the roll-off! 72 points is a strong victory in case of equal strength of teams compositions.

We can use this strategy against more powerful teams to get a draw or even a victory! Later on I’ll try to investigate the strategy for the game when we have a stronger composition then our opponent has. So, I want to win the game without full information! It must be interesting;)

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