Deeper analysis of pairings with team Belgium

Team Belgium captain Tom Adriany presented me their pairings table for team Belarus so I did some more analysis based on it.

I post again the team Belarus table:

And the team Belgium table is here:

 

Team tourney theory - Advantage realization

In the previous article I discovered the situation, where you want to risk against more powerful, usually, opponent. But there can be different situation – when you have advantage in composition and don’t want to be outplayed in the game of pairing. So, this article is about “how to minimize risks versus less powerful teams”.

I showed that opponent can guess our champion to maximize points. So, it’s the worst case for our team, actually and let’s count that opponent successfully did it – he knows our champion! How to hold the ground if such a shit has happened?

How can we choose our champion?

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.

Team tourney theory – Minimax strategy calculation

To clear out what is minimax strategy I’ll make an example with a 3x3 player game. We’ll have 3*3*2*2 = 36 pairing variants in this game, but not all of them are acceptable for us or our opponents! Let’s take a look at the evaluations table:

	BA	GK	SB
IG	3	10	11
DE	16	8	2
Tyr	6	4	15

Team tourney theory – Pairings with full information

When I just started to play team tourney I heard that “champions in a team tourneys make it unable to calculate the whole pairings process throughout”. But how? I decided to investigate that with a minimax strategy taken from the game theory of the mathematical statistics. Let’s look at the pairings evaluations table, like I posted in the previous aticle (values range from 0 to 20 according to the expectations of points taken from the game):

		Enemy 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

I did this example in 5th edition, so don’t try to think on the values itself:)

If you want you can count that the average of this table is 10. So. It must be the game with equal composition strength.

Now let us consider the game of pairings without champion game! If both team’s evaluation tables are the same, then one can calculate all 518400 combinations of pairins for this table. On each step each captain chooses the best variant for his team. I did this calculations for the table and the results are:

Team tourney theory – Composition

Composition is, actually the list of armies in a team or the army lists included in your team.
For simplisity lets assume that all the players are of equal strength and there are no luck or unluck in the games and the outcome of each game depends only on army lists. I mean that Tyranids with 18 raveners looses to venomspam DE, DE looses to mech IG while mech IG looses to Tyranids:)
I'll cover the game for 6 persons in a team again.

How to build a perfect team?

1. Toolboxes. We can take the most powerful army lists possible, according to the results of the singles tournaments - they are called toolbox lists or allcomers. It's easy - just look at the top-10 of the Grand Tournaments around the world and choose the best armies. For example: Tau+SM, Eldar+Tau, CSM+Necrons, Necrons, Tyranids, Daemons+CSM. Looks solid and every list is designed to play with any kind of the opponent army.

Team tourney basics – The game of pairings

I was asked to do some translations on the topic on team tourneys. I'll start with covering the rules for the team tourneys for 6 players in a team.

The team consist of 6 players, one player is a team Captain. Every player in a team should run an army from a unique codex (at least its primary detachment).

Every player play with his army and only his army at the tourney, no rotating usually possible. Each round a team plays with a different team simultaneously at 6 tables. The opponent team is chosen by the tourney organizers (TO). After opponent team is defined – team captains have to do the pairings (I’ll call it “the game of pairings”).

The game of pairings routine:

First each captain secretly write down the name (or army) of one of his players. Then captains roll off to see who should start the game of pairings first. The captain who lost the roll off chooses one of his players as the first defender (he cannot choose champion, though). Then the captain who won the roll off choose one player from his team to play with the first defender. So, the first pair is defined. Then the first defender chooses the table on which to play (he can choose any table from 6 available).

Then the captain who won the roll off chooses the second defender and the opposite captain chooses the player to attack that defender. Second defender chooses the second table and so on, until all 5 players find their pairs and chose tables.

After all five pairs are done, captains reveal the champions, who play at the last (unchosen) table.