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?

If to say it simple, than just “choose defender as a champion”. If to be more correct, you should calculate minimax strategy for every champion variant for loosed rolloff. Let’s look at the pairings evaluations table with the advantage in composition:

		Oponent's team
		GK	CSM	Eld	Tyr	BA	DE
Our team	Eld	5	13	10	15	14	6
	IG	15	16	18	2	7	16
	Dae	15	5	3	2	14	3
	GK	9	14	13	14	8	13
	SM	6	5	8	9	16	4
	SW	6	14	17	16	10	14

According to this table, we have quite strong team, but nevertheless we can lose the game of pairings. Let’s try to use our advantage! I’ve calculated minimax strategy for every player in our team set as a champion. Every time I allowed opponent to guees our champion correctly and play the best way he can! The resulting score for the team for different champion variants:

Eldar – 54

IG – 52

Daemons – 53

GK – 55

SM – 52

SW – 57

The main idea here: if we set SW as our champion – we CAN NOT GET LESS THEN 57 POINTS! So, WE CAN NOT LOSE AT ALL!!!

In practice the outcome can be much better because we can win the rolloff and opponent can make a mistake with high probability -> we’ll get more points!

Let’s go through the example:

We set SW as our champion and opponent know it (guessed it)! Then we lose the rolloff and have to set the defender first. The problem here is that WE DO NOT KNOW OPPONENTS CHAMPION. It means, that we have 5 players, but opponent has 6, so the opponent has more flexibility in taking decisions.

0 – If opponent can calculate minimax strategy correctly – he set BA as a champion!

1 – With the not square table the best first defender for our team is Daemons! Surprise!)

2 – Opponent, for sure, attacks with Tyranids.

3 – The best defender of the opponent, GK, defends.

4 – We attack GK with SM. Surprise again? Nope, pure math.

5 – We defend with GK, predictable.

6 – Opponent has not good pairing for our GK and has to attack with DE.

7 – The last pairings are obvious. And the resulting game table will look like this:

champ	SW	10	BA	champ
1	Dae	2	Tyr	2
4	SM	6	GK	3
5	GK	13	DE	6
8	IG	16	CSM	7
9	Eld	10	Eld	10
		57

So, we played without mistakes, as well as our opponent and we have 57 points (a draw) as a result. It’s good for us, cause we lost the rolloff and opponent guessed our champion!

But one can say:
"Hey, stop! Why to put BA as a champion?! Let’s attack with GK and get more points on those SW!!!”

Okay, let’s look at this example too:

0 – Champions are defined (SW against opponent’s GK)

1 – We do not know opponent’s champion and our strategy is the same as before! We lost the rolloff and defend with Daemons!

 2 – Opponent attacks with tyranids as before – it’s clear.

3 – Opponent defends with BA! It looks logical but it’s a mistake!

4 – We attack BA with SM (great match for our SM actually).

5 – We defend with GK, it’s clear too.

6 – Opponent has no good pair for GK again and attacks with DE again.

7 – The last pairs are predefined and bring us even more points!

The resulting game table:

champ	SW	6	GK	champ
1	Dae	2	Tyr	2
4	SM	16	BA	3
5	GK	13	DE	6
8	IG	16	CSM	7
9	Eld	10	Eld	10
		63

So, opponent chose the best counter-champion but as a result got even less points. Actually, you can calculate it throughout and find that if we win the roll-off then we have almost no possibilities for a draw – only victory. With lost rolloff we get a draw with GK or BA as an opponent’s champion. Any other army as an opponent’s champion give us a victory!

The main goal of this strategy is not to lose the game if we have advantage in composition, even with lost rolloff and guessed champion. The probability of this is about 1/16 actually, so in most cases we’ll win anyway:)

Afterword.
I have finished my game of pairings theory translations, but not finished to discover the methods and strategies for the game of pairings.
I wonder if this can be interesting or useful for anybody, casue, actually a have almost no feedback. Maybe, it's because captains prefer to keep their strategies in secret, or because we are so lazy to use math statistics for the toy soldiers game.