Wednesday, December 26, 2012

Card Advantage P1: Battle Advantage Standards

Battle Advantage Standards, or B.A.S.S values are the output of your deck in optimal conditions. Basically put, your average output.

Let's start from the basics. Let's say your field has 3 16K columns all across, and your opponent is at 5 damage and has to guard every attack. What would be the minimum they must guard for? They guard the Vanguard for 15K for a 2 to pass, and both Rear-Guards for 10K, assuming you are facing an 10-11K Vanguard.  This sort of situation would require the opponent to use up at least 35K shield in the form of at least 4 cards.

Of course, probability comes by and throws a monkey wrench in things, so now we must watch out for triggers. Basically, there is a 22/49 chance to draw 0 triggers, 22/49 for 1 trigger, and 5/49 for 2. Let's put these aside for now, however, and calculate the shielding necessary for 1 and 2 triggers. A few numbers later, we now come to 40K shield in the form of 5 cards for a single trigger, and 45K shield in the form of 6 cards for 2. Now we must multiply each amount of shield by the probability they would happen for the average, which is about an average of 38.3K shield. Repeat this process again with the amount of cards you need and you get about 4.7 cards forced out. Simples.

What this basically means is that a vanilla set up, 3 16K columns all across, forces out on average 38.3K shield in the form of at least 4.7 cards. This number is known as a b.a.s.s. number, the average amount a deck can force out at maximum. Now here's the important stuffs.

This principle is extremely vital to beatdown decks, as it is literally how they work. Because we know that, on average, a player will generate about 15K shield within 3 cards over the course of a match, a vanilla set up will constantly minus them through the end game by about 23.3K shielding and 1.7 cards. Of course though, if you can force out even more than this, then you are generating auxiliary advantage, and creating +s in the process. For example, let's think of 13K attackers. When paired up with the right boosters, the 20K or 21K columns they can create become invaluable to you. Upon further inspection, assuming you have a vanilla set up but one of your Rear-Guard columns hits for 21K, you note that at 0 triggers, the amount forced out is 40K shield in the form of 5 cards and adds on. Once again with the math, using a 13K attacker for a 21K column has a b.a.s.s. value of about 43.3 shield in the form of about 5.6 cards. This means that using a 13K attacker will force out 5K shield more than normal, and generate about a +.9 each turn from forcing out cards. That's right, Palamedes generates almost +1 each turn just from having a decent attacking force.

This article is more for me, but it will be a great way to evaluate how powerful a unit's combo is. By finding the b.a.s.s. values of units like Dudley Emperor, Asura Kaiser, and the Break Rides, I can put a tangible and hopefully accurate number on exactly how powerful they are, along with giving a far greater understanding of what units are powerful and how powerful they are.

For future reference, Vanilla b.a.s.s. values are 1875/49K shield, and 228/49 cards. To gauge the value of an attack pattern or a certain power boost, you must first find the b.a.s.s. value of said attack pattern and subtract the vanilla b.a.s.s. values from it. If the shielding or amount of cards is positive, that is the card advantage you gained from the attack pattern. If the shielding or card advantage is negative, then the attack pattern has been a net loss for you.

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