Simplified Standard Form Game
- Brampton Booster
- Jan 14, 2014
- Comment
#Class MaxDamage Extends Standard, Standard Form Game
| Criticals Checked | Heals Checked | Net Damage | Probability |
| 0 | 0 | 3 | 111/196*7095/9212 |
| 0 | 1 | 2 | 111/196*495/2303 |
| 0 | 2 | 1 | 111/196*135/9212 |
| 0 | 3 | 0 | 111/196*1/4606 |
| 1 | 0 | 4 | 37/98*21285/30268 |
| 1 | 1 | 3 | 37/98*14190/52969 |
| 1 | 2 | 2 | 37/98*1485/52969 |
| 1 | 3 | 1 | 37/98*45/52969 |
| 1 | 4 | 0 | 37/98*1/211876 |
| 2 | 0 | 5 | 11/196*19393/30268 |
| 2 | 1 | 4 | 11/196*2365/7567 |
| 2 | 2 | 3 | 11/196*2365/52969 |
| 2 | 3 | 2 | 11/196*110/52969 |
| 2 | 4 | 1 | 11/196*5/211876 |
| 2 | 5 | 0 | You are funny |
Average Damage = 111/196*(7095/9212)*3+111/196*(495/2303)*2+111/196*(135/9212)+4*37/98*(21285/30268)+3*37/98*(14190/52969)+2*37/98*(1485/52969)+37/98*(45/52969)+5*11/196*(19393/30268)+4*11/196*(2365/7567)+3*11/196*(2365/52969)+2*11/196*(110/52969)+11/196*(5/211876)
Don’t worry if you didn’t get that. This is a data dump to show how much damage you can deal to the opponent if:
- you run 12 Crit
- they have 4 Heals
- you have a 2/2/2
- They didn’t guard any attack
Pretty standard stuff. Turn out, the average comes out to be ~3.2. But why do this? Well if you look at my massive data dump, it can be a pain to read through all that. So this time, I devised a simpler way to understand intuitively what all those random numbers mean.
Thought Process
Think about it. If I attack 3 times, my opponent guards none, how much damage would I expect to deal? Without triggers, the exact number is 3. So when you include triggers, with Critical Triggers > Heal Triggers, you can obviously expect the total to be higher. The chart shows all the possible outcomes and displays it in a chart. So when you get the average, you get the maximum damage that can be dealt in a turn. I shall denote it as Dmax. So let’s continue with this train of thought. We would use cards in hand to reduce the damage dealt to us. Cards used can be denoted as Cused. The damage we end up will be denoted as Dend (Get the pun?). So with all the variables in place, let me show you the following equation:
X = Cused / (Dmax-Dend)
Woah, slow down! What the hell is all of this?
Okay, let’s approach (Dmax-Dend). You’ll realize that this number represents the damage we did NOT take, or saved**. Cused / Dsav is simply a ratio. Kinda like sales that say “4 buns for $2″, it can be represented as 4/2 [bun/$] or 2 buns/$1. In less mathematical terms, with $1 you can get 2 buns. (Or if you go 2/4 [$/bun] you’ll find out a bun costs about $0.50, which makes it a lot easier to compare prices of similar products). You can also say two buns per dollar. When you look at Cused / Dsav it should be interpreted as cards used per -b-u-n- damage saved. So in the end, X represents the number of cards used to prevent 1 damage.
**If I’m boring or irritating you with so-called obvious math, then just keep going.
Question: If I have two values of X, which value will be better? The higher one or the lower one? Well, ask yourself: “Would I like to use 8 cards to prevent myself from taking one damage, or use 1 card instead?” Obviously, the lower the number is better.
So now we come to the standard form game. Rather then detract you, I’ll just provide some of the key values.
| Opponent’s Attack Plan | Your Defense Plan | Cards Used in total | Damage taken at End of turn |
| R>R>V | First attack through, guard rest | 2.673 | 0.9 |
| R>R>V | Last attack through, guard rest | 2.000 | 1.4 |
| R>V>R | First attack through, guard rest | 3.078 | 0.9 |
| R>V>R | Second attack through, guard rest | 2.311 | 1.4 |
| V>R>R-P | Non-crit rearguard through, guard rest | 3.434 | 0.9 |
| V>R>R-P | First attack through, guard rest | 2.311 | 1.4 |
*V>R>R-P means you put the second trigger you check to the same rearguard you applied the first trigger to.
Hey look! We can apply the formula! Let’s see what we get:
| Opponent’s Attack Plan | Your Defense Plan | Cards used to prevent one damage |
| R>R>V | First attack through, guard rest | 1.16 |
| R>R>V | Last attack through, guard rest | 1.11 |
| R>V>R | First attack through, guard rest | 1.34 |
| R>V>R | Second attack through, guard rest | 1.28 |
| V>R>R-P | Non-crit rearguard through, guard rest | 1.49 |
| V>R>R-P | First attack through, guard rest | 1.28 |
So now I can show something that is very easy to understand.
If your opponent V>R>R-P you, then you can see that letting the first attack through is much MUCH better than letting the rearguard. Likewise, R>V>R is the same but the difference is smaller.
If your opponent R>R>V you, then you can take the 1.11 or 1.16 (Letting the second attack through is 1.16 as well). But it doesn’t matter which you choose, because they are both weaker than 1.28! Say thanks to your opponent helping you conserve your hand!
Conclusion
^ Read above