Monday, November 17, 2014

Hard, Very Hard, Extremely Hard, & Ridiculously Hard to Kill! … Yeah, Really Not that "Hard" [Part 1/5: Understanding the Problem]

** PART 1/5 in the Hard to Kill Analysis Series **

Having finished the post on Mordor, the "Hard to Kill!" special rule (abbreviated H2K) came back to mind - and I realized that we had a lot of problems with that rule - since any time we played a Monster with H2K or the more "harder" versions of "Very Hard to Kill!" (VH2K), "Extremely Hard to Kill!" (EH2K), or "Ridiculously Hard to Kill!" (RH2K) - it really wasn't that hard to kill them …

In fact, the very first time we used this rule was against a Mordor Troll with the H2K rule facing off against a formation of Minas Tirith Warriors comprised of four companies.


GONDOR'S PERSPECTIVE OF THE ENSUING FIGHT
  • I have 100 120 Points of Minas Tirith Warriors; therefore 32 Models.
    • This means that I can take 28 casualties before my final company "runs away".
  • My troops are Infantry.
    • This means that the Troll (Type: Monster) will attack first - before I get to inflict any damage to him.
  • My troops have a Defense of 7 (from the front) and Resistance 1.
    • Going into hand-to-hand combat with the Troll's Strength of 7 means that he will need 4+ on his "To Hit" rolls (this is a probability of 50.0% of success and 50.0% chance of missing) and each hit will remove a soldier - again before I can even roll my dice.
                    P(4+) on a single die = P(4) + P(5) + P(6)
                                                      = (1/6) + (1/6) + (1/6)
                                                      = 3/6 = 0.50 = 50.0%

  • My troops have a Fight of 3.
    • Going into hand-to-hand combat with the Troll's Fight of 7 means that I will get no combat modifiers (pg. 47) for this fight other than Charging.
    • It also means that he will get 4 extra dice for Battle Skill when rolling "To Hit" against me.
  • My troops have a Courage of 3.
    • Getting charged by the Troll means I will need to pass a Courage Test for his Terror special rule or my fight value will be reduced to 0.
      • This would give him 7 extra dice for Battle Skill, then ...
    • I will need to roll a 7, 8, 9, 10, 11 or 12 on two dice to pass that Courage Test, meaning I have about a 58.3% chance of successfully passing the test & a 41.7% chance of failing the test.
                    P(7+) on two dice = P(7) + P(8) + P(9) + P(10) + P(11) + P(12)
                                                  = (6/36) + (5/36) + (4/36) + (3/36) + (2/36) + (1/36)
                                                  = 21/36 = 0.583 = 58.3%
  • In the current orientation of the battle, my troops have a 8 Direct Attacks with 3 Supporting Attacks.
    • This means that when I Calculate the Number of Dice I will have 8 for the Direct Company and 1 for each Supporting Company = 11 dice to roll (without a charge bonus).
  • My troops have a Strength of 3.
    • Going into hand-to-hand combat with the Troll's Defense of 7 means that I will need 6's to hit the troll, plus with the Troll's Resistance of 2 - I will need at least 2 sixes to wound (and roll on the Hard to Kill! table).
    • If I don't charge and I pass the Courage Test for Terror, this means that I will have 11 dice to roll when attacking him ...
    • If I don't charge and I don't pass the Courage Test for Terror ... oh wait ... this doesn't effect the number of Attacks, so I will still have 11 dice to roll when attacking him ... Ok, Terror isn't so scary anymore!
    • The probability of getting a 6 on a single die is 1/6 = 16.7%
***** CLEARS MIND *****

OK, OK, OK ... Long story short: I'm going to have 11 dice to roll ... each with a 16.7% chance of getting a 6 - so this means that of those 11 dice about 1-2 of them will statistically be 6's ... If I get 2 6's then I get to roll on the Hard to Kill! table ... and then looking at the table:



Wait a minute ... this says that I have a 16.7% chance of doing nothing … a 33.3% chance of adding a single wound counter, a 33.3% chance of adding two wound counters (which will only improve my chances of killing it outright on the next roll on the table), and finally a 16.7% chance of killing it outright?!? That means that 1 out of every 6 fights that I encounter with a Troll he will die outright on the first roll on the table?!? LMAO! That's what I'm talking about! And that stupid Troll cost 100 Points by himself? And Hard to Kill!?! HA! I'm going to spank that guy!

In fact, here is the Probability Table for the likelihood of obtaining a given result on the "Hard to Kill!" table based upon the number of counters on the Monster when rolling against the table:


This basically says that a Monster with the "Hard to Kill!" special rule will not last more than 4-5 Fight Phases and the likelihood of the Monster dying increases rapidly after each fight he is in. Here is an example of a few scenarios:

Case 1: A Heroic Knock-off

Let's assume that during the first Fight Phase the Troll kills 3 Gondor Warriors and the Gondor Formation has a Hero in the Command Company and scores only 2 hits on the Troll. The Gondor player then rolls on the Hard to Kill table for the 1 wound they have inflicted. They roll a 5 on the die - and then immediately the Hero uses a single point of Might to bump the 5 up to a 6 - and "Tada!" - the Troll is dead.

Case 2: A Rapid Kill

Let's assume that during the first Fight Phase the Troll kills 4 Gondor Warriors and the Gondor Formation scores 2 hits on the Troll. The Gondor player then rolls on the Hard to Kill table for the 1 wound they have inflicted. They roll a natural 6 on the die - and this means that the Troll is dead. Good Game Mr. "100 Mordor Army Points".

Case 3: A Slower Death

Let's assume that the Gondor Formation scores 3 hits during the first Fight Phase on the Troll. Since the Troll has a Resistance of 2, the 3rd hit is discounted - so still only one roll on the Hard to Kill table. They roll a 3, which means that the Troll gains 1 wound counter. During the second Fight Phase, the Gondor Formation scores 4 hits on the Troll. Now the Gondor player gets to roll twice on the Hard to Kill table … first roll is a 1. Adding the 1 wound counter that is already on the troll give a value of 2 … which means that the Troll now gains a second wound counter … totaling 2 wound counters currently on the Troll. The Gondor player still gets a second roll on the table - and if they roll a 4, 5 or 6, once they add the 2 wound counters that are already on the Troll they will get the 6 that is necessary to Outright Kill the Monster … 50% chance of success only after 3 rolls on the table. The third roll is a 4 … adding the 2 for the wound counters on the Troll - this gives 6, which kills the Troll.

Case 4: The only way this could be "Hard"

Let's assume that the Gondor Formation scores 1 hit during the first Fight Phase on the Troll. Resistance of 2 means that this hit is discounted. During the second Fight Phase, they get the 2 hits that they need to roll on the table, but as luck would have it they roll a 1 and there's nothing that can be done. During the third Fight Phase, they get 3 hits - again only a single roll on the table, but again they roll a 1 on the table … no effect. I guess this string of "bad luck" could go on for quite a while, but once the bad luck breaks then it's all down hill for the Troll.

So, a couple of things to note … 1) Once there is at least 1 wound counter on the Troll … the "ignore the blow" ability of the table goes away … Even if the second roll on the table is a 1, adding the wound counter immediately makes it a 2 - and there is another wound counter added to the Troll - he is well on his way toward death. 2) Once there are at least 2 wound counters on the Troll … the roll to kill becomes 50% (needing only a 4, 5 or 6). In fact, you are more probable to Kill the troll than to add a single or two more wound counters! 3) Once there are at least 3 wound counters on the Troll … it is pretty much game over for that poor Monster … the roll to kill becomes 66.7% (needing only a 3, 4, 5 or 6 - can only "fail" on a 1 or 2).

MORDOR'S PERSPECTIVE OF THE ENSUING FIGHT
  • I have 1 single 100 Point Troll; therefore 1 Model.
    • I need to be able to kill 28 Models of Minas Tirith Warriors before he kills me.
    • I have a Resistance of 2 and the Hard to Kill! & Terror special rules.
  • I have a Monster.
    • This means that the Troll (Type: Monster) will attack first - hopefully dealing enough damage to destroy a company or 2 before they get to attack.
  • My Monster has a Fight of 7.
    • It also means that he will get 4 extra dice for Battle Skill when rolling "To Hit" - So with my number of Attacks I'll be consistently rolling at least 7 dice against his formation in addition to charging bonuses.
    • Plus, if he fails his Courage Test for Terror, then I will have 10 dice to roll, even better!
  • My Monster has a Defense of 7 and Resistance 2.
    • Going into hand-to-hand combat with the Warrior's Strength of 3 means that he will need 6's on his "To Hit" rolls (this is a probability of 16.7% of success and 83.3% chance of missing) and if he only gets 1 hit ... it is discounted by my Resistance of 2.
    • HINT: HERE IS THE FLAWED INFLATED COMFORT LEVEL --> Plus the Troll is "Hard to Kill!" ... so even if he does get statistically lucky, it'll be "hard".
  • My Monster has a Strength of 7.
    • Going into hand-to-hand combat with the Warrior's Defense of 7 means that I will need 4+'s to hit, plus each hit will remove a model.
I'm going to have 7-10 dice to roll during each Fight Phase ... each with a 50.0% chance of getting a 4 or higher - so this means that of those 7-10 dice about 1/2 of them will statistically be 4+'s ... That means I'll be killing about 3-5 Models per Fight Phase ... In order to get through the 28 models that means I need about 6-10 Fight Phases to destroy the entire formation of Warriors. LOL, I guess that I got this! (Remember: Based upon the statistics above the most that he will be killing is about 20 Gondor Models … 5 Models per Fight Phase * 4 Phases.)

So, I think that the "problem" is somewhat understood … now, let's get on to the solution in Parts 2-5 for each of these special rules and what can be done to address the issues. Here is the plan for upcoming posts over the next week or so ...

Part 2/5 = Examining the "Hard to Kill!" rule in detail with help from a simulator and combat example.
Part 3/5 = Examining the "Very Hard to Kill!" rule with similar treatment.
Part 4/5 = Examining the "Extremely Hard to Kill!" rule with similar treatment.
Part 5/5 = Examining the "Ridiculously Hard to Kill!" rule with similar treatment.

No comments:

Post a Comment