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Official Rules & FAQ's Compilation and discussion of official HeroScape Rules and Frequently Asked Questions. **Special attacks never receive any bonuses.**


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  #25  
Old March 2nd, 2007, 09:26 AM
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Quote:
Originally Posted by gibberish_47
I tend to role 3 attacks of 3. When attacking Sentinels, I use 9 attacks of 1, hoping for them to whiff. This usually works to great effect.
Here is the math that confirms your strategy.
(Except that if the Sentinnels ever have their defense pumped up to 10, then you would want to switch to 3 att dice. )

Suppose the defender has d defense dice and double shields (Shields of Valor).

With 1 attack die, the chance of scoring one wound is 1/2 (2/3)^d.
With 3 attack dice, the chance of scoring...
3 wounds is P3 = 1/8 (2/3)^d
2 wounds is P2 = 3/8 (2/3)^d
1 wound is P1 = 3/8 (2/3)^d + 1/8 * d/3 * (2/3)^(d-1).
You can see how the double shields morphed the math from the previous long post.

I will simplify the discussion and say that using 2 attack dice is always worse than using 1 att die twice
because of the double shields. So we will just leave using 2 att dice out of this discussion.

(A) If the goal is to maximize the average number of enemy 1-Life units killed, then here is the calculation:

With 1 att die 9 times, the average number of kills is
9 * 1/2 (2/3)^d = (2/3)^d * 3/16 * 24.
With 3 att dice 3 times, the average is, after some algebra simplification,
3 * (P3 + P2 + P1) = (2/3)^d * 3/16 (d + 14).
If you compare these two expressions , you can easily see that the 3 att dice method is better if and only if
d > 10
(and equal if d=10).
So this proves that for defense more than 10, use 3 att dice; and for defense less than 10, use 1 attack dice,
if the goal is to maximize the average number of enemy 1-Life units killed (where they have double shields).



(B) If the goal is to maximize the number of wounds on one single hero, the best strategy again is
to attack with the highest possible number of attack dice. Again, the math verifies this.

With 1 att die 9 times, the average number of wounds is
9 * 1/2 (2/3)^d = (2/3)^d * 3/16* 24
With 3 att dice 3 times, the average number of wounds is
3 * (3*P3 + 2*P2 + P1) = (2/3)^d 3/16 (d + 24).
It is obvious the 3 att dice is always better, and equal only when d=0,
when the goal is to maximize the number of wounds on one single hero.


(C) If the goal is to get at least one wond on one enemy, then the calculation is...
With 1 att die 9 times, the chance of NO wounds is
(1 - 1/2 (2/3)^d)^9.
With 3 att dice 3 times, the chance of NO wounds is
(1 - (P3 + P2 + P1))^3 = [1 - (2/3)^d 1/16 (d + 14)]^3.
So 3 att dice is better when
[1 - (2/3)^d 1/16 (d + 14)]^3 < (1 - 1/2 (2/3)^d)^9
1 - (2/3)^d 1/16 (d + 14) < (1 - 1/2 (2/3)^d)^3
1 - (2/3)^d 1/16 (d + 14) < 1 - 3/2 (2/3)^d + 3/4 (4/9)^d - 1/8 (8/27)^d
(2/3)^d 1/16 (d + 14) > 3/2 (2/3)^d - 3/4 (4/9)^d + 1/8 (8/27)^d
1/16 (d + 14) > 3/2 - 3/4 (2/3)^d + 1/8 (4/9)^d
d + 14 > 24 - 12 (2/3)^d + 2 (4/9)^d
d > 10 - 12 (2/3)^d + 2 (4/9)^d.
For d at least 10, it is clear the left hand side is bigger because the righthand side is less than 10.
And you can manually check the lefthand side is bigger for d=1 to d=9, and equal of course when d=0.
The conclusion is Therefore, using 3 attack dice is better if the defense is at least 10,
if the goal is to try to score at least one wound. Use 1 att die if the defense is between 1 and 9. This is for double shields.


Note that when d=10, the average number from (A) was the same for both methods; but the higher variance for the 1-att-die method says you should use 3-att-dice when d=10 if your goal is to get at least one wound in (C). But the variance was not so great that it affected any other case other than d=10.
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  #26  
Old March 2nd, 2007, 11:37 AM
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Quote:
Originally Posted by rehlers
While it may seem like rolling 1 attack dice against 1 defense dice would come out to an advantage for the attacker (I thought this initially as well), once you calculate the probability on it, its actually less likely that the attacker scores a hit. The reason for this is that there are two ways the defender can avoid a wound. 1) The attacker rolls no hit, and thus it doesn't even matter what the defender rolls or 2) The attacker rolls a hit and the defender rolls a shield. Here are the 4 outcomes of rolling the 2 dice (atk/def) with the odds of each:

1- No Hit / No Shield (1/2 * 2/3 = 2/6 or 33.3%)
2- Hit / No Shield (1/2 * 2/3 = 2/6 or 33.3%)
3- No Hit / Shield (1/2 * 1/3 = 1/6 or 16.7%)
4- Hit / Shield (1/2 * 1/3 = 1/6 or 16.7%)

So out of the 4 outcomes, only #2 results in a wound (Hit / No Shield), which is only a 33.3% chance.
This is true, but don't think of it as attacker has a better chance to wound, it is the attacker has a better chance of rolling a skull than the defender a shield.
That does not translate to wounding, as your statistics pointed out.


Here is some statistics about the Krav Maga and Q9.
When rolling one attack dice you have a 50% chance of a skull.
For the Krav to roll 0 defense out of 3 is a 29.6% chance.
Now with Q9, usually my goal or my opponents is to kill 1 Krav each turn.
There is a 14.8% chance of getting both a skull and 0 dice on the Krav defense roll.

What are the chances of this happening 1 or more times during 9 rolls?
They are the same as 100% - Prob(it happening 0 times)

So now we have to look at the chance of not hitting a Krav
Probability of not hitting a Krav = 70.4% of a Krav rolling 1 or more defense + 14.8% the prob of Q9 rolling no attack while Krav roll no defense = 85.2%

Which makes sense.
Q9 has a 14.8% chance of killing a Krav on each roll of 1 dice
Q9 has a 85.2% chance of not killing a Krav on each roll

Lets see what the chances of not killing a Krav 9 times in a row is using the binomial probability.
let p = 0.852 (the probability)
Prob(Not killing a Krav in 9 rolls) = (9 Choose 9) x p^9 x (1-p)^0
= 0.237

Therefore there is a 23.7% chance of Major Q9 not killing any Krav... uh oh... that leaves a large chance he will kill at least one krav each turn.

There is a 76.3% chance of killing at least 1 Krav per turn with Major Q9

Unbelievable eh, but the Math doesn't lie.

What are the chances he could kill at least two in a turn?
Prob(Killing 1 Krav in 9 rolls) = (9 Choose 8 ) x p^8 x (1-p)^1
= .370

Therefore Killing 0 + killing 1 = 60.7%

There is a 39.3% chance of killing at least 2 Krav per turn with Major Q9

Q9 has a 2 in 5 chance of killing more than half of your Krav in one turn if they do not have height advantage.

There is a 13.6% chance Major Q9 will kill all three Krav in one turn

*EDIT* Hey Mathguy, nice posts!
I didn't see that before I posted... guess I shoulda gone to page 2 haha.

I knew that rolling 1 dice per attack was probably more advantageous than most people thought, but really, after calculating the Krav, I started to really understand.

In fact, ANY single life unit with 3 defense can be killed this often.

::Nathan Hoel::
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  #27  
Old March 2nd, 2007, 05:22 PM
daevablacc daevablacc is offline
 
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Great info.

So, do you guys know the odds on when to use his normal attack vs special attack, including when he has height bonus, extreme height bonus, attack glyph, Taelord bonus etc? :P
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  #28  
Old March 3rd, 2007, 09:27 PM
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Quote:
Originally Posted by daevablacc
Great info.

So, do you guys know the odds on when to use his normal attack vs special attack, including when he has height bonus, extreme height bonus, attack glyph, Taelord bonus etc? :P
We could... but it would take a long time..
You can look up a tutorial on how to do statistics, it might be a bit of work but you could do it.

::Nathan Hoel::
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  #29  
Old March 13th, 2011, 09:38 PM
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Re: Q-9 vs. luck of the dice

Im probably out of the loop, but whats the deal with rolling the 2 dice option with Queglix gun, is it a mix-up option? Ive heard people say that you use the 1 die attack for weak (1-2 defense) squads and the 3 die attack for strong (3 - max defense) squads and heroes. So, whats the point of using the 2 dice attack option?? I just wanted to get this cleared up.
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  #30  
Old March 16th, 2011, 09:46 PM
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Re: Q-9 vs. luck of the dice

Woah nice necro Agent Mike! 4 years 10 days 11 minutes _impressive. Q-9 may roll 1,2,or 3 dice at a time up to a total of 9. I imagine this is well explained in The Books of Q-9. I have always been a big fan of the sandblaster ~ 9 rolls of one. Great against the Krav... peace

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