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-   -   The great myth of Skulls versus Shields. (https://www.heroscapers.com/community/showthread.php?t=26071)

Kroc July 20th, 2009 04:41 AM

The great myth of Skulls versus Shields.
 
I don't know how many times I have heard (and maybe even said myself) that offense has an advantage in this game because there are three skulls and only two shields. People usually says that this makes it easier to wound someone than defend against a wound. This is not true.

In order to successfully wound someone you have to roll MORE skulls than they roll shields.

To get down to some numbers, if offense had an advantage then the probability of a wound should be more than .5 when you roll an equal number of attack and defense dice. However if you roll one attack dice against one defense dice then the chance of wounding is
(probability of a skull)*(probability of no shield) =
1/2*2/3 =
1/3.

This means that 2/3 of the time there will be no wound, or the defender wins.

EDIT:
Quote:

Originally Posted by Eclipse (Post 880069)
What it actually has a greater affect on is the difference in greater offense vs greater defense.

Since this thread has been given the exalted "thread of the week" rating I just want to say that I now no longer agree with this post. Or I should say, I now understand what the myth is really based on, and its not a myth at all.

In his post (linke above) Eclipse got it in one, basically the marginal benefit of adding an attack die is higher than the marginal benefit of adding a defenese die. I checked this out using Sisyphus's tables and found that no matter how you slice it, in terms of expected number of wounds or a probability of a wound, adding an attack dice helped more than adding a defense die. On average with the probability of a wound adding an attack dice gave a 53% higher benefit, with the number of wounds it gave a 78% higher benefit.

So, the "myth" is true, but only if you understand its not talking about an ABSOLUTE advantage, rather a MARGINAL advantage. Gosh, the economist in me loves this.

Quote:

Originally Posted by Kroc (Post 880619)
(For those of you who forget your economics, the marginal benefit is how much the probability of a wound is increased by increasing the number of attack dice by one, or for defense the amount it is decreased.)


Parduz July 20th, 2009 05:02 AM

Re: The great myth of Skulls versus Shields.
 
True, with one die.
But (if i'm not wrong) with 2 dice things goes different:

1/2 * 4/9 = 2/9 (1 skull - 1 wound)
1/4 * 8/9 = 2/9 (2 skulls - 1 wound)
1/4 * 4/9 = 1/9 (2 skulls - 2 wounds)

Chances to cause at least 1 wound = 5/9... am i right?

TnT2 July 20th, 2009 06:47 AM

Re: The great myth of Skulls versus Shields.
 
Seems to be a small error in your calculations... breaking it down, with two dice

Chance of skulls
no skulls = 1/4
one skull = 2/4
two skulls = 1/4

Chance of shields
no shields = 4/9
one shield = 4/9 (you had 8/9 here)
two shields = 1/9

So,
1/2 * 4/9 = 2/9 (1 skull * no shields = 1 wound)
1/4 * 4/9 = 1/9 (2 skulls * 1 shield = 1 wound)
1/4 * 4/9 = 1/9 (2 skulls & no shields = 2 wounds)

Thus, the chance of at least one wound is 4/9

And though the average number of wounds is 5/9

Isn't there are probability chart around for all of this in the download sections
http://www.heroscapers.com/community...o=file&id=1279

And this thread is even better
http://www.heroscapers.com/community...ad.php?t=16263

SuperflyTNT July 20th, 2009 09:11 AM

Re: The great myth of Skulls versus Shields.
 
I don't know, Kroc. It seems pretty precarious to think that the odds are about even, give or take, when there's 1/3 more skulls on every die than there are shields.

The odds of rolling one Skull on every die is 50/50. The odds on rolling one shield is 33.33333/66.666666, thus if you take every die and look at them individually, you've got a better shot of rolling a skull every time than the odds of rolling a shield every time to defend against that skull.

Now the other aspect to this little exercise is that almost all the units in Heroscape have higher attack than defense (or even dice), which I'd think would be another indication that the game is offense-driven. Another factor is that there (I think) are more offensive cheerleaders than defensive ones, and he defensive ones (with the exception of Raelin) are weaker, and special attacks/powers that either boost attack or diminish the target's defense dice are also more plentiful than those that bolster defense.

So, in short, I think that with all things being equal (lucky dice-wise) you're more likely, all things considered, to land a hit on someone than to block a hit.

As for the odds and "multiple dice calculations", I think it's all tripe. Every roll should be thought of looking only at the individual dice. I think it's a gross misrepresentation to say that the more dice you roll, the lower the probability of rolling any given symbol. In reality, the odds are the same if you roll one die or 100 dice - there's the same chance on each die to roll whatever symbol you're looking for, and stacking the probabilities is really a poor way to determine your shot at scoring a skull or shield. You have a 50/50 shot, regardless of how many dice you roll, of landing a skull on each die, so I look at each die as a coin toss when rolling for skulls rather than break it down to what my odds are for rolling 4 skulls on 4 dice in their totality.

dok July 20th, 2009 09:17 AM

Re: The great myth of Skulls versus Shields.
 
If you're looking at wound chance in the probability tables, then defense has the edge in a 1v1 or 2v2 matchup. The attacker has a 1% advantage at 3v3, and it gets progressively better for the attacker as the number of dice increase.

The matchups that are closest to 50/50 are 1v0, 3v3, 5v6, and 7v9. Note that they follow an "add 2 attack and 3 defense" trendline -- but it starts at 1v0, not 1v1.

Harlax July 20th, 2009 09:40 AM

Re: The great myth of Skulls versus Shields.
 
Consider a match up of squads with four figures. Squad A attacks first. Even with a kill rate of 40%, on average you get 1.6 kills. Assuming even one kill, Squad B has 25% fewer attack dice on its turn.

An oversimplification to be sure, as it ignores the possibility of multiple squads on one or both sides, the effect of SAs, and the possibilities created by OM placement.

MegaSilver July 20th, 2009 11:28 AM

Re: The great myth of Skulls versus Shields.
 
There is also a way to skew the roll of a single dice: by rolling the dice instead of dropping it. The odds of a certain symbol to show then depend on what side it is rolling on.

The chance of skulls could jump to 75% on one side. (I do this when I have one attack die to roll.) Or, on another side shields could show 50% of the time, with a skull to show 25%.

The way you roll the dice can change outcomes, too.

MegaSilver

jschild July 20th, 2009 11:37 AM

Re: The great myth of Skulls versus Shields.
 
If you are purposely fudging the way you roll, you are cheating. My 2 cents anyway.

R˙chean July 20th, 2009 11:43 AM

Re: The great myth of Skulls versus Shields.
 
I am not entirely sure what Megasliver is saying, but it certainly does not sound like a good, sporting thing to do.

Rich10 July 20th, 2009 11:46 AM

Re: The great myth of Skulls versus Shields.
 
Quote:

Originally Posted by MegaSilver (Post 875472)
There is also a way to skew the roll of a single dice: by rolling the dice instead of dropping it. The odds of a certain symbol to show then depend on what side it is rolling on.

The chance of skulls could jump to 75% on one side. (I do this when I have one attack die to roll.) Or, on another side shields could show 50% of the time, with a skull to show 25%.

The way you roll the dice can change outcomes, too.

MegaSilver

Rolling a die should have a random outcome. Unless you are dropping the die, I would be surprised if you can affect the outcome. If you can affect the outcome, go to Las Vegas and make lots of money.

Aldin July 20th, 2009 11:46 AM

Re: The great myth of Skulls versus Shields.
 
MegaSilver,

Why would you ever want to do that?

~Aldin, who doesn't play games with people who try to cheat him

MegaSilver July 20th, 2009 12:28 PM

Re: The great myth of Skulls versus Shields.
 
No, no, what I am saying is if you roll the dice instead of dropping it, the way the dice lands can be different.

If you roll the dice, the side it is rolling on will mostly stay on that side. Thus, you could have a greater chance to roll a shield or skull, depending on the side it is rolling on. What I said above was that with a single dice, I prefer to roll it instead of dropping it so that I hope I can get a better outcome.

With dropping, your chances are more random than rolling. The dice jump around, thus making which side it lands on less predictable.

Sorry if anyone misunderstood, but no, I never cheat on any game I play. I was just trying to point out how rolling the dice can affect the odds differently than dropping.

MegaSilver


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