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  #73  
Old August 1st, 2009, 05:01 PM
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Re: The great myth of Skulls versus Shields.

I wood gladly take 5 more A Dice and Give you 5 more D Dice. Whatever the odds I can cause more damage.
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  #74  
Old August 1st, 2009, 05:04 PM
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Re: The great myth of Skulls versus Shields.

Quote:
Originally Posted by Li Mo View Post
I wood gladly take 5 more A Dice and Give you 5 more D Dice. Whatever the odds I can cause more damage.
And mathematically, you'd be justified in doing so. Once you pass 2 dice, it's always better to take extra attack dice than defense dice. Math does not lie.
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  #75  
Old August 1st, 2009, 05:18 PM
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Re: The great myth of Skulls versus Shields.

I think the whole point is to focus your army on attack or defence. In the games I play my opponents never go on the offensive so I must or the game cannot move forward. So attack is nice for me because they, more often than not, have high ground. And my weakness on the defence is also a down fall. So range plays king against a castle.
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  #76  
Old August 1st, 2009, 08:25 PM
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Re: The great myth of Skulls versus Shields.

If you have to roll 1 extra skull for every shield rolled, you are ALWAYS at a disadvantage over the defender, if the dice are equal.

If you roll an attack, you always need 2 skulls to cause a wound for every shield. If someone rolls 3 shields, you need at least 4 skulls. That is the disadvantage that is ALWAYS present, irrespective the amount of symbols on the die - you must always one-up the shields to cause injury.

That's the crux of what I, and Kroc, are talking about here - the "myth" that the attacker has an advantage because of one extra skull on any given die is untrue, because you are always at the disadvantage of needing to have 1 more skull than the defender needs shields to do anything to him.

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  #77  
Old August 1st, 2009, 08:38 PM
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Re: The great myth of Skulls versus Shields.

But that's what you're missing. The probability of you rolling those 4 skulls can be higher than the probability of your opponent rolling 3 shields, depending on the total number of dice. In fact, most of the time, it is.

Just look at the math. The numbers don't lie. If you roll more than 2 dice, rolling an extra attack die does give you an advantage. The "myth" is true. If you disagree, please show me the actual math to back it up, or show me where my math is wrong.
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  #78  
Old August 1st, 2009, 11:31 PM
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Re: The great myth of Skulls versus Shields.

EDIT: This was just more of the same blah-blah-blah from me. Skip to bottom of post, please.

Quote:
If you have to roll 1 extra skull for every shield rolled, you are ALWAYS at a disadvantage over the defender, if the dice are equal.
No. False. Everyone can see this except you. Your "if" clause does not apply in Heroscape. Until you understand this, you are just digging yourself a deeper hole.

Quote:
If you roll an attack, you always need 2 skulls to cause a wound for every shield. If someone rolls 3 shields, you need at least 4 skulls.
Can you not see that the two consecutive sentences you wrote there directly contradict each other? Your first statement claims I need 6 skulls; your second claims I need 4. You'll never get anywhere as long as you're arguing against yourself.

Quote:
That is the disadvantage that is ALWAYS present
No. False. The disadvantage is a fixed cost which is amortized over the number of dice rolled, which is why it turns to an advantage at the proper number of dice (3 vs. 3). If you can't see that, then find somebody you trust who can explain it to you.

Quote:
That's the crux of what I, and Kroc, are talking about here - the "myth" that the attacker has an advantage because of one extra skull on any given die
Before you invoke Kroc's good name yet again, perhaps you should go back and read his first post, in which he states that the "myth" turns out to actually be true in a marginal sense. You and Kroc are not advancing the same argument; if you think you are, then that's another thing you may want to make sure you understand before you proceed.

Quote:
... you are always at the disadvantage of needing to have 1 more skull than the defender needs shields to do anything to him.
It is true that you always need 1 more skull than the shields rolled; but it is false that this means you are always at a disadvantage, because, as the number of dice increases, the higher per-die likelihood of skulls vs. shields (3:6 vs. 2:6) eventually overcomes the fixed-cost disadvantage. The disadvantage is a fixed +1 need regardless of the number of dice (I think this is the part you keep getting wrong), but the offsetting advantage is scalable and grows as the number of dice grows.

For heaven's sake man, take Rÿ's advice. A crumbling argument can not be shored up by stubbornness. This incomprehensible trail of flawed reasoning is killing your credibility at light speed.

EDIT: I would like to publicly apologize for getting out of control on this topic. I should have just made my point once and let it go at that, but instead I got too wound up about it. I became a broken record and, worse, I made personal comments about SuperflyTNT that were not appropriate, constructive, or courteous.

I like to argue for the truth as I see it, but when spirited debate morphs into personal comments that risk damaging community relationships, then somebody has taken a wrong turn. I think that somebody was me and I am sorry about it.

I apologize to everyone about the bandwidth drain and the attitude, and to Kroc for gunking up his thread. I have already sent a private apology to SuperflyTNT.


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Last edited by Just_a_Bill; August 2nd, 2009 at 08:29 AM.
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  #79  
Old August 2nd, 2009, 08:37 AM
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Re: The great myth of Skulls versus Shields.

Math sucks. I think that's the lesson we can all take away from this.
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  #80  
Old August 2nd, 2009, 10:12 AM
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Re: The great myth of Skulls versus Shields.

Enjoy, Greyowl.
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  #81  
Old August 2nd, 2009, 12:38 PM
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Re: The great myth of Skulls versus Shields.

Quote:
Originally Posted by SuperflyTNT View Post
And what exactly is that supposed to prove? I know about Binomial Probability Distribution. I studied it in college and have used it in practice as an engineer. It's what I used to generate the table I posted earlier that disproves your theory. If you want to check my work and formulas, go to the "Customizing Tools" link in my signature and download the "Probability Tools" Excel spreadsheet. All of the formulas are in there.

Look, I'm not trying to be argumentative here, but it sounds like you're arguing against actual math based purely on your intuitive feel of how you think it works. And one of the first things you learn when studying probability theory is that people's intuition about probabilities is often wrong. I can agree with you that "intuitively" it may seem wrong for it to work that way, but nonetheless the math proves otherwise.

Instead of posting a link for a Binomial Probability Distribution study sheet, show me how you used it to arrive at your conclusion (or how you used some other form of math), or show me how I used it incorrectly to arrive at mine (I'm always open to the idea that I made a mistake somewhere). Like I said, my formulas are freely available for download, so you can inspect them. It's the same math that Sisyphus' Probability Tables are generated from, as well. The numbers match on both.

Last edited by GreyOwl; August 2nd, 2009 at 05:54 PM.
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  #82  
Old August 2nd, 2009, 03:46 PM
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Re: The great myth of Skulls versus Shields.

Quote:
Originally Posted by ollie View Post
Math sucks. I think that's the lesson we can all take away from this.
And all things being equal, that some of the best units have a higher DEF than ATK?

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  #83  
Old August 2nd, 2009, 03:57 PM
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Re: The great myth of Skulls versus Shields.

Quote:
Originally Posted by Carnival Man View Post
Quote:
Originally Posted by ollie View Post
Math sucks. I think that's the lesson we can all take away from this.
And all things being equal, that some of the best units have a higher DEF than ATK?
To see the reason why, go see this thread: Attack Scale vs. Defense Scale. The short of it is that a higher defense than attack is actually equal (meaning equal skill at attacking and defending).
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  #84  
Old August 3rd, 2009, 04:38 AM
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Re: The great myth of Skulls versus Shields.

Quote:
Originally Posted by GreyOwl View Post
But that's what you're missing. The probability of you rolling those 4 skulls can be higher than the probability of your opponent rolling 3 shields, depending on the total number of dice. In fact, most of the time, it is.

Just look at the math. The numbers don't lie. If you roll more than 2 dice, rolling an extra attack die does give you an advantage. The "myth" is true. If you disagree, please show me the actual math to back it up, or show me where my math is wrong.
I don't know whether I should jump in here or not. First of all I'd like to mention that I corrected my original post, I also explained all this in a post a few pages back.
Quote:
Originally Posted by Kroc View Post
Quote:
Originally Posted by Eclipse View Post
What it actually has a greater affect on is the difference in greater offense vs greater defense.
...In his post 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. ....
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.
But returning to GreyOwl's rather strongly worded post, I still think the "absolute" advantage is wrong. Sure, if you use 3 or more dice then you get have a better than 50% chance of getting 1 wound, isn't that kind of wasting attack dice??
As I pointed out in a previous post, no matter how small the probability of one attack dice succeeding if you use a million A versus a million D then you will successfully wound your opponent. Yes, I know that 3 is less than a million, but the basic point is that if you roll enough dice attack always wins.

Now as far as adding an extra attack dice? Here he is absolutely right, the math does not lie. The benefit of adding x attack is always more than the benefit of adding x defense, no matter how you slice it. That is the marginal benefit, which I believe is what people are saying when they talk about this myth.
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