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Heroscape Strategy Articles Heroscape Strategy Articles with discussions. Including Order Markers, Units, Game Play, etc. |
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#61
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Re: The great myth of Skulls versus Shields.
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#62
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Re: The great myth of Skulls versus Shields.
I'm not quite clear what everyone is trying to figure out in this thread, but it seems like the goal is to find out if adding an extra attack die is better or worse than adding an extra defense die (all else being equal). If so, and absolutely no disrespect meant, but there's a lot of incorrect mathematics being thrown around.
For example, an X percentage point increase is different from an increase of X percent. Just to give an example, if the probability of something happening is 50%, an increase of 25% percentage points would result in 75% (50 + 25). An increase of 25% would result in 62.5% (50 + 12.5, which is 25% of 50). The premise that adding an extra attack die is not as good as adding an extra defense die, because you have to roll 1 extra skull to cause a wound is also flawed. Here's why: if you figure out the probability of causing a wound in a 1A/1D situation (1 attack die vs. 1 defense die), it is 33%. That already takes care of the fact that you have to roll 1 more skull than shields to cause the wound. So when you start adding extra attack or defense dice, you don't have to account for that again - it's already been accounted for in the base probability. Take a look at the below table (click on it if it's too small, there's a larger version). This table shows the probability of causing at least one wound for even attacks (meaning equal number of attack dice vs. equal number of defense dice) from 1 attack/defense dice all the way up to 7. It then shows how the probability would change if you rolled 1 extra attack dice, and then if you rolled 1 extra defense dice. So looking at the first column, as an example, the first row shows that 1 attack die vs. 1 defense die has a 33% chance of causing a wound. The second row shows that if you have an extra attack die, 2 attack dice vs. 1 defense die, you have a 58.33% chance of causing a wound. The third row shows the opposite, 1 attack die vs. 2 defense dice has a 22.22% chance of causing a wound. I hope everyone's with me so far. So the key now is the 4th and 5th rows. The 4th row shows how much the probability of causing a wound went up by adding an extra attack die. The 5th row shows how much the probability of causing a wound went down by adding an extra defense die. So as you can see, for 1 attack die vs 1 defense die, you get a 76.76% increase in your chances to cause at least a single wound by adding 1 more attack die. Conversely, if the defender adds 1 extra defense die instead, your probability of causing at least 1 wound only goes down by 32.67%. So going across the 4th and 5th rows, you can compare the relative value of adding an extra attack die vs. adding an extra defense die for all the equal attack/defense combinations up to 7. Note that in every single case, adding an extra attack die makes a much bigger difference. This is because there are 3 skulls and only 2 shields on a die - and the fact of having to roll an extra skull was already built into the original probability (1st row). What is interesting to note is that as the number of attack and defense dice increase, the two probability differences seem to converge, because their effects become less and less important. This means that adding an extra die, of either kind, is much more valuable when rolling a few dice than it is when rolling a lot. That's because you have to think of it as a percentage increse. Adding 1 extra die to 1 existing one is a 100% increase in the number of dice. Adding 1 extra die to 4 dice is only a 25% increase in the number of dice. Note that at 1A/1D the difference is between 76.76% and -32.67%, but at 7A/7D the difference is down to between 13.41% and -11.03%. I didn't work the math any further, but it seems that around 9 or 10 dice, they may start equaling out. Customs: Superhero Sci-Fi Classic Terrain Tactical Meeples (My Game Blog) Customizing Tools Star Wars Campaign Last edited by GreyOwl; July 31st, 2009 at 10:51 PM. |
#63
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Re: The great myth of Skulls versus Shields.
Well, I did work out the math to 20A/20D, and they never become equal. They do get closer and closer (about 8% difference at 20A/20D) though. It seems like before they get out to a point where they're statistically the same, it would be close to 100A/100D, which of course is completely unrealistic in the realm of normal HeroScape.
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#64
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Re: The great myth of Skulls versus Shields.
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2. There's that calculator, Bill. Although you have more opportunity, you have less odds of rolling more skulls. Mathematically, the more dice you throw the less the chances of getting all skulls. 3. See #2. 4. Dude, can you read? Allow me to quote: Quote:
5. I don't want to point fingers, but seems like others have got this down, amigo.... I was famous, once... http://www.heroscapers.com/community/blog.php?b=1715 Visit my site: http://www.superflycircus.com "I'm not cute...I'll mess you up!" ~Jake The Dog Last edited by SuperflyTNT; August 1st, 2009 at 08:00 AM. |
#65
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Re: The great myth of Skulls versus Shields.
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Interestingly, what all of this implies is that the scale used for the Attack number on a card is a different scale than the one used for the Defense number. Meaning, if you want to make a figure that is equally good at attacking and defending, they should not have the same number for both - they should have a higher defense than attack. How much higher depends on the exact numbers, though. |
#66
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Re: The great myth of Skulls versus Shields.
Jeeeezus.
What I am saying is that the fact that a die has an extra skull on it does not equate to a massive, overwhelming advantage as some believe. The REASON for this is that regardless of how many dice you roll, you are always at a disadvantage on attacking because YOU NEED TO ROLL MORE SKULLS than your opponent needs shields. That's what Kroc is saying. That's what I am saying. So... If the odds of rolling one skull is 1:2 and the odds of rolling one shield is 1:3, you have to consider that THOSE ODDS DON'T MATTER. You need to look at it as: "What are the odds of rolling 2 skulls for every shield rolled?" You need 2+ skulls for every shield rolled for the skulls to make a difference. I was famous, once... http://www.heroscapers.com/community/blog.php?b=1715 Visit my site: http://www.superflycircus.com "I'm not cute...I'll mess you up!" ~Jake The Dog |
#67
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Re: The great myth of Skulls versus Shields.
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#68
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Re: The great myth of Skulls versus Shields.
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Unless you're attacking the Venoc Vipers on an equal plain. It's funny, until reading this, I never stopped to think about it. Mega Kudos to you Kroc. Heroscape is a gateway into a wonderful world of games that I never would've known existed otherwise. |
#69
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Re: The great myth of Skulls versus Shields.
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For 1 die, the probability is 33% (so that's a disadvantage - less than 50%) for 2 dice, it's 44.44% (still a disadvantage) 3 dice, 50.93% (now it's an advantage, and keeps getting better) 4 dice, 55.56% 5 dice, 59.18% 6 dice, 62.17% 7 dice, 64.73% So it's not as simple as saying the attacker always had an advantage or disadvantage, because it changes based on the number of dice you're rolling. But most of the time (3 or more dice rolled), the attacker has the advantage. For 1-2 dice, the attacker is at a disadvantage. Customs: Superhero Sci-Fi Classic Terrain Tactical Meeples (My Game Blog) Customizing Tools Star Wars Campaign Last edited by GreyOwl; August 1st, 2009 at 01:34 PM. |
#70
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Re: The great myth of Skulls versus Shields.
This will be my last post trying to show why your posts are confusing to me. (Because, really, it just doesn't matter. Everyone understands the basic concepts being discussed here; I was just just struggling to understand your particular take on it due to your incorrect math and confusing choice of words.)
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You need to think through what you're trying to say and make sure it holds water. Otherwise people are going to have to keep pointing out your mistakes so you don't confuse others. Good traders: tdemirji, AbsintheAddict, Blubberguy22, Toa Matoro, SuperSamyon, Bl1ndsn1per, Ericth74,
Clipper423, Oh Freek, Nikkomon, DarthBaggins, quizzcode, Astroking112 & more on my trade list |
#71
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Re: The great myth of Skulls versus Shields.
I think superfly was under the influence the last couple times he posted in this thread.
I am giving you an out superfly; I suggest you take it. |
#72
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Re: The great myth of Skulls versus Shields.
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Under that assumption I've began to wonder if drafting squads with 3 defense (assuming they are cheaper than those with 4) is better than drafting high defense squads for more points. So if we revisit the Dwarves vs KoW discussion. Is that one defense dice really all that much, looking at how the numbers add up? We now have 2 different statistics: The "Optimal amount", and the "Advantage Changing amount" Most squads have 2-4 attack(?), so more often than not the defender will be at a disadvantage that is less than 1%! (3Attack vs 3Defense = 50.93% advantage to the attacker.) I don't really know which thread holds more weight in my mind. Anyone else have an opinion on the matter? In forest dark or glade beferned
No blade of grass shall go unturned Let those who have the daylight spurned Tread not where this green lamp has burned. |
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