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Dice

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Re: Dice

Postby Count Mohawk » Wednesday May 20th, 2015 9:44am

slev wrote:For those better at probability than I...

That would be me. And Anderas, actually, but I got here first.
For those of you who don't like math, feel free to ignore this post.
slev wrote:Dice with only one symbol per face are easy to compare. But how do we compare them with multi-symbol faces?

For example, is a black die (four skulls) better or worse in the attack than a purple (two skulls and a double-skull)?

Obviously the black is more likely to do *some* damage, but the purple capable of more damage...

The difference between the black and the purple dice lies in their variance. Both dice have the same expected outcome of 0.667 skulls per die, but the purples will generate more 'extreme' results more often than the blacks. Here's a comparison of 3 purples vs 3 blacks:
Image
As you can see, the black dice are more reliable, but the purple dice have more potential, although it is also easier to fumble with them and get 0 skulls.

Now for a more challenging thought process: What happens when you attack a Chaos Warrior with them???:
Image
Image
The two dice are very close in expected damage. The Purples have a slightly higher damage expectation, but this is mitigated by the fact that many of their high-skull rolls will overkill the targeted monster, leading to some wasteage. On the other hand, they also have a better chance of one-shotting monsters, which is of course very good. (The faster you kill the monsters, the less they get to attack you.) I may have to update the MSC Excel file to better visualize the impact of this sort of thing.


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Re: Dice

Postby el_flesh » Wednesday May 20th, 2015 9:58am

Maybe you should call the double skull hit crit (critical hit).

....I gotta say, if I were still playing regularly, I would jump on some crit skull dice. Even if they're purple.
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Re: Dice

Postby slev » Wednesday May 20th, 2015 10:52am

Sol what you're saying Mohawk, is that mathematically, the purple dice are better in this case by about 4%?

I had suspected this sort of result, but it's good to have it confirmed mathematically...

Of course these "crits" also increase thedamage potential of that single die, which is useful...


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Re: Dice

Postby Anderas » Wednesday May 20th, 2015 11:27am

In long term average, they do the same.
However, the double skull dice is less reliable, but has a chance to hit harder. This is nice to give some weapons kind of a character.

It gets interesting if you combine two or three of them. I wouldn't present it here because you get tables as result and tables are not well presentable.

Ah Monsieur Count Mohawk was faster. :mrgreen:

The killing chance is of course better with the purple because it is harder to defend two skulls at the same time. :) the difference is so low you wouldn't "feel" it, however.


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Re: Dice

Postby Count Mohawk » Wednesday May 20th, 2015 11:37am

(Anderas ninja'd me this time.)

Yeah. Actually, the more Defense dice the monsters roll, the more powerful Purple dice become compared to Blacks. I checked against monsters with 2 and with 6 Defense, and in all three cases the Purples outdamage the Blacks, although the difference is most pronounced against the 6 Defense monster. This disparity is mostly due to the Purples' higher variance; their higher rate of missing is more than compensated for by the few times when they roll 4 or more skulls, a result which is typically not blocked.

The 'illogical conclusion' would be a set of dice that has one face with 4 skulls on it and the other 5 faces with various types of shields. Rolling 3 of these would result in a failure to damage the enemy monster over half the time, but the rest of the time they get at least 4 skulls, which is enough to kill or maim almost all non-boss monsters. Furthermore, no skulls are 'wasted' from the enemy monster's defense rolls (e.g. if you get 1 skull and the monster gets a shield to block, resulting in no damage).


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Re: Dice

Postby slev » Wednesday May 20th, 2015 12:11pm

This is the point though. While black may do the one skull more consistantly, the chance of casuing two skulls outweigs this reliability in a matter of preacticality. Less frequent kills is more usefull than more-frequent blockable damage.

I'm thus counting the "crits" as more valuable than two singles on a tie-break basis.


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Re: Dice

Postby clmckay » Wednesday May 20th, 2015 12:15pm

Count........I hate your freaking math skills! :)

I've been trying to make an excel sheet for these dice for the past week. With crappy results! Any chance you could post your spreadsheet so we could cannibalize the proper math?


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Re: Dice

Postby Anderas » Wednesday May 20th, 2015 12:38pm

If Monsters get attacked by 3 purples, they should defend on yellows. :)


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Re: Dice

Postby slev » Wednesday May 20th, 2015 12:50pm

Anderas wrote:If Monsters get attacked by 3 purples, they should defend on yellows. :)


I've ranked the dice this way, tie-breaks based on the re-rolls I sometimes use (not allowing re-rolls of enemy shields):

Hero Attack:
Orange
Purple
Black
Yellow
White
Blue
Green

Montser Attack:
Hero Attack:
Orange
Purple
Black
Yellow
Blue
White
Green

Hero Defence:
Purple
Yellow
Green
Orange
White
Black
Blue

Monster Defence:
Orange
Yellow
Blue
Black
White
Green
Purple


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Re: Dice

Postby Anderas » Wednesday May 20th, 2015 1:20pm

Whereas for defense, reliability is better. In attack a random high result is quite piercing and good. But in defense you avoid the zero at all cost.


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