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Old July 24th, 2019, 05:42 AM
Xanderby Xanderby is offline
 
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Post New dice probability graphs (pretty colors)

So I've seen the posts from Sisyphus and mccombju about probabilities and statistics, but they didn't convey the information as well as I hope these graphs do.

A brief explanation of the graphs: they start out with attack dice only then defense dice only (future posts will show complete probabilites of attack vs. defense combinations).

The "PDF" (probability density function) graphs show the probability of getting any given number of skulls (0A, 1A, 2A...) (or shields (0D, 1D, 2D...)) when rolling "N" dice. E[X] is the expected value (the mean, or average) of a dice roll. SD is the standard deviation of a dice roll (a measure of how spread out the probability is, a smaller number means your actual roll will be pretty close to the calculated average, a larger number means your actual roll has a better chance of being way off the calculated average). The numbers under the bars indicate the percent each bar is (to one decimal place), the second number is the "1 in <number>" description of the bar. Like if a certain outcome has a 25% chance, the number below the percent will be "4", because 25% is "1 in 4", a 2% chance is "1 in 50", etc. when the numbers get too large scientific notation is used so X.Xe+NN = X.X*(10^NN), so 3.5e+09 = 3.5*(10^9) = 3,500,000,000.

The "Modified CDF" (cumulative distribution function) shows the probability of rolling "N-or-more" skulls (or shields) when rolling "N" dice. I only listed the percent under the bar, because over 50% the "1 in <number>" description of the probability loses relevance.

What ultimately motivated me to make these graphs was my appearance on The Dork Forest podcast discussing Heroscape, and how the Samurai's counterstrike ability made me want to figure this out. The episode:
or http://tdf.libsyn.com/heroscape-with...errmann-ep-528

The graphs: https://sites.google.com/site/beagle...ice_graphs.pdf
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Old July 24th, 2019, 03:01 PM
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Re: New dice probability graphs (pretty colors)

Nice!

You may be interested in my Android app, linked in my signature. I was a freshman in college when I made it so I didn't know the terminology of PDF and CDF but that's essentially how it works. It gets all discrete values of the number of input attack die pdf, all discrete values of the input defense die pdf, makes an expected wound pdf by iterating through the matrix of all potential skull and shield numbers, then converts the pdf into a cdf to get the probability of at least one wound dealt in the attack, at least two wounds, etc.

Eventually I'd like to make it into a web app or something as I think it's fun and useful. And some graphs would be nice too. Your graphs are visually quite good but I think looking at just potential shields and skull outcomes can sometimes be misleading since every skull amount really only matters relative to your opponent's shield amount and vice versa.
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Old July 25th, 2019, 01:58 PM
Xanderby Xanderby is offline
 
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Thumbs up Re: New dice probability graphs (pretty colors)

I agree that isolated attack and defense graphs don't tell the whole story of a Heroscape interaction. I will produce graphs (many, many graphs) that show the possible outcomes of, say, 1 attack vs 5 defense, 2 attack vs. 3 defense, 8 deadly shot orc battle cry attack vs. 9 shields of valor heroic defense aura defense...


Here's a thumbnail of the attack and defense graphs:
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Old July 30th, 2019, 01:36 PM
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Re: New dice probability graphs (pretty colors)

Does it even help that much to get these things into graphs I guess is the big question I have.

Like this is just a quick spin up I did of the graph of a 4v4 attack.



I'm not sure how seeing this as bars actually is more helpful than just the raw numbers. In general the probability of >1 wound isn't even that relevant to gameplay decisions as it gets too far into augury to try to figure out when a hero will die, and your opponent and you will both be playing different based on how many wounds heroes take anyways.

Not to pile on you in this post. But data visualization is what I work in and Heroscape probability is really interesting to me. It's important to make sure your data analysis is always motivated and isn't just producing bar charts for the sake of bar charts.

Something that I think could be a useful bar chart is probability of at least one wound for a variety of attack/defense dice.
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