Plotting average result against a variable

Question

I'm trying to figure out how to create an odd dice curve - specifically, odd when plotting between an axis of average result versus amount of dice (so xd6 gets 3.5 for x=1, 7 for x=2 and so on).

But, I can't figure out how (if?) anydice can let me control what the plot axis will be, or how to work around it anyway. Any pointers?

Answer 1

You can output each of your rolls with an appropriate title, as in:

loop N over {1..10} {
  output Nd6 named "[N]d6"
} 

and then switch to the summary view. Here, the uppermost chart (titled "mean") shows the average of each roll your program outputs:

If you prefer, the summary output can also be viewed in graph mode, with the black line showing the mean:

Unfortunately, there does not seem to be any way (short of writing a userscript or something like that to manipulate the AnyDice UI) to hide the "deviation", "minimum" and "maximum" outputs in summary mode and to show only the mean. This can be a problem especially in graph view mode, since for some distributions (such as those involving "exploding dice") the maximum can be significantly higher than the mean, and thus make the mean line hug the bottom of the chart when graphed.

However, one possible (though somewhat time-consuming) workaround is to switch to the "export" view mode, copy-paste the raw numeric CSV data from there to a spreadsheet (such as Excel, LibreOffice Calc or Google Sheets) and graph it there.

Answer 2

You do not actually need anydice to do this.

Beside Ilmari Karonen's answer, you can consider the math behind this kind of dice rolling.

We know that a d6 follow a discrete uniform distribution, whose expected value \${\rm E}[d6]\$ is 3.5. The expected value operator is linear, meaning that the expected value of the sum of the outcomes of two dice \$d_1, \, d_2\$ is the sum of the expected values of the two outcomes:

$$ {\rm E}[d_1 +d_2] = {\rm E}[d_1]+{\rm E}[d_2] $$

and it can be generalized to \$X\$ dice.

Then, you can directly compute the expected value of Xd6, which reads as $$ {\rm E}[Xd6] = X\cdot{\rm E}[d6] = X\cdot3.5 $$

Hence, you can plot the dependence of the expected value on the number of d6 rolled, by considering the function

$$ y = 3.5x $$

in the Cartesian Plane. Down below you can find an example written in Python.

import numpy as np
import matplotlib.pyplot as plt

average = np.zeros(10)
for x in np.arange(1,11,1):
  average[x-1] = x*3.5 
  
plt.plot(np.arange(1,11,1),average,'o--')
plt.xlabel("Number of Dice")
plt.ylabel("Expected value")

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You can generalize this approach: for example you can plot the variance or the standard deviation of Xd6, or the expected value of Xd12 or other kind of dice.