Expected Values

[Joe_Mello]

Anyone figure out the EV for rolls? I know that we did the rate of difficulty, but I don't think we did straight up expected value.

Fwiw, the EV for a regular roll of dice is 3.5X where X is the number of dice.


ETA: Answer to my own question (to some extent)

-2: 2.53
-1: 3.50
0: 5.03
+1: 6.31

I'm sure there's some formula that involves e or something.

[Father of Dragons]

It's a little tricky to calculate straight out, partially because ones don't add up. However, I can get this from the program I wrote for the difficulties -- I'll take a stab at that on Monday, if I remember.

[Father of Dragons]

OK, here it is (note, my first column is the number of dice after modifiers are applied, whereas Joe's post above is using modifiers against the Ricochet system's base of two dice, so his +1 is the same as my 3):

Code: Select all

Calculate average values for Ricochet Dice Pools
=================================================
-8:          1.17984
-7:          1.22182
-6:          1.27565
-5:          1.34588
-4:          1.43971
-3:          1.56906
-2:          1.75540
-1:          2.04167
 0:          2.52778
 1:          3.50000
 2:          5.02778
 3:          6.29630
 4:          7.52238
 5:          8.75141
 6:          9.97494
 7:         11.17996
 8:         12.35955
 9:         13.51303
10:         14.64482
11:         15.76163
12:         16.86901
13:         17.97007
14:         19.06583
15:         20.15623
16:         21.24072

Remembering, of course, that 0 is roll 2d6 and choose the lower, -1 is roll 3d6 and choose the lowest, etc.

[Clay]

Thanks FoD. It's always interesting to see the cold, hard math. The mechanic itself was playtested quite a bit, but it wasn't created with true math in mind. It always pleases me to see that the progression is fairly linear. More than I expected from OVA's oddball way of handling things.

[Father of Dragons]

Thanks FoD. It's always interesting to see the cold, hard math. The mechanic itself was playtested quite a bit, but it wasn't created with true math in mind. It always pleases me to see that the progression is fairly linear. More than I expected from OVA's oddball way of handling things.

It's not exactly linear, but rather has a nice curve to it (this is, in my opinion, a good thing, since it keeps high end abilities from being hopelessly powerful). For instance, the average value for 4 dice is 7.52238, but the average value for 8 dice is only 12.35944, a ratio of of about 1.64:1 instead of 2:1 (and the ratio between 4 dice and 12 dice is 2.24:1 instead of 3:1). It's not a big curve, but it's there. And there's a reverse curve below 2 dice that keeps it worthwhile rolling even when the numbers are against you.

Your mathematical insticts were clearly good.

[Joe_Mello]

And there's a reverse curve below 2 dice that keeps it worthwhile rolling even when the numbers are against you.

Except....

Code: Select all

Chance of rolling at least one 1
================================
#  Mod  Chance
2   0    .3056
3   -1   .5177
4   -2   .6651
5   -3   .7674
6   -4   .8385
7   -5   .8878
8   -6   .9221

That's not so appealing.