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[Thanee]

Yep.

For example, a d10 has an average of 5.5 and a 10% chance to explode, which results in another d10 to be added to the total, and another 10% of 10% chance to explode, and so on (an infinite series).

So the actual average is 5.5 + 10% x 5.5 + 1% x 5.5 + 0.1% x 5.5 + ...

In total...

5.5 + 0.55 = 6.05 + 0.055 = 6.105 + 0.0055 = 6.1105 + ...

As you can see here already, the series will result in 6.11...1105 (with an infinite number of 1s where those '...' are).

So for practical purposes, the actual average of the d10 with exploding is below 6.12 (much closer to 6.11 already).

The average of a d12 is 6.5; so even without exploding, that is more than the d10 with exploding.


It's the same for the other dice.

d4 -> average 2.5

2.5 + 25% x 2.5 + 25% x 25% x 2.5 + ...

2.5 + 0.625 = 3.125 + 0.15625 = 3.28125 + 0.0390625 = 3.3203125 + 0.009765625 = 3.330078125 + ...

As you see, when looking at the intermediate sums (after the '='), the amount added to the total (which represents the added total of continuously rolling 4s, which just becomes highly improbable eventually, and thus only adds a very small amount to the actual average) gets smaller and smaller and eventually becomes so insignificant, that the running total doesn't really get any bigger (practically).

A d6 without exploding already has an average of 3.5, and with exploding it will be above 4, the d4 never reaches that (not even the 3.5 in fact).


The thing that is a bit misleading, the fact that a d4 has a much higher chance to explode (25%) as opposed to a d10 (10%), just to look at a more extreme example, is counteracted by multiplying it with the smaller average (2.5 as opposed to 5.5). The actual amount added isn't that different for any dice type (0.625 for the d4 in the first step as opposed to 0.55 for the d10, for example, so the actual change (since both dice types get the exploding 'bonus') is in the vincinity of ~0.1 between those... even fewer, when you actually look at the difference between d4 and d6, or d6 and d8, etc).

The full 1-point-shift in average (2.5 > 3.5 > 4.5 > 5.5 > 6.5) for going to the next higher dice type is always a much bigger change.

Bye
Thanee