# Impacts caused by attribute progression in Cairn/Mausritter?

What impacts will attribute progression cause in Cairn?

In Cairn and Mausritter (based on Into the Odd), advancement is largely undefined or loose.

I've decided to use the Mausritter attribute advancement method but roll after every session. We're not increasing HP, just attributes.

Roll for attribute increase: roll d20 once for each of your mouse’s STR, DEX and WIL. If a result is higher than the attribute’s current value, increase it by one.

My first impression is characters will increase to average (11 on a d20), but progression will dramatically slow down at higher STR, DEX, and WIL.

The random variable for going from $$\n\$$ to $$\n+1\$$ is geometrically distributed with $$\p={{20-n}\over{20}}\$$. The sum of multiple geometric variables with different $$\p\$$ is non-trivial, but we can say things about the expected values and the variances because the variables are independent.
The median of a geometric distribution is $$\1\over p\$$, and the variance is $$\{1-p}\over p^2\$$. So, to go from $$\a\$$ to $$\b\$$, the mean is $$\\sum_{i=a}^b {20\over {20-i}}\$$ and the variance is $$\\sum_{i=a}^b {{1-{{20-i}\over 20}}\over \left({{20-i}\over 20}\right)^2}\$$.