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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.

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1 Answer 1

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There's nothing special about 11

The lower the score, the greater the chance that the ability will increase, but the fall-off is linear.

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}\$.

You can work this out for any change you are interested in, but, for example, to go from 6 to 11 has an expected value (i.e. an expected number of rolls) of 10.67 with a variance of 8.76. From 11 to 16 has an expected value of 19.91 with a variance of 51.55. So, you would expect that it would take about twice as many rolls to go from 11 to 16 as it does to go from 6 to 11, but the actual number would be more variable. In general, the higher your starting figure, the more rolls it will take to raise the score by any given amount and the more "random" that number of rolls will be.

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