The value of the unexpected

Some game have die rolls that represent really terrible or really awesome outcomes, you know, the dreaded 1 or desired 20. Usually these values are at the extreme end of the game's dice distribution curve, be that a 1 on a d20 a 3 with 3d6 a -4 with four fudge dice, six 10s with four exploding d10s, etc. Yet these values have very different odds of occurring. This begs the question of how much should we grant the unexpected in terms of odds of occurring.

Let us take a moment to look at really infinitesimal odds of something happening and the value of such out comes in games. Is it valuable to consider a die roll that occurs 0.1% or 0.01% of the time as a significant outcome? Does it make sense to create a rule around a roll outcome that occurs once in 1000 rolls or once in 10000 rolls?

While it may initially seem ludicrous to contemplate such small odds as significant, personally I believe it does make sense, more so if the odds are adjusted by skill. Lets imagine for a moment that the most experienced character has 0.1% odds of rolling a crit, but the crit odds get doubled by every step down in skill. The next skill level has a 0.2% odds of a crit, the next  0.4%, the next 0.8%, the next 1.6%, the next 3.2% and the next 6.4%. Six skill levels have taken the possibility of a crit form nearly impossible to a bit over a 1 on a d20. What about the progression starting an one in then thousand (0.01%)? Starting level 0.01%, 1 below 0.02%, 2 below 0.04%, 3 below 0.08% (we're awfully close to 0.1% now, not far to go to 5%), 4 below 0.16%, 5 below 0.36%, 6 below 0.72%, 7 below 1.44%, 8 below 2.88%, 9 below 5.76%. That's only 9 skill level drops before the odds reach 5%+ once again. Dividing the odds of the unexpected by 10, from 0.1% to 0.01% only added 3 levels required to bring them back to awfully probable.

This of course can be written in more human readable terms in the following way. A 1st level character has a 5% odds of a crit and the odds get halved for each level. Thus a 10th level character will have whereabouts of a 0.01% odds of a crit. Something more reasonable because it really sucks to be super good at something and then drop the ball on a 1.

Next issue of course is actually rolling such awfully low odds. These are rolls that we simply can't achieve straight out on a d20 or even d100. Although some games do have a roll again to confirm which give a 0.25% with a double 1 on a d20 and a 0.01% on a double 1 on a d100.

Now what about exploding dice? Well certainly rolling 8 tens with 4 exploding dice is very small odds indeed, but achievable. Certainly way more achievable than rolling 8 ones with 4 exploding dice, the probability of this being exactly 0. That is unless you explode low dice values, but that is the topic of another blog post.

So rolling for the unexpected can certainly add a plot twist to your story. Take the whole adventure down a very different and interesting path, but it presents two challenges. One is actually rolling such low odds and the second is rolling them "easily" and in accordance with character level progression. It makes sense that a 5th level character has lesser odds of a crit than a lowly 1st level one, but how do we adjust this? More so, how do we adjust this easily if at all? A bit more into dice mechanics in the next post in which we try to defuse a nuke.