Sunday, January 22, 2012

The Dice of Doom

Last night, during a frenzied session of Dungeons & Dragons, Jeff was locked in battle with a hyena. His character, an elf ranger, has sufficient skill to fight with a sword in each hand; thus, rather than rolling one 20-sided die to attack, Jeff rolls two.

Rolling a twenty on the die means your character has scored a "critical hit" on his or her opponent, dealing your weapon's maximum possible damage. Rolling a twenty is rare enough - a five percent chance on any given roll of the die - but as seen above, Jeff managed to roll double twenties, dealing out 57 points of damage in one attack and essentially carving the hyena into gory giblets.

As we all ooohed and aaahed in amazement, the question of odds came up - how likely was such a roll? I missed much of Mike's explanation in all the clamor, but it boiled down to something like this:

"It's not really that unlikely...should probably happen once every, oh, [some number of] sessions or, so yeah, probably once every ten years."

It was certainly the most improbably roll I've seen since one memorable event in high school. Vern Ryan was serving as DM while Jeff, Paul and I were on the run from assassins or some similar doom. Things looked pretty bad - our party had messed up pretty profoundly, and our deaths were pretty much inevitable. We were out of options, so in desperation I called upon my character's deity.

"Fine," Vern said, rolling his eyes. "If you roll a one on percentile dice, the goddess will hear your plea and save you."

A one percent chance of salvation! Palms sweating, I rolled - and the dice came up 01. Saved! Vern was appalled, but the rest of us laughed our heads off. Geek drama!


Totty said...

1 in 20 per die with 2 dice leads to 1 in 400 chance.

I then estimated that he rolled the pair of dice 5-10 times a night.

The 10 years estimate was a joke about how often we play. If I actually continued the math, we might expect to see it, on average (as statistics and probability tend to be) about every 40 sessions, which might be 4-ish years for us.

[verification word: suctagus - I'm sure we can work that into the lexicon]

Earl J. Woods said...

I was hoping you'd be along to explain the math, Mike. Thanks!