D&D General 1 in 1000 chance

[The Shadow]

So what are the odds of rolling three "1"s on d20 in 10 rounds of combat?

The odds of rolling exactly three 1's is:

C(10,3) (1/20)^3 (19/20)^7 = about 1.05%, or about 1 chance in 95.5.

The chance of rolling 3 or more 1's is about 1.15%, or about 1 in 86.9.

Now for a couple stories of my own! I was playing a solo superhero game and the GM says, "Make a Notice check." I roll a 1.

He says, "What the heck. Go ahead and roll again." I roll a 1.

He must have kinda wanted me to notice whatever it was, because he said, "Third time's the charm?" I roll a 1.

1 chance in 8000!

On the other hand, years ago I was playing TORG, which has d20 rolls explode on 10s and 20s. We come across an enemy camp, and my cyberpriest decides to attempt a minor miracle to make their lives harder before we attack. (Miracles in TORG are usually very subtle and unpredictable.)

I roll a 20. Then a 10. Then a 20. Then a 17. (If I'm not mistaken, there's odds of about 1 in 4211 of doing that well or better.)

The GM just glares at me and says, "Fine! A pillar of fire descends from the sky and burns up the entire camp! Satisfied?!"

 

[Stalker0]

Two games ago I had a player roll 3 20s in a row!

1 in 8k!

 

[Composer99]

Never roll dice with the clergy - that woman could roll a nat 20 on a D6...

Not a D&D story, but apropos of this, I was in a gaming circle that played a lot of Here I Stand (the card-driven Reformation Era game) for a spell several years back.

Anyway, my brother, the Anglican priest, would always want to play the combined Protestants/English side. (We usually had four players at the time.)

We had to institute a table rule that he wasn't allowed to quote from Tyndall's English Bible or put on Protestant hymns before rolling dice. Although no matter what he tended to roll uncannily well playing that side in that game.

 

[coyote6]

Playing GURPS years ago, I rolled all 1s on 5d6 (1 in 7776) for damage enough times that it became a "Bob did it again" thing. Of course, that was the damage of my character's full auto primary weapon, so I rolled 5d6 a lot. Still, all ones happened more than all sixes with that weapon.

OTOH, I tossed some explosives (maybe a grenade, I don't recall) doing 8d6 damage, and did 48 damage. All sixes - that's 1 in 1,679,616.

 

[The Shadow]

I roll a 20. Then a 10. Then a 20. Then a 17. (If I'm not mistaken, there's odds of about 1 in 4211 of doing that well or better.)

I got the chance to sit down and thoroughly work this out today - it actually comes out to 1 chance in about 5130. (124747 chances in 6.4e8, to be precise.)