Three Natural 20's in a Row

Nivek · Mar 7, 2011

As a DM I've rolled two 20s in a row followed by two 1s.
Ever since that day it seems like I haven't been able to roll as many 20s as I have done in the passed.

SSquirrel · Mar 7, 2011

Ainamacar said:
He was saying a 1 in 8000 chance if you spent $20 a week for the entire year...not those odds per $1 ticket or anything like that. That's roughly $1000 dollars, and if the odds are as stated, one would expect needing to pay that 8000 times in order to win once...expending 8 million dollars in the process. That passes the sniff test.

We've had the triple 20 on an attack come up a few times in play, but I can't remember whether or not the DM at the time ruled it an instant slaying attack or not, probably because it wasn't in a clutch situation.

I still say that's an easy lottery. Powerball is 195M:1 odds or over 24 times harder to win than that math.

haakon1 · Mar 7, 2011

Best I ever saw was in the 1980s, in Oriental Adventures (AD&D).

They messed with an altar to Orcus, and I rolled for a chance for Orcus to notice (yes) and gate in (yes).

They were only 4th level at the time.

The samurai (PC of the youngest player) was a very good archer, and a very lucky character. He fired an arrow at Orcus and got a natch 20. That was a crit in our rules, I believe at the time it was double damage + a free roll. He ended up getting 4 NATCH 20's in a row. Orcus ended up pretty low on HP and gated out on his initiative, never actually attacking the party.

Never seen anything like it, in my 30 years (in August) of D&D.

Luckily, Oriental D&D had an honor system . . . honors were heaped upon him!

Heathen72 · Mar 7, 2011

Ainamacar said:
He was saying a 1 in 8000 chance if you spent $20 a week for the entire year...not those odds per $1 ticket or anything like that. That's roughly $1000 dollars, and if the odds are as stated, one would expect needing to pay that 8000 times in order to win once...expending 8 million dollars in the process. That passes the sniff test.

We've had the triple 20 on an attack come up a few times in play, but I can't remember whether or not the DM at the time ruled it an instant slaying attack or not, probably because it wasn't in a clutch situation.

The maths is complicated, but suffice to say it's nothing like 1 in 8000, because he is still only spending $20 each week, even if he is spending $1000 over the course of the year.

Ainamacar · Mar 7, 2011

spunkrat said:
The maths is complicated, but suffice to say it's nothing like 1 in 8000, because he is still only spending $20 each week, even if he is spending $1000 over the course of the year.

spunkrat said:
...I find it hard to believe you will win the Oregon lottery by buying 8000 tickets, though to be honest I don't know how the Oregon lottery works...

The math is not complicated if we make some reasonable assumptions, and based on your second quote you appear to have misunderstood the original poster in the first place.

Haltherrion said:
Interestingly, the odds of rolling 3 20s in a row is the same odds as winning the Oregon state lottery (average payout around $6M i think) during one year if you spent about $20 a week on the lottery.

The original post states that the odds of winning the Oregon state lottery in a year are about 1 in 8000 if you spend $20 a week for that entire year. The number of tickets this buys isn't specified, and doesn't matter if every ticket has the same chance of winning over the course of a year. How frequently they select a winner is also not specified and doesn't matter, or at least doesn't matter very much. (Depending on the details of the lottery both of these may affect the expected number of winners per drawing, so there may be some effect depending on the pot sharing rules for multiple winners. Likewise, if the probability of a ticket winning depends on the number of people playing or if the pot size is not fixed, then some corrections would be necessary. But unless they do something really bizarre these are 2nd order effects that can be ignored in a back-of-the-napkin calculation, particularly one in which only information about the average results over the course of a year are provided).

What matters is that on average you would have to spend that kind of money (i.e. 20*52, or about $1000) 8000 times to expect to win the lottery once over the period of time specified. Well, 1000*8000 is 8 million, which is greater than the winnings of 6 million. And, of course, to the state it doesn't actually matter whether that money comes from one guy or from thousands, or if it is spent over 1 giant year long lottery or lots of daily ones. All that matters is the probability that someone who bought a ticket won. (If multiple prize winners don't split the pot, they also care about the probability of there being two or more prize winners each time there is a drawing or whatever, which will be minuscule in any case). In other words, for every 8 million dollars in lottery tickets the state takes in from any source, it could expect to pay 6 million dollars to winners. If there are no other prizes and there is sufficient volume to account for fluctuations about this average, this is a perfectly sustainable lottery for the state. Assuming a single ticket costs no more than $20, and all tickets are equally likely to win, the best possible odds to win with a single ticket based on the given information would be 1 in 8000*52, or about 40000. If, instead, every ticket costs $1, then each ticket has about a 1 in 8 million chance to win 6 million dollars.

Whether the actual Oregon lottery uses these approximate odds is of no interest to me.

So as to marginally contribute to the thread's topic, I will chime in with a fun story involving somewhat implausible odds:

We were fighting some kind of demon or devil in 3.5, and the party was in rough shape. The cleric (of the god of death) perished, but was returned by his deity to finish the battle, with the understanding that whether he ended up succeeding or failing, he would permanently return to the higher planes immediately after the fight (if not during). In the end he struck the final blow against the last remaining enemy...which proceeded to explode in its death throes and knock him to precisely -10 hp. We never settled whether that was how the god chose to take his servant back, or if he was simply spared the trouble of needing to do it himself.

Heathen72 · Mar 8, 2011

Ainamacar said:
based on your second quote you appear to have misunderstood the original poster in the first place.

Hmm, You are correct there, at least. My bad.

Noctos · Mar 8, 2011

when i dm 2 edition years ago i had to often rule on enemy creatures that a natural 20 did cause double damage or instant kill as suggested in dm's manual. More than once i had to allow a second or third roll by the player if they really wanted the instant kill a second 20 on main boss's meant double damage third meant instant death.

yes it happens it's a stoke of pure luck but it happens
just like players roll nothing but 1-3 all night long.

TheYeti1775 · Mar 8, 2011

A rat killed my 4th level Rogue(2)/Wizard(2) human in 3E with a Triple 20.

Simple clear the tower of rats.
Splinter the Ninja Rat as he is known nowadays, somehow survived the Burning Hands of the room. To rip the thoart out of Theo.
It than proceeded to successfully avoid the rest of the party for 10+ rounds as they couldn't hit it.
This was one of Theo's many deaths.

outsider · Mar 9, 2011

In the 2e days, I had a character with a vorpal sword. In one session, I one shotted every single monster I attacked with it. 5 hour long session, probably at least 15 monsters. It wasn't a continuous streak of 20s, there were lots of saving throws, proficiency checks, etc, I didn't roll a 20 on. It was just every time I rolled an attack check, I got the 20. The campaign fell apart that night, due to me one-shotting what was intended to be a powerful recurring villain, and the DM trying to deny me of the kill "You can't decapitate a dragon. You cut off the end of it's tail instead". Pity he couldn't adapt to how the dice fell, because fighting that dragon was a hugely heroic effort on my character's part(fueled by my ridiculous confidence I would yet again roll the 20, which is what happened).

There's a lesson in that. Never give a vorpal sword to an unnaturely lucky risk-taker.