What are the odds, three 20s in one full attack!


Gamer Life General Discussion


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So, tonight I saw something happen I have NOT seen in all my years of Roleplaying. I saw three 20s rolled in a row. They seemed pretty legit, and the player has no history of trying to cheat.

The player chose to play a fighter, but one that is an archer, so has everything focused on the Longbow.

They had a Rapid Shot feat and are level 9. They had three attack rolls they tossed in row for one turn.

First roll...a natural 20.

Second roll...a natural 20.

Third roll a natural 20.

I actually have the confirmation rolls made after the normal rolls, just to help keep things in order...and all of them got confirmed...but without natural 20s.

However, I was shocked...three 20s in a Row!!!

They also used three different D20s (our way of keeping track of what they rolled during their round).

I started thinking about it, isn't that like a 1/8000 chance of something like that happening?

No idea, never seen that happen, still kind of shaking my head about it.

It was absolutely the highlight of the evening. It was right after a Frost Giant had bashed the Paladin and was coming right at the Archer/fighter, anything short of what happened (with the crits) probably would have meant the Giant would have reached them next and started bashing at the archer/fighter. The archer dropped the Giant as the crits did the final amount of damage to drop the baddie.

Still can't figure the odds completely, left me gaping.


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Yeah I've seen it happen in a couple of sessions. It's quite a sight to behold. Though mathematically, it's just as likely for the dice to roll 3 twenties in a row as it is to roll any other combination. Like say, a 5 a 12 and then a 9. That's the thing about probabilities, unlikely combinations come up every game if you think about it that way.

Chance is such a fickle thing.


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That reminds me of a funny event...

My friend and his unlucky Paladin (guy has more natural 1s than every other player combined!) managed to roll 3 natural 1s in the same round an enemy rolls 3 natural 20s against him. LOL!


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Yes, 1 in 8000 ... but these things are skewed by our perception. (You don't stop to think about all the times you threw three d20s and got any other combination).

If you think about how long you've been playing, the number of people at the table - and therefore the number of throws that are taken in total over your gaming career - then the chance of some extraordinarily high dice combination/sequence happening sometime is actually pretty high.


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Odds of rolling three natural 20s in a row, 1 in 8000.
Odds of confirming all three crits, fair.
Pulling it off after your meatshield just bit it and the angry Giant is barreling down on you? Priceless.

That scene described has tons of awesome. It's like the archer saw his friend just drop, and pulls a "Screw that, I'm ending this." moment. Love it!


I've seen it happen twice that I can recall. Real showstoppers, both times! One was with a weapon that did 3x damage on a crit. All that was left were fond memories of that foe.


And here I am sitting crestfallen that my equivalent moment is rolling 3 ONES in a row (and a total of 6 ones in a 3 round combat).


That seems to happen more often to me than the triple crit... LOL


GreyWolfLord wrote:

So, tonight I saw something happen I have NOT seen in all my years of Roleplaying. I saw three 20s rolled in a row. They seemed pretty legit, and the player has no history of trying to cheat.

The player chose to play a fighter, but one that is an archer, so has everything focused on the Longbow.

They had a Rapid Shot feat and are level 9. They had three attack rolls they tossed in row for one turn.

First roll...a natural 20.

Second roll...a natural 20.

Third roll a natural 20.

I actually have the confirmation rolls made after the normal rolls, just to help keep things in order...and all of them got confirmed...but without natural 20s.

However, I was shocked...three 20s in a Row!!!

They also used three different D20s (our way of keeping track of what they rolled during their round).

So, provide the relevant attack bonuses and acs and we can have a precise set of odds.

I started thinking about it, isn't that like a 1/8000 chance of something like that happening?

No idea, never seen that happen, still kind of shaking my head about it.

It was absolutely the highlight of the evening. It was right after a Frost Giant had bashed the Paladin and was coming right at the Archer/fighter, anything short of what happened (with the crits) probably would have meant the Giant would have reached them next and started bashing at the archer/fighter. The archer dropped the Giant as the crits did the final amount of damage to drop the baddie.

Still can't figure the odds completely, left me gaping.

Get the guys attack bonuses for the three attacks and figure out the odds of beating ac on the confirmation rolls. Take the five percent chance of a twenty and multiply it my the chance of confirming, then multiply the chance of each confirmed crit by each other and you will have your final answer. For example, if he had a 95% chance of confirming! it takes it to 1 in 9,330. If its a ninety percent chance of rolling the confirm it take it to nearly 1/11,000.

So provide the archers attack bonuses with relevant modifiers(range, et al) and the giants ac, and we can give you precise odds.


Has a total of a +15 to hit with the Long bow against a Frost Giant that had a 21 AC. However, +15 is just the first attack and Rapid Shot (normal attack would be at +16, but it gets a -2 due to Rapid Shot, but I allow the +1 on the rushing giant since it was basically at point blank range), second attack was at a +10 with the long bow. So good chances to hit and confirmation. However, getting three natural 20s in a row was the shocker...though having all of them confirmed was very nice, it wasn't completely unexpected with the bonuses to hit.


Rynjin wrote:
And here I am sitting crestfallen that my equivalent moment is rolling 3 ONES in a row (and a total of 6 ones in a 3 round combat).

I am reminded of a Werewolf: the Apocalypse game once, long time ago. I was rolling 21 dice for damage and the net result was -1 success. Probably the worst roll I have ever seen.

(For those not informed on oWoD, you roll d10s and any die that comes up 6+ is a success. Each 1 subtract one from your total number of successes. So I had more 1s than 6+s.)


1 in 22,270, by rough math.


Its always nice when that kind of thing happens it was just so much cooler that it happened after the paliadin got pounded and the giant was heading straight for him .
That story will make it in to your party's list of "Do you remember when" moments


Pathfinder Adventure, Adventure Path Subscriber

Given the sheer number of rolls that happen at the table, one in 8,000 isn't all that much. That's a big part of why we don't play with the insta-kill rule at our table. DMs roll a lot more dice than players, so it's kind of imbalanced.


That reminds me of the time a character in one of my campaigns rolled three natural ones in a row. Considering this was a non-serious campaign where one of the rules was that random bad things happen whenever you roll a natural one ... things got interesting. Was fun having everyone ask the halfling monk why there was a tree growing out of his head for the rest of the campaign.


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One of the GMs I play with has a houserule where if we/he confirms an attack, which rolled a natural 20, with a natural 20 on the confirm roll, then we rolls another d20. If this is also a natural 20 then the character/enemy is simply slain. He has killed 2 characters that way so far in a good 8 years. So yeah, really rare that it even happens, but it can happen.


I used a few crit methods that could get to three dice (20-20-confirm to kill/expand crit). I've seen 20-20-20's about ten times in 15 years for those - but that's on a single consecutive attack (but haven't used those rules the entirety of that time).

Three 20's out of three attacks is 1 in 8000, but another way of looking at it is for every time someone rolls a 20, they'll roll two more 20's 1 in 400 times.

You roll a 20 at some point most times you sit down at a table, often more than once. At just once, with 5 people at a table, gaming once a week, you should see three 20's once every year and a half or so. 7 People at the table, gaming twice a week it goes up to every 6 months.


Slaunyeh wrote:
I am reminded of a Werewolf: the Apocalypse game once, long time ago. I was rolling 21 dice for damage and the net result was -1 success. Probably the worst roll I have ever seen.

I'm not surprised. The White Wolf system was mathematically flawed from the beginning. The more dice you have in your dice pool, the more chances you have of rolling 1s, each of which, in addition to being a failure, further subtract 1 from your successes. IIRC, the only mechanism available to counteract that is you roll 10s on a roll involving one of your character's rarified specialties; which allows you to roll that dice again for additional possible successes. The problem is that 1s always subtract while 10s don't always provide re-rolls nor do those re-rolls always amount to additional successes.

It's a matter of diminishing returns; the better your character is at something, the better his chances are of suffering a critical failure at it. It's counterintuitive and kind of dumb.


I've done it myself a few times, unfortunately I only seem to get rolls like that when I'm the GM. Add to that the fact that we use the instant kill rules and it makes for sad players from time to time. I had a 6th level paladin get instant killed by a lizard man with a spear once, we had a good laugh about it after the paladin got raised.


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Was playing a Gunslinger who got 4 shots in this particular round.

Rolled four d20's at one time.... got three 20's and something else.

Rolled three d20's (all at once) to confirm the three possible crits... got three 1's.

Ah, the fickle things that are the dice gods.


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One time I rolled four 16s in a row.


EvilMinion wrote:

Was playing a Gunslinger who got 4 shots in this particular round.

Rolled four d20's at one time.... got three 20's and something else.

Rolled three d20's (all at once) to confirm the three possible crits... got three 1's.

Ah, the fickle things that are the dice gods.

It's like finding a beautiful sparkling diamond then having the surface flake off to reveal a dried old turd.

Silver Crusade

My coolest story is just back to back natural 20s, but it's got a funny twist. I was playing a blackened aasimar life oracle who carried a heavy shield. Between the blackened curse, a 7 Str, and the non-proficiency with the shield, I needed a natural 20 to hit anything. I decided at one point to try and shield bash a skeleton.

Before I rolled I said, "Not even going to figure out my bonuses and penalties, just assuming I need a natural 20 to hit." So I rolled a nat 20. Then I say, "Need another nat 20 to confirm." And rolled another nat 20.

Then rolled my damage:

2d4 - 4 = 1 + 2 - 4 = -1 = 1 non-leathal damage.

Against a skeleton.

Which isn't affected by non-lethal damage.

So in the end, I rolled back to back nat 20s to do absolutely nothing.


I did this last year as well in PFS, also with an archer character (a barbarian). I guess you roll a lot of dice as an archer but...

Yep, three 20's to hit and threaten...

...and then three rolls that failed to confirm any of the crit threats

The thrill of victory, the agony of defeat

Silver Crusade

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Lamontius, I roll so many 19s on my archer inquisitor that I am seriously considering taking Improved Critical as my level 11 feat.


So basically...
Your Oracle wound up and GODSMACKED the skeleton upside the skull using their shield with both hands. The skeleton's skull spun around about 4-5 times on its neck before coming to a rest. It grabbed its skull with both hands and re-adjusted it to face forward with the same rictous smile, albeit missing another couple of teeth.


Ambrus wrote:


It's a matter of diminishing returns; the better your character is at something, the better his chances are of suffering a critical failure at it. It's counterintuitive and kind of dumb.

Yes, I found I got as many or more successes with 9 dice than 12. Ten dice was kind of a sweat spot for me in WoD.


A guy I gamed with in college had a character with 5 18s and 1 17 in his PCs ability scores. We watched him roll; even made him change to someone else's dice.


I actually saw a friend roll 4 natural 20s in a row. At the time, we played that two natties in a row was an instant death. He wasplaying a Monk and instant killed two demons in one flurry. It was a sight to behold.

Shadow Lodge

Lamontius wrote:

I did this last year as well in PFS, also with an archer character (a barbarian). I guess you roll a lot of dice as an archer but...

Yep, three 20's to hit and threaten...

...and then three rolls that failed to confirm any of the crit threats

I was going to chime in on this thread about that exact sequence of rolls, which interestingly broke a streak of almost a dozen rolls that failed to break 5.

I've rolled three 20s before on a single attack when we dabbled briefly with the rules that such a confirmation meant an insta-kill. After successfully doing so, we stopped using said rules.

I've also seen three 20s on a PbP roll sequence, but I blame the Paizo forum's RNG for that one. :)


yeah rolling less than 5 is pretty much the norm for me on a d20, as wakedown and many of the other players I game with regularly can attest

:)

:|

:(

*sobs*


Lamontius wrote:

yeah rolling less than 5 is pretty much the norm for me on a d20, as wakedown and many of the other players I game with regularly can attest

:)

:|

:(

*sobs*

I know this pain. I consistently roll low. And what's worse is the likelihood of me rolling low is directly proportional to how important the roll is. This has happened so much that the term "to kBro" in our group means to roll poorly when it matters most.

Example : got dropped to from 12 to 1 CON by box jellyfish poison because I failed every single save, even with healing aid by our cleric

I've also rolled multiple 1s at the same time on full attacks multiple times.

Dice gods hate me.

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