Not to spam the board overmuch, but I just had a ludicrous series of dice rolls in one of the games I'm GMing.
That's five consecutive 3s, on 5 consecutive d20s. (Yeah, a 4 on a d8 snuck in there, but the d20s did a solid progression of suck... For the ten d20 rolls I made in that post, we have a: 3, 3, 3, 3, 3, 6, 2, 19, 16, and a nat 1. For a net average of slightly less than 6.)
How am I supposed to kill any PCs like that?*
I'm sure we all have the stories of the ridiculous string of bad (or good) rolls (usually we remember the bad ones more...).
I had a brief, glorious period where when I looked at my PBPs over the last week, almost 1/3 of my dice rolls had been natural 20s. Alas, it couldn't last.
What are your 'Really, Dice?' moments?
I thought it would be fun to try out an investigator with a rapier in my friend's new campaign, since he lets Weapon Finesse add Dex to damage. In two sessions I haven't been able to roll over a 1 for damage with four different d6s. It got so annoying that my GM started rerolling 1s for me. It only happens to damage, though. Everything is fine when I use inspiration.
WoD, 18 dice in the dice pool due to pulling out all the stops for a desperate attack. No successes, three ones...
We were doing opposed d20 checks and tied 3 times in a row. Statistically slightly less likely than tossing yahtzee on the first roll, but it was fun at the time.
Thought of another one.
In a recent Deathwatch session my Raven Guard who's supposed to be a sniper missed about half the shots he fired despite having a nearly 90% chance to hit while aiming. I ran out of Fate Points about halfway through the session rerolling misses. It's a good thing I have a Dodge of over 100 or I might have needed those.
This is what it looked like this Friday when we rolled initiative for the boss fight. (The party did have two more members present, but I don't remember how well they fared).
All in all that session saw 109 d20 rolls and 10 of them came up 1. That's 9% ones...
At a convention, my ranger rolled 1s twice in a row while using true strike. I crammed that D20 into the bottom of a full trash can. Since then I use a marbled green D20 for such to hits, in case I have to throw it away.
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I get the impression that the thread was made to be tongue-in-cheek, but since I'm studying for my finals right now, I feel a compulsion to write about this logical fallacy.
Setting aside any physical or coding abnormalities in the dice or the rolling thereof, what folks are experiencing is a consequent of the representativeness heuristic.
The representativeness heuristic is the sentiment that a series of random results should look a certain way to seem proper. We all know that the likelihood of seeing a particular number on a D20 is 5%. As a result of knowing that probability, we intuitively expect to see a large variety of numbers before seeing a repetition, particularly one that is consecutive. The fallacy herein lies with the generalization of one roll's result to be influential of the next roll. Try the following question.
A. 1, 13, 16, 10, 11, 6, 20, 7
B. 1, 4, 2, 1, 5, 3, 1, 2
C. 20, 1, 20, 1, 20, 1, 20, 1
D. 1, 2, 3, 4, 5, 6, 7, 8
E. 20, 20, 20, 20, 20, 20, 20
Most folks probably chose A since it averages 10.5 and the numbers are spread rather haphazardly in no particular order. B is unappealing since all of its rolls are 5 or less, averaging 2.375. C is distasteful, even though it averages the same as A, as it alternates between the maximum and minimum rolls. D is typically rejected due to its ascending arrangement of one through eight as much as for its low roll inclination, (averaging 4.5).
What that exercise tells us is that our probabilistic expectations deceive us regularly. Every number rolled on a D20 is constantly, invariably, at a 5% chance of showing its face. We expect randomness to look a certain way, but we need to keep in mind that if randomness were to conform to our expectations, then it would no longer be truly random.
The first roll this die ever makes will be truly random, that is all results having a likelihood of 5%. Let's say we rolled an 8. To determine the possible results of the second roll, we need to eliminate any answers that may seem suspect. 8 is out since we just rolled it. 7 and 9 are out since they would either count upward or downward by one. 4 and 16 are likewise out for halving or doubling the prior number. 2 is the cube root, so it is out. Finally, 18 is out since it has the number 8 in it. We immediately run into the issue that suspect numbers are defined by subjective criteria. What seems suspect to one person is not necessarily suspect to another. This culling reduces the options of the second roll down to thirteen possibilities, each of which has approximately an 8% chance of occurring.
Let's say we got a 3 as our second roll. Since 8 is still within our prior rolls: 2, 4, 7, 8, 9, 16, 18 are still unusable. A result of 3 would, in my mind, rule out all primes, multiples of three, and odd numbers. These two results have eliminated 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, and 19. Seventeen answers are no longer legal, fabricating a 33% chance for a 10, 14, or 20.
At this point, I hope it is evident why a system of having interrelated dice rolls would be undesirable. Even with a concretely defined set of patterns, the die would ultimately be compromised in a way that makes it not fun to play with. Tasks would devolve into making a few garbage rolls so as to "unlock" more desirable rolls. Conversely, your character could fail to do things they are skilled at simply because the desired results are invalid possibilities.
I'm not entirely sure what point I was trying to make with this aside, likely it was something to the effect that randomness is good and that faulting the dice for doing their job is silly.
Besides, if randomness is just the property of doing what is unexpected, then we should infer that rolling five or more threes consecutively in a game session is just as random as rolling any other set of five numbers. The odds for each roll stay the same, 1:20 and 1:20 and 1:20 and 1:20 and 1:20.
Sorry for the longwindedness, I hope that this was informative.
Thanks for the opportunity to study for my final.
I once used a Color Computer to generate endless random numbers. The longer it ran the more the same number recurred. Twice, then three times, 4 times, ect. Reality is the ultimate random number generator. It's been running so long that some people win the lottery twice or three times. I on the other hand have horrible luck.
@Dieben:
You fool! Mentioning probability and statistical distribution offends the Random Number Gods! All players know their rolls are based on the fickle fortunes of fate! I can only assume you are new to gaming to taunt Lady Luck so defiantly!
My dice just suck. I played a monk last game. That Flurry of Misses stuff had nothing to do with the class, it was all my Dice. I would bring in a different set. The first time I rolled them they would be fine. Then they got used to me and then they would start rolling low again. I have lots of d20s.
@Dieben:
You fool! Mentioning probability and statistical distribution offends the Random Number Gods! All players know their rolls are based on the fickle fortunes of fate! I can only assume you are new to gaming to taunt Lady Luck so defiantly!
Prove your a grognard. Who was Zenopus and where was Portown described!
I will start saying, "Hail Eris" before I roll, and see if that helps.
Sadly, I am only a moderately-leveled grognard. My experience goes back to the latter years of second edition, so I fail the true test of the grognards. But I'm still experienced enough to know how Lady Luck can curse people.
You've seen those players. The ones who have to optimize and min/max just to have a half-decent shot at accomplishing anything.
I get the impression that the thread was made to be tongue-in-cheek, but since I'm studying for my finals right now, I feel a compulsion to write about this logical fallacy.
Setting aside any physical or coding abnormalities in the dice or the rolling thereof, what folks are experiencing is a consequent of the representativeness heuristic.
The representativeness heuristic is the sentiment that a series of random results should look a certain way to seem proper. We all know that the likelihood of seeing a particular number on a D20 is 5%. As a result of knowing that probability, we intuitively expect to see a large variety of numbers before seeing a repetition, particularly one that is consecutive. The fallacy herein lies with the generalization of one roll's result to be influential of the next roll. Try the following question.
** spoiler omitted **...A. 1, 13, 16, 10, 11, 6, 20, 7
B. 1, 4, 2, 1, 5, 3, 1, 2
C. 20, 1, 20, 1, 20, 1, 20, 1
D. 1, 2, 3, 4, 5, 6, 7, 8
E. 20, 20, 20, 20, 20, 20, 20
Yes, but this particular example is exploitative. When people answer A, what they are really saying is "I expect a mix similar to this with an average of near 10.5" And they are absolutely correct.
What you are asking is "what is the likelihood of this specific array in this order?" People aren't equipped to deal with that type of question, but that doesn't mean that the all 20's array is a more likely "type" of array (particularly that you use an optical trick to make them all seem the same length). An all 20's array (ie, an array with an average of 20) is 13 standard distributions above the mean. Giving it an extremely unlikely (read 0) chance of occurring. Where as, an array with a mean of at least 9.5 occurs 92% of the time.
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I get the impression that the thread was made to be tongue-in-cheek, but since I'm studying for my finals right now, I feel a compulsion to write about this logical fallacy.
Setting aside any physical or coding abnormalities in the dice or the rolling thereof, what folks are experiencing is a consequent of the representativeness heuristic.
The representativeness heuristic is the sentiment that a series of random results should look a certain way to seem proper. We all know that the likelihood of seeing a particular number on a D20 is 5%. As a result of knowing that probability, we intuitively expect to see a large variety of numbers before seeing a repetition, particularly one that is consecutive. The fallacy herein lies with the generalization of one roll's result to be influential of the next roll. Try the following question.
** spoiler omitted **...A. 1, 13, 16, 10, 11, 6, 20, 7
B. 1, 4, 2, 1, 5, 3, 1, 2
C. 20, 1, 20, 1, 20, 1, 20, 1
D. 1, 2, 3, 4, 5, 6, 7, 8
E. 20, 20, 20, 20, 20, 20, 20Yes, but this particular example is exploitative. When people answer A, what they are really saying is "I expect a mix similar to this with an average of near 10.5" And they are absolutely correct.
What you are asking is "what is the likelihood of this specific array in this order?" People aren't equipped to deal with that type of question, but that doesn't mean that the all 20's array is a more likely "type" of array (particularly that you use an optical trick to make them all seem the same length). An all 20's array (ie, an array with an average of 20) is 13 standard distributions above the mean. Giving it an extremely unlikely (read 0) chance of occurring. Where as, an array with a mean of at least 9.5 occurs 92% of the time.
Hi, thanks for the response!
People are wired per-say to expect an average like that of A, however, the original issue brought up in this thread is about series of dice rolls that are either identical or are just particularly low (specifically referring to the five consecutive 3's). The topic was already about a degree of perceived order in dice rolls. Had order been irrelevant, I would have made more use of combinational formulae.
The core premise of the representativeness heuristic fallacy is defying what people expect to see. Given that a mean is comprised of multiple rolls averaged together, this causes the result of roll X to be dependent on the result of roll Y if a particular mean is desired or in this case expected.
3, 3, 3, 3 (Avg.= 3 over four rolls)
By this point, most folks have some thought along the lines of "This die sucks" or "It's gotta roll high soon" or "There's no way I'll get another 3", etc. Take your pick, in this situation we all think this. We are surprised that this has occurred as it is contrary to what we expect, predict, and desire. It just does not seem like this series of numbers is fair to us. So we conclude that the die will roll differently next.
This is the representativeness heuristic in play: We've concluded that in order to both preserve the "average die roll" as well as to satisfy our desire for a result that is not 3 so that we have a series of rolls that looks representative of a proper die, the results of the prior rolls will dictate what the next roll should be.
In short, we have erroneously changed the chance of "not 3" from 95% to 100% in our minds.
When that fifth 3 is rolled, we are as surprised by our "rotten luck" as we are by the violation of the "100% not 3" expectation.
Yes, a mean of 9.5 is more likely than a mean of 20, but my point here is to illustrate how relying on the mean leaves the mind susceptible to exploitation like I used in my example. The "optical trick" was a happy coincidence due to the board font's kerning.
The expectation of a die rolling average does not lead us astray usually, it is a useful mental shortcut. That does not change the fact that it is still a fallacy to use it with a D20 as there is a uniform distribution of chance for all results with all rolls. In contrast, expecting the average is completely appropriate when rolling 3d6 where the results of each die jointly impact the overall result thereby creating a bell curve. On this chart, you can see the respective roll chances for 1d20 (in blue) vs. 3d6 (in green).
END NOTE: I would have gone into more detail in this post, particularly on how the heuristic can appear in 3d6 rolls, but my final is in two hours and I need to be there on time. Wish me luck!
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A vampire once got into the druid's hat because bad perception rolls.
Granted it was a small bat in the dark and we were all level 4, but the ranger/wizard and the druid both maxed out perception in a party of 7 people plus a wolf and pseudodragon, but after a bunch of failed checks it popped out of the druid's hat in an inn room (we didn't think much of it because small animals had a tendency to pop out at random because our gm is silly sometimes.) Thankfully it just wanted out of vampire city and not a snack.
- Roll will save against charm person. 2+3 = 5
- Be commanded to turn on my friends, opposed charisma check! 16-2 = 14, caster rolls 20. Thanks dice, that 16 would've been nice to have on the save...
- Nothing to do, turn on friends. Attack healer. Natural 20. 17+6 = 23. Confirmed. Healer drops into negatives.
Why, Nuffle... Whyyyyy?
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- Roll will save against charm person. 2+3 = 5
- Be commanded to turn on my friends, opposed charisma check! 16-2 = 14, caster rolls 20. Thanks dice, that 16 would've been nice to have on the save...
- Nothing to do, turn on friends. Attack healer. Natural 20. 17+6 = 23. Confirmed. Healer drops into negatives.Why, Nuffle... Whyyyyy?
Ouch.
I TPK'd my own party once as a dominated barbarian. :( Sad day. I didn't even roll parTICularly badly or anything, just... barbarian. Low will save.
- Roll will save against charm person. 2+3 = 5
- Be commanded to turn on my friends, opposed charisma check! 16-2 = 14, caster rolls 20. Thanks dice, that 16 would've been nice to have on the save...
- Nothing to do, turn on friends. Attack healer. Natural 20. 17+6 = 23. Confirmed. Healer drops into negatives.Why, Nuffle... Whyyyyy?
Ouch.
I TPK'd my own party once as a dominated barbarian. :( Sad day. I didn't even roll parTICularly badly or anything, just... barbarian. Low will save.
I was at least allowed to go out of rage. It might have been a slight bit metagame-y, but I really didn't want to kill her, and with a beast totem barbarian that means not just strength dropping by 6 points (due to fatigue), but also two fewer attacks. Someone would surely have died otherwise.
That barbarian will save, though... I'm gonna need something for that.
I picked up Iron Will with my barb after that. It helped a little. And then further on we got my character a clear spindle ioun stone and a wayfinder (if you're playing with wayfinders and the resonant wayfinder rules, that might be useful to you, but if your campaign/GM isn't using those, not so much).
4 1s in a row last combat. My griffons did not do well. The players however, looked great. :D
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Sometimes the dice are not in your favor, as this post shows.
Hah, weaklings; I've rolled 32/51 rolls as nat 1s in a single night! That d20 went in the trash.This is what it looked like this Friday when we rolled initiative for the boss fight. (The party did have two more members present, but I don't remember how well they fared).
All in all that session saw 109 d20 rolls and 10 of them came up 1. That's 9% ones...
In fairness, Thymus, I think most of us have tried having nights where every roll seems to come up bad. I remember when Evil_Diva played a monk once, years ago, on one of my Legend of the Five Rings-groups, and she went through an ENTIRE campaign without a single successful attack. She literally missed on every single attack she launched throughout a campaign lasting most of a year. The absolute dead last attack in the entire campaign was a punch she threw in desperation. It hit. It critted. She killed the BigBad.
And there was much rejoicing (Gratuitous Monty Python Reference).
It somehow didn't make up for an entire campaign's worth of frustration. I still remember how exasperated she became whenever combat started. She literally seemed to roll 1s and 2s on everything. I remember one fight where she rolled no less than five 1s in a row.
On the other hand, every second or third time someone asked me to roll a to-hit with Kismet in our WotW-campaign, it seemed to come up a Nat 20 (for outsiders: we use Roll20 as our VT, and we use the dice-roller in the system ... everything was above board, I just rolled an abnormally large number of Nat 20's on a golden musket ... +1 human bane thundering rifled musket, allowing golden shots to upgrade the size category for damage calculation purposes by 1)
One-shotting that self-righteous cleric-bastard by turning his head into a canoo remains a particularly pleasant memory.
Bad rolls suck, but karma usually swings around in the end.
Next time one of your dice misbehaves like that, put it in the freezer for three hours.
It works.
One-shotting that self-righteous cleric-bastard by turning his head into a canoo remains a particularly pleasant memory.
I thought the self-righteous cleric-bastard was on our side ;P
Man, it felt like that roll20 dice roller was against me. Of course, my own dice were against me as well, back before the GM asked us to all use the dice roller, but... During those 5 levels, I never rolled a crit (whereas you critted many times during the 3 or so levels that you were with us), but I had many nat 1's.
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Back in the early months of 3.0 I had a character with 20 dex and improved ininative. For almost 4 whole levels (5-8 3/4) he went on 10. It became a running joke that I or or evenualy others would announce that I go on double digits because I can't go on singles anymore. At this point I think ties to init were settled by Wisdom mods so when the multiple characters with +1 to +3 init mods went on 10 I went after them.
One-shotting that self-righteous cleric-bastard by turning his head into a canoo remains a particularly pleasant memory.I thought the self-righteous cleric-bastard was on our side ;P
Man, it felt like that roll20 dice roller was against me. Of course, my own dice were against me as well, back before the GM asked us to all use the dice roller, but... During those 5 levels, I never rolled a crit (whereas you critted many times during the 3 or so levels that you were with us), but I had many nat 1's.
Nono, the -other- self-righteous cleric-bastard. The one with the icky friend.
I had a Minotaur fail to cross a stream that was a DC12. The party lined up and shot him with slings. 7-8 rounds. SMDH.