So, tonight I had an issue with the way the DM was doing a miss chance.
It was a 20% miss chance. He was rolling a D10 and saying that if it landed on a 1 or 2, it was a miss.
I argued that you had to roll percentile dice, two D10's, since it was a 20%. I argued there was a greater chance that since you were rolling actual percentile dice, and rolling two dice, there was a greater chance of failure, however minute, since the second dice could push the the percentage to 21-29%.
I'm not sure if I'm making sense, but it just seems like since you're rolling a D10 only, you're ignoring the 21-29%.
Everyone at the table said I was wrong, but I'm not so sure.
Any help with this would be great.
He was right; you are wrong. I don't fully understand your reasoning but the chance of each number on a d10 is 10%.
Suppose you roll d100 and the first dice is a 1. That's a range from 10 to 19 - a 10% chance (not a 9% chance as you might think - count them out on your fingers if you're unsure). If the first dice is a 2, that's a range of 20 to 29 - another 10% chance. Total range from 10 to 29: 20%.
I understand what you're getting at, but it really makes no difference. Because while you are ignoring the 21-29 with a 10 sided die, you are also ignoring the 1-9, which balances it out. So both have the same chance of success and failure.
Rolling a 100 sided dice, failing on 1-20, so we have a 20% chance to fail.
Now rolling a 10 sided dice, failing on 1-2, again we have a 20% chance of fail.
He was right; you are wrong. I don't fully understand your reasoning but the chance of each number on a d10 is 10%.
Suppose you roll d100 and the first dice is a 1. That's a range from 10 to 19 - a 10% chance (not a 9% chance as you might think - count them out on your fingers if you're unsure). If the first dice is a 2, that's a range of 20 to 29 - another 10% chance. Total range from 10 to 29: 20%.
Total range from 10 to 29%, that means its actually a 29% miss chance. Man, that makes Blur 29% miss chance, a much better spell.
I'm not trying to be a jerk here. Sorry Matthew, I appreciate the response. It just doesn't make sense to me.
1 to 29 would be 29%. 10 to 29 would be 20%.
Think of it this way.
When rolling the percentile, you're going to have a miss 20% of the time. That would mean numbers 1-20, giving you 20 chances for a miss out of the possible 100 outcomes. So, 20/100.
With a d10, and a miss on 1 or 2, that gives you 2 chances for a miss out of 10. So, 2/10.
20/100 = 2/10
They are indeed the same miss chance.
1 to 29 would be 29%. 10 to 29 would be 20%.
Sigh, this is why I'm a history major, I think you're right Matthew. Sorry if I cam off as a jerk.
Well it kinda depends.
Does a d10 die actually have a 1 in 10 chance of landing on any number, or is it similar to a standard d6 where there are unequal percentages?
...is it similar to a standard d6 where there are unequal percentages?
?
Actually that might be one of the first cases in history of someone on the internet realizing they were wrong and admitting it. You're whatever the opposite of a jerk is.
Now, should I get into an argument with Rynjin about about the percentage chance of rolling any given number on a d6 or should I let it go? I think I'll quite while I'm ahead.
Now, should I get into an argument with Rynjin about about the percentage chance of rolling any given number on a d6 or should I let it go? I think I'll quite while I'm ahead.
Go ahead. I'm a little rusty on my statistics, but so far as I remember a 3 or 4 on a d6 is much more likely than any other number. Hence why a 7 is by far the most commonly rolled number when rolling two d6's.
Of course it's past 5 AM and at second glance the idea of a d10 having the same thing going on looks stupid.
Rynjin is technically correct.
A theoretically perfect dice has an equal chance of landing on any side. However, dice are not perfect, and mass production dice are even less so. Minute production flaws, differences in the viscosity of the plastic during the pour, even the pips being drilled out (or numbers carved out or differences in density of paint due to size of numbers) can throw off a dice and weight it one way or the other. Thus why some dice are 'hot' and others are 'cold'.
However, in this case, since the percentile dice and the d10 are both equally likely to be off, they really are just noise in the statistics.
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OK, I think I can handle that one too.
The only way to get a 12 on 2d6 is if both dice are sixes, which makes it unlikely (1 in 36), but there are multiple ways of getting a 7. (First dice 1 and second dice 6, or first dice 2 and second dice 5...)
7 is the most likely number on 2d6 because no matter what you roll on the first dice, you can still get a 7. That makes it a 6 in 36 or a 1 in 6 chance.
That is not the same as saying a 3 or 4 is more likely on a single dice roll. Try rolling a single dice fifty times and I bet you won't get significantly more 3s and 4s than anything else.
Now, should I get into an argument with Rynjin about about the percentage chance of rolling any given number on a d6 or should I let it go? I think I'll quite while I'm ahead.
Go ahead. I'm a little rusty on my statistics, but so far as I remember a 3 or 4 on a d6 is much more likely than any other number. Hence why a 7 is by far the most commonly rolled number when rolling two d6's.
Of course it's past 5 AM and at second glance the idea of a d10 having the same thing going on looks stupid.
Ok, and I'm wrong. You are not correct. You ninja'd me.
You're thinking of combinations of numbers on the dice. Craps uses 7 as the break point because it's the number that has the most combinations when you add up the pips on two dice. However, you're much more likely to get some other number than 7, but much more likely to get a 7 after getting that number rather than getting that number again. For example, there's only 2 ways to get 3 on 2 dice (1/2 and 2/1), but to get a 7 you can get (6/1, 5/2, 4/3, 3/4, 2/5, 1/6), so you are much more likely to get a 7 before you get another 3.
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Well it kinda depends.
Does a d10 die actually have a 1 in 10 chance of landing on any number, or is it similar to a standard d6 where there are unequal percentages?
Did you just mis-understand the 2d6 bell curve?
Or do you really think that a single d6 has a greater likelyhood of resulting in a 3 or 4?
If it's the second, I'd really like to read your reasoning, and so would the casino where I work!
Well it kinda depends.
Does a d10 die actually have a 1 in 10 chance of landing on any number, or is it similar to a standard d6 where there are unequal percentages?
Did you just mis-understand the 2d6 bell curve?
Or do you really think that a single d6 has a greater likelyhood of resulting in a 3 or 4?
If it's the second, I'd really like to read your reasoning, and so would the casino where I work!
Your casino pays through the nose to ensure their dice are as near perfect as possible. Standard gaming dice vary wildly in their manufacture, and are quite likely to not have an equal chance of landing on any given number.
A set (5) of casino A grade dice can go for anywhere from $12 to $25 dollars, that is, from $2.10 to $5 per dice. The average gaming dice sold in a gaming store goes for about $0.25 to $1.00, depending on the material.
So while yes, he did misunderstand the bell curve in the original post, gaming dice are not actually all that accurately manufactured and individual dice will have some numbers they favor over others.
Dice that aren't visibly malformed only favor certain sides maybe 1-2% more often, which is less impactful on your rolling than the surface of the table.
It's a pretty common belief that dice are "hot," because of factory imperfections, but more likely, it's just you getting into a rhythm picking the dice up and rolling them in the same manner.
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Although imperfections can result in any die not being 'true', I know if no reason that 3 and 4 would be more common results in randomly imperfect dice, especially when the 3 and the 4 are on opposite faces!
This is what would make me really curious, if indeed that is his assertion! Although it probably isn't his assertion, I'd like to know. : )
If you doubt the randomness of your dice, just roll them a couple thousand times and tally up the results.
For most practical purposes any decently made die will be random enough for gaming purposes.
As far as the original question is concerned, from a pure mathematics, probability and statistics perspective your GM is right, rolling a 1 or 2 on a d10 is a 20% chance.
I do similar things all the time. On a 25% chance, if a d4 is in front of me, I'll just pick up the d4. On a 50% chance I might even flip a coin.
It's all the same from a probability perspective.
I appreciate all the responses guys, I really do. I didn't mean for any arguements to get started, but this is the internet. It still makes little sense to me, but since everyone at my gaming table and several people on here have gone to great lengths to explain that I was wrong, I will settle in, bite the bullet and admit that I was wrong.
Now I'll just accuse him of fudging dice behind the DM Screen :). Lol, j/k.
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Rynjin,
if you roll a single die, d2, d3, d4, d6, d8, d10, d12, d20, d100, you have an equal chance for each value to come up. this is a linear 'curve'.
if you roll (two or more) summing dice, the middle values will come up more frequently than the outlier values. this is a 'bell curve'.
it is said that a d6 'averages' to 3 or 4, or more correctly 3.5, but this is only so when summing dice, not when rolling a single die.
(to find out what a die averages for summing purposes, you add all it's possible values together, then divide by the number of possible values. example: 1d4+3 will give you 4 + 5 + 6 + 7 = 22, divided by four equals 5.5)
(shortcut: on a regular die only, d4, d6, d8, d10, d12, d20, to discover the average, you can add the lowest value to the highest value then divide by two. example: 1d20 will give you 1 + 20 / 2 = 10.5)
now take 3d6. the most common or 'average' value will be 3.5 + 3.5 + 3.5 = 10.5, effectively 10 or 11, with the range of values being anywhere from 3 (1+1+1) to 18 (6+6+6). thus it is that since 1E (which has a great essay on this in the player's handbook!), an 'average' ability score for any character is set at 10, and rare indeed was a character who actually rolled a 3 or an 18 in any ability score.
hope this helps!
cheers
Never said that standard gaming dice aren't good enough for gaming, only that they aren't perfect dice and therefore don't have exactly equal chance of each number. :)
Yes, it might only be a 1-5% increase that 1 comes up over a 6 on a d6, but that is still 'out of true'.
On the other hand, non-d6 dice are not quite so good at randomness, because they aren't squares. Game Science Dice blog entry. You can get some of the game science dice, which are about $10 to $15 for a set, and they're built more along the lines of casino dice.
Yeah it was 5:25 AM and I hadn't slept in quite a while when I wrote that.
I don't do math on little sleep. At all. I can barely do addition in those circumstances.
So, while I appreciate it, ya really didn't need to make the entire thread about it, I was just going to dig up my old Stat textbook and look through it again.
Never said that standard gaming dice aren't good enough for gaming, only that they aren't perfect dice and therefore don't have exactly equal chance of each number. :)
Yes, it might only be a 1-5% increase that 1 comes up over a 6 on a d6, but that is still 'out of true'.
On the other hand, non-d6 dice are not quite so good at randomness, because they aren't squares. Game Science Dice blog entry. You can get some of the game science dice, which are about $10 to $15 for a set, and they're built more along the lines of casino dice.
As much as I love Zocchi for his salesmanship and passion, I kind of hate my Game Science Dice. They're hard to read (very poor paint jobs wore off very quickly--also makes them kind of ugly), they're really strangely light-weight compared to every other die I've ever rolled which is uncomfortable, and if they are "more random" at all, and I doubt they are, it's absolutely not "more random" enough for me to use them over heavier, nicer looking, easier to read dice that I own.
Not to complicate the matter but I have a thought that I didn't see an answer to in the comments (apologies if I over looked it).
I get that if there are 10 possible out comes you could arbitrarily pick any two of those and that would be 20%. But I think the confusion lies in the minor details.
If you have a percentile set and roll the tens place (00-90) and 00 is what comes up that is not in the bottom 20% automatically. It has the possibility of being 01-09, but also 100 assuming a zero on the other die.
I'm not an expert but the relationship of the percentile dice to each other and that you can roll low on on the tens die and still end up with a 100 seemes to change the dynamic some, while most likely not really effecting overall probability.
To the OP's point though, you can just say 1 and 2 are a miss and everything else is a hit and you get your 20% on one die. Just thought I would point out where I personally believe some confusion came from.
--Pharazon
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Not to complicate the matter but I have a thought that I didn't see an answer to in the comments (apologies if I over looked it).
I get that if there are 10 possible out comes you could arbitrarily pick any two of those and that would be 20%. But I think the confusion lies in the minor details.
If you have a percentile set and roll the tens place (00-90) and 00 is what comes up that is not in the bottom 20% automatically. It has the possibility of being 01-09, but also 100 assuming a zero on the other die.
I'm not an expert but the relationship of the percentile dice to each other and that you can roll low on on the tens die and still end up with a 100 seemes to change the dynamic some, while most likely not really effecting overall probability.
To the OP's point though, you can just say 1 and 2 are a miss and everything else is a hit and you get your 20% on one die. Just thought I would point out where I personally believe some confusion came from.
--Pharazon
The confusion you mention comes from attempting to "map" the 20% from the percentile dice to the 20% from the d10. There's no reason to do so, it's just a numerical coincidence that you use similar numbers in each case.
In fact it doesn't matter which numbers you use in either case. You can pick any random 20 numbers between 1 and 100 (inclusive) and have a 20% chance that one of those numbers will show up when you roll. And you can pick any 2 numbers on the d10 for the same 20% chance.
The fact that we generally pick "01-20" on the percentile dice and "1-2" on the d10 are arbitrary choices that have no relationship to each other beyond that each is a convenient way for human minds to adjudicate the outcome.
40 posts / correct answers already a lot = oh my gawd why is this still happening * cats = srsly why is this happening and not yet done as a thing on this board.
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I do similar things all the time. On a 25% chance, if a d4 is in front of me, I'll just pick up the d4. On a 50% chance I might even flip a coin.It's all the same from a probability perspective.
I usually roll my D30 for 50% and do Even/Odd on it
Mainly because I don't use it much otherwise (Random Day Generator)
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I do similar things all the time. On a 25% chance, if a d4 is in front of me, I'll just pick up the d4. On a 50% chance I might even flip a coin.It's all the same from a probability perspective.
I usually roll my D30 for 50% and do Even/Odd on it
Mainly because I don't use it much otherwise (Random Day Generator)
I've got a d30 too and I wish PF had uses for it. The amount of space it takes up in my dice bag, versus the frequency with which i actually use it-- it's not exactly good value.
Are there any games that use a D30 system? ;)
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Now, should I get into an argument with Rynjin about about the percentage chance of rolling any given number on a d6 or should I let it go? I think I'll quite while I'm ahead.
Go ahead. I'm a little rusty on my statistics, but so far as I remember a 3 or 4 on a d6 is much more likely than any other number. Hence why a 7 is by far the most commonly rolled number when rolling two d6's.
Of course it's past 5 AM and at second glance the idea of a d10 having the same thing going on looks stupid.
A 7 with 2d6 is more common not because a 3 or a 4 on n individual die is more common, but because there are more combinations that make 7.
Treat the left die and right die separately. You can get the total of 7 from:
L6 R1
L5 R2
L4 R3
L3 R4
L2 R5
L1 R6
As opposed to, say, 4, which can only be obtained with:
L1 R3
L2 R2
R3 R1
----
You can't sum dice to get a true percentage (you could get 5% -100% by using 5d20, 10%-100% with 10d10, etc), so you don't get the bell curve effect that you get with 2d6 and the plethora of sevens. Combined with the explanations already given, I believe this horse is dead.
People keep saying rolling 2d6 gets you a bell curve, but properly speaking 2d6 is a triangular distribution. It isn't until you get to more dice that the number distribution makes a bell curve.
Not to complicate the matter but I have a thought that I didn't see an answer to in the comments (apologies if I over looked it).
I get that if there are 10 possible out comes you could arbitrarily pick any two of those and that would be 20%. But I think the confusion lies in the minor details.
If you have a percentile set and roll the tens place (00-90) and 00 is what comes up that is not in the bottom 20% automatically. It has the possibility of being 01-09, but also 100 assuming a zero on the other die.
I'm not an expert but the relationship of the percentile dice to each other and that you can roll low on on the tens die and still end up with a 100 seemes to change the dynamic some, while most likely not really effecting overall probability.
To the OP's point though, you can just say 1 and 2 are a miss and everything else is a hit and you get your 20% on one die. Just thought I would point out where I personally believe some confusion came from.
--Pharazon
The relationship is irrelevant. Just look at the % you're aiming for and convert it to a fraction.
20% is 20/100, which, when reduced, is 1/5. You can do a 20% roll on a d100 01-20 (100/5=20)
d20 1-4 (20/5=4)
d10 1-2 (10/5=2)
25% has even more possibilities
d100 01-25 (100/4/=25)
d20 1-5 (20/4=5)
d12 1-3 (12/4=3)
d8 1-2 (8/4=2)
d4 1 (4/4=1)
And you can roll a 50% chance on any die, or just flip a coin.
5% can be done on a d20; 20*5=100, so 1/20 times 5 = 5/100.
d100 01-05
d20 1
As long as you can convert the percentage you're looking for to a simple fraction, you can use it on any die that has a factor of that number.
One important thing to remember, and that I noticed a friend of my do at our game last week, is that if you need to roll a d3, do NOT divide the die number to get your result. He rolled a d6 and divided in half, figuring that 6/2=3, but what you end up with is a distribution of 1, 1, 1, 2, 2, 3, instead of 1, 1, 2, 2, 3, 3. You can roll a d3 on a d6 or a d12 (though why you'd use the bigger die, I don't know).
Instead, you can either go 1, 2, 3 as the numbers read, 4=1, 5=2, 6=3, which is what I do, or 1, 2 =1, 3, 4 =2, 5, 6 =3. On a d12, 1-4 would be 1, 5-8 would be 2, and 9-12 would be 3 since 12 divided by 3 is 4.
As for dice not having statistically equal results... You could say that that is the case, but it's likely going to be less than a 5% discrepancy, requires thousands of rolls to determine, and would be different from one die to the next, unless there is some correlation between pips and results.
That said, you can occasionally get a die that is seriously weighted. My group has banned one of our friends who mostly DMs from using a certain green d20 of his, because after years of being frustrated by his consistently lucky saves and attack rolls, we decided to actually test the thing.
Now, we didn't have the patience to do thousands of rolls, but we did a couple hundred, and the 20 came up something like 20% of the time; that is, FAR more than it should have been.
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Might as well pipe in here. :)
How to check your dice for balance:
1) Get a micrometer and measure each axis. On a D20 if there is going to be a short axis it should be the 10-11 axis and not the 1-20 axis.
From what I understand this is a manufacturing convention. Somewhere along the line they decided that if there is going to be a short axis it should be 10-11 since 10's and 11's should come up slightly more often than 1s and 20s (due to the shorter axis).
2) Get A LOT of epsom salt, an entire carton. Get a bowl. Pour hot water into the bowl (no more than halfway up..or you will be sorry). Pour Epsom salt in. Stir. Let the salt get fully absorbed. Repeat until your dice float. This may take awhile. Note: some dice are so dense they will not float with this technique, but Ive gotten most dice to float doing this.
Now, spin the dice while in the water. If the dice ever radically change the direction of spin, then the weight is imbalanced.
Example: If a D20 that is spinning 'north to south' slows down and then rolls over hard 'east to west' it is weighted improperly.
There are other factors, but these are two that you can measure relatively easily.
Edit: One other note: on almost all dice the opposing sides of a die should add up to the same number as all other opposing sides.
Examples:
D4 = Does not have opposing sides. :)
D6 = 7
D8 = 9
D10 = 11
D12 = 13
D20 = 21
If the die you have does not then it is in error and should be rejected.
- Gauss
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We banned using those d20s that came out with Magic: The Gathering collector sets way back when because they were weighted to have the 20 symbol be on top, since 20 was your starting life total.
Really?
I never noticed that when they were used by some players.If there is evidence to support that, I would love to see it, as I would like to bring it to some players.
Totally serious here. I am against unfair dice. It's just how I roll.