Odds the same rolling a d20 or d6 d10


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I was playing with my group and started rolling d6 d10 for my to hit in stead of a d20. The group almost had a stoke lol. I said to them that the odds were the same. Kinda like 50% displacement if you roll a d6 1to 3 low 4-6 high. Anyone know where I could find odds reference chart.


Not even close. If you have an attack bonus of +7, how are you ever going to hit AC 18? With a d6 or d10 you have a 0% chance to hit. With a d20 you have a 50% chance to hit.

Grand Lodge

thorin001 wrote:
Not even close. If you have an attack bonus of +7, how are you ever going to hit AC 18? With a d6 or d10 you have a 0% chance to hit. With a d20 you have a 50% chance to hit.

That's not what he's saying. d6+d10 is rolled as thus: If the d6 is a 1-3 you take the d10 as is. If the d6 is a 4-6 you add 10 to the d10 roll.

@OP: As far as I'm aware the odds are exactly the same, but I don't have a chart or anything to back me up.


thorin001 wrote:
Not even close. If you have an attack bonus of +7, how are you ever going to hit AC 18? With a d6 or d10 you have a 0% chance to hit. With a d20 you have a 50% chance to hit.

Rolling a d6 and a d10 you would read it like this

D6 1-3=0 4-6=1 and a D10 is read what ever is rolled on the die.

So if you roll a 3 on a D6 and a 6 on a d10 then you would read it as
total of 6.

Now if you rolled a 5 on a D6 and a 6 on a d10 then you would read it as
total of 16.


Jeff Merola wrote:
thorin001 wrote:
Not even close. If you have an attack bonus of +7, how are you ever going to hit AC 18? With a d6 or d10 you have a 0% chance to hit. With a d20 you have a 50% chance to hit.

That's not what he's saying. d6+d10 is rolled as thus: If the d6 is a 1-3 you take the d10 as is. If the d6 is a 4-6 you add 10 to the d10 roll.

@OP: As far as I'm aware the odds are exactly the same, but I don't have a chart or anything to back me up.

Thanks Jeff


Jeff Merola wrote:
thorin001 wrote:
Not even close. If you have an attack bonus of +7, how are you ever going to hit AC 18? With a d6 or d10 you have a 0% chance to hit. With a d20 you have a 50% chance to hit.

That's not what he's saying. d6+d10 is rolled as thus: If the d6 is a 1-3 you take the d10 as is. If the d6 is a 4-6 you add 10 to the d10 roll.

@OP: As far as I'm aware the odds are exactly the same, but I don't have a chart or anything to back me up.

Okay.

Yes, it is exactly the same as a d20. In fact the originals d20s were 0-9 twice, and you used different colors to determine 1-10 and 11-20.

You essentially have a d2 and a d10. 2X10=20 discrete rolls, just like a d20.


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If the odds actually are the same, then question then becomes, Why? What benefit is there in rolling a d6 and a d10 instead of a d20?

The only benefit I could see is if you don't actually have a d20 die.


Jeff Clem wrote:
Jeff Merola wrote:
thorin001 wrote:
Not even close. If you have an attack bonus of +7, how are you ever going to hit AC 18? With a d6 or d10 you have a 0% chance to hit. With a d20 you have a 50% chance to hit.

That's not what he's saying. d6+d10 is rolled as thus: If the d6 is a 1-3 you take the d10 as is. If the d6 is a 4-6 you add 10 to the d10 roll.

@OP: As far as I'm aware the odds are exactly the same, but I don't have a chart or anything to back me up.

Thanks Jeff, my other gaming group has used this method sometime.


Yeah it'll be the same because essentially you're just using the d6 to choose whether the d10 will be rolling for 1-10 or 11-20. Since the d6 represents 2 choices and the d10 10 choice, there are 20 possible equally likely outcomes. Just like a d20. You're rolling an extra die for no particular reason but it should not impact your luck.


Jeff Clem wrote:
Jeraa wrote:

If the odds actually are the same, then question then becomes, Why? What benefit is there in rolling a d6 and a d10 instead of a d20?

The only benefit I could see is if you don't actually have a d20 die.

I was having better luck with that method lol.


Pathfinder Adventure Path, Lost Omens, Rulebook, Starfinder Adventure Path, Starfinder Roleplaying Game Subscriber

Like the man said, way back in the early, early days, when adventures were just beginning to leave the Chainmail-driven miniatures battle and get onto home-written character sheets with six stats & long lists of miscelaneous equipment, we didn't have icosahedral dice numbered 1-20. They were numbered 1-10 twice, or more specifically 0-9 twice. Although some folks would color in their dice (usually with scrounged crayons) to differentiant, I never trust that method, and found a few friends coloring in extra numbers. <g>
So it was d6 (odd=+10) and d20 (numbered 0-9, reading 0 as 10)

Ah, the memories!


Pathfinder Adventure Path, Starfinder Adventure Path Subscriber

Technically, having 2 dice increases the odds of having a bad die by a factor of 2. If the dice are good, you'll have the same odds but, y'know… Occam's Razor.

The best way to roll randomly in any given range is with the fewest possible dice of the highest value. For example, a 100-sided die would be better than 2 d10's, but 100-sided dice are much more expensive, and not used as frequently, so people use the simplest solution available to them. A d20 is both better than a d6/d10 combination and simpler. Win-win. I'm not sure that this actually qualifies as a rules question.


The rules question could be:

"Is it PFS legal to roll this way?"


Jeff Clem wrote:
Jeff Clem wrote:
Jeraa wrote:

If the odds actually are the same, then question then becomes, Why? What benefit is there in rolling a d6 and a d10 instead of a d20?

The only benefit I could see is if you don't actually have a d20 die.

I was having better luck with that method lol.

There are a number of gambler's fallacies at work here.


Cuuniyevo wrote:
Technically, having 2 dice increases the odds of having a bad die by a factor of 2. If the dice are good, you'll have the same odds but, y'know… Occam's Razor.

I wonder if this is true. I suspect it is easier for flaws to exist in a d20 than either a d6 or d10. But this is all base speculation.

The Exchange

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D10s are not Platonic solids and must be eradicated.


The only advantage I can see to this system is that you can just look at the d6 ... if it's a 1-3, you don't have to do math. Just announce your failure.


What are the odds of rolling 10d10 and at least one of them be a 10?


Cuuniyevo wrote:

Technically, having 2 dice increases the odds of having a bad die by a factor of 2. If the dice are good, you'll have the same odds but, y'know… Occam's Razor.

We're really getting into gamer's superstitions now.


Kchaka. The math is to calculate the odds for none of the dies to be a 10 and then subtract from one. So the odds on one d10 not being a 10 is 9/10 or 0.9. Raise it to the tenth power (multiply it by itself ten times) for the chance of none of ten dies coming up a 10. My handy calculator says this is 0.34867844 Subtracting from one gives 0.65132156, which is almost two out of three rolls (0.6666666....)


Eh, it may be the same statistically, but I think it would make it easier to fudge die rolls simply due to it being a non-standard method that other people can't read at a glance.

If you can trust the guy, no problem. If you don't think the guy is trustworthy, then it would exacerbate the situation. (Of course, if you really can't trust him, then even rolling a d20 in front of everyone won't be enough.)


Jeff Clem wrote:

Rolling a d6 and a d10 you would read it like this

D6 1-3=0 4-6=1 and a D10 is read what ever is rolled on the die.

So if you roll a 3 on a D6 and a 6 on a d10 then you would read it as
total of 6.

Now if you rolled a 5 on a D6 and a 6 on a d10 then you would read it as
total of 16.

I always went even = +10, odd = +0. Then I could use any die, not just a d6.

Belafon wrote:
D10s are not Platonic solids and must be eradicated.

Check out these dice. None are platonic solids, yet all are have rotational symmetry. I own a set.

Of course, given your icon, Activation Cube, you might be biased.

/cevah

Grand Lodge

been a while since statistics, but isn't the average roll of a d10 (theoretically) 5 or 6?

If that is true, then wouldn't the peaks be 5, 6, 15, and 16? (d2 being basically a flip of the coin)

If that is true (again, statistics was a while ago) this rolling method is much better for you, as you are more commonly rolling in a possible crit range, keen rapier being 15-20. The odds are different from the d20 roll, which peaks around 10 and 11.


Pathfinder Maps, Pathfinder Accessories, Starfinder Adventure Path, Starfinder Maps, Starfinder Society Subscriber; Pathfinder Roleplaying Game Superscriber

It's exactly the same and no more "lucky" (or unlucky) than rolling a d20.

To see this, consider the probability of rolling a 1 using a d20: its 1/20 = 5%

Now consider the chance of rolling a 1 using the d6/d10 method. To do this, you need to know that the probability of two things occurring is equal to the probability of the first times the probability of the second*.

Thus, the probability of rolling a 1 is the probability of rolling 1-3 on the d6 times the probability of rolling a 1 on the d10.

This is 3/6 x 1/10 = 3/60 = 1/20 = 5%

*:
This is true if (as in this case) the two events are "independent events" which essentially means that the outcome of one doesn't affect the outcome of another.

The same is true for every number - there is an exactly equal probability of obtaining any number from 1-20. "Luck" will have exactly the same impact on either method. In the long run, you'll roll each number from 1 to 20 just as often - no doubt you won't remember the 11s the way you do the 20s though.


Pathfinder Maps, Pathfinder Accessories, Starfinder Adventure Path, Starfinder Maps, Starfinder Society Subscriber; Pathfinder Roleplaying Game Superscriber
Dafydd wrote:

been a while since statistics, but isn't the average roll of a d10 (theoretically) 5 or 6?

If that is true, then wouldn't the peaks be 5, 6, 15, and 16? (d2 being basically a flip of the coin)

If that is true (again, statistics was a while ago) this rolling method is much better for you, as you are more commonly rolling in a possible crit range, keen rapier being 15-20. The odds are different from the d20 roll, which peaks around 10 and 11.

The average of a d10 is 5.5. This means that the average of the d6/d/10 method is the average of 5.5 and 15.5 - which is 10.5. Exactly the same as the average of a d20.

There are no "peaks" with one unbiased die - every number is equally likely. The fact the average is 5.5 doesn't mean you're more likely to roll 5s and 6s.


The use of two dice does not create a bell curve in this case, as they are not added.

You have a 50% chance of rolling a 1-10.
You have a 50% chance of rolling a 11-20.
Ten numbers each, 50% chance, division, 5% per number, just like a d20.

Now, if you were adding numbers together, say with the 2d8+1d6-2 Gaussian d20, you would have a bell curve peaking at 10.5.


Mathematically, these are the same.

If you're worried about 'bad' dice, you can do a chi-square test with Excel and about ten minutes of free time.

And the reason d100s are weak isn't about math. It's because they're nearly round, and usually roll off the table, across the floor, and under something really heavy. They work less well for more money, like leather socks.


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Belafon wrote:
D10s are not Platonic solids and must be eradicated.

So true.

And, incidentally, that's the reason I hate soccer. Not only does it improperly marry hexagons and pentagons but purports to distort them into spherical geometry. Gah! Thales, Pythagoras, Euclid, Archimedes... all spinning in their graves.

so sad...

Sovereign Court

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Kchaka wrote:
What are the odds of rolling 10d10 and at least one of them be a 10?

The odds of rolling 1d10 and having it not be a 10 is 9/10, or 90%.

The odds of rolling 2d10 and having no 10s is 9/10 of 9/10, or 81%.

The odds of rolling 3d10 and having no 10s is 9/10 of 9/10 of 9/10, or ~73%

You see the pattern.

The odds of rolling 10d10s and having no 10s is ~35%. If no 10s is ~35%, then the odds of rolling 10d10 and having at least one 10 is therefore ~65%.


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Quark Blast wrote:
Belafon wrote:
D10s are not Platonic solids and must be eradicated.

So true.

And, incidentally, that's the reason I hate soccer. Not only does it improperly marry hexagons and pentagons but purports to distort them into spherical geometry. Gah! Thales, Pythagoras, Euclid, Archimedes... all spinning in their graves.

so sad...

But Cthulhu rejoices!


thorin001 wrote:
Quark Blast wrote:
Belafon wrote:
D10s are not Platonic solids and must be eradicated.

So true.

And, incidentally, that's the reason I hate soccer. Not only does it improperly marry hexagons and pentagons but purports to distort them into spherical geometry. Gah! Thales, Pythagoras, Euclid, Archimedes... all spinning in their graves.

so sad...

But Cthulhu rejoices!

Joyless chaos feels no exultation! You! are no adept.

Minions, seize him and throw him to the churning chaos!


Pff. Real gamers flip coins in series and translate the result from binary.


Dafydd wrote:

been a while since statistics, but isn't the average roll of a d10 (theoretically) 5 or 6?

If that is true, then wouldn't the peaks be 5, 6, 15, and 16? (d2 being basically a flip of the coin)

If that is true (again, statistics was a while ago) this rolling method is much better for you, as you are more commonly rolling in a possible crit range, keen rapier being 15-20. The odds are different from the d20 roll, which peaks around 10 and 11.

Dafydd, you're confusing "average" with "most likely". With a single die, d10 or any other, every side is equally likely, so there wouldn't be peaks like that. Rolling two d10's to simulate a d20 would increase the average roll slightly because (mostly because) you can't get a 1; the lowest roll is now a 2.


daimaru wrote:
Dafydd wrote:

been a while since statistics, but isn't the average roll of a d10 (theoretically) 5 or 6?

If that is true, then wouldn't the peaks be 5, 6, 15, and 16? (d2 being basically a flip of the coin)

If that is true (again, statistics was a while ago) this rolling method is much better for you, as you are more commonly rolling in a possible crit range, keen rapier being 15-20. The odds are different from the d20 roll, which peaks around 10 and 11.

Dafydd, you're confusing "average" with "most likely". With a single die, d10 or any other, every side is equally likely, so there wouldn't be peaks like that. Rolling two d10's to simulate a d20 would increase the average roll slightly because (mostly because) you can't get a 1; the lowest roll is now a 2.

Yes you can get a one. One d10 is read as high or low meaning (1-5 is read as 0) (6-10 is read as 1). The second d10 is read as what ever is rolled. First d10, 3 rolled= 0 second d10 rolled 6. Roll is read as a 6.

If the first rolled d10 roll was a 6 then that's read as 1. Second roll is a 6, then the roll is read as a 16.


Pathfinder Adventure Subscriber

Yes, I've done this before when I (somehow) couldn't see a d20 on the table. But in that event, I would explain before you roll, or yeah you'll have a mutiny on your hands.

On the same note, I encountered a group that rolls percentile differently than I do. I don't add a d10 to another d10 - I roll both d10s designating one as "first" then use the numbers that come up as the digits of the numbers 1-100 (with 0-1 being a "1" and 0-0 being "100"). I was attacking a 50% concealment, called that 1-50 would be a hit, rolled 5-0 ("50" to me, and "60" to the rest of the table). I acted all excited that I barely hit and everyone else just about threw me out the door for cheating. Awkward argument ensued.

Lantern Lodge

thundercade wrote:

Yes, I've done this before when I (somehow) couldn't see a d20 on the table. But in that event, I would explain before you roll, or yeah you'll have a mutiny on your hands.

On the same note, I encountered a group that rolls percentile differently than I do. I don't add a d10 to another d10 - I roll both d10s designating one as "first" then use the numbers that come up as the digits of the numbers 1-100 (with 0-1 being a "1" and 0-0 being "100"). I was attacking a 50% concealment, called that 1-50 would be a hit, rolled 5-0 ("50" to me, and "60" to the rest of the table). I acted all excited that I barely hit and everyone else just about threw me out the door for cheating. Awkward argument ensued.

"Odd misses"


thundercade wrote:

Yes, I've done this before when I (somehow) couldn't see a d20 on the table. But in that event, I would explain before you roll, or yeah you'll have a mutiny on your hands.

On the same note, I encountered a group that rolls percentile differently than I do. I don't add a d10 to another d10 - I roll both d10s designating one as "first" then use the numbers that come up as the digits of the numbers 1-100 (with 0-1 being a "1" and 0-0 being "100"). I was attacking a 50% concealment, called that 1-50 would be a hit, rolled 5-0 ("50" to me, and "60" to the rest of the table). I acted all excited that I barely hit and everyone else just about threw me out the door for cheating. Awkward argument ensued.

Your way is how I've always seen it done for actual percentile. One die is the tens place, one die is the ones place. I'm not sure how the other way would even work. What happens when you roll a 9 and then a 0? Is that 100? Then what is a 0 then a 0? Wouldn't that be 110? That's just weird.

Of course, when it comes to 50% miss chances, my groups usually don't bother with percentile and just do a high/low.


thundercade wrote:

Yes, I've done this before when I (somehow) couldn't see a d20 on the table. But in that event, I would explain before you roll, or yeah you'll have a mutiny on your hands.

On the same note, I encountered a group that rolls percentile differently than I do. I don't add a d10 to another d10 - I roll both d10s designating one as "first" then use the numbers that come up as the digits of the numbers 1-100 (with 0-1 being a "1" and 0-0 being "100"). I was attacking a 50% concealment, called that 1-50 would be a hit, rolled 5-0 ("50" to me, and "60" to the rest of the table). I acted all excited that I barely hit and everyone else just about threw me out the door for cheating. Awkward argument ensued.

Wait... How would adding them together result in a percentile? Designating one d10 as the tens place and the other for the 1s place is the only way to make 2d10 become 1d100.


blahpers wrote:
Pff. Real gamers flip coins in series and translate the result from binary.

Penny drop landing on its side!

Discussion of the probability of a Coin Landing on Edge.

The result is not binary, but trinary. A little harder to read, and not evenly distributed.

/cevah


thorin001 wrote:

...In fact the originals d20s were 0-9 twice, and you used different colors to determine 1-10 and 11-20.

You may be kidding, or being sarcastic. But it's worth noting, for historical reasons, that the d20 predates Roman times. And as far as I know, the game was always played with real d20s. I have never heard of there being a time when 2d10 was substituted (other than as a houserule).


Pathfinder Maps, Pathfinder Accessories, Starfinder Adventure Path, Starfinder Maps, Starfinder Society Subscriber; Pathfinder Roleplaying Game Superscriber

He means that the "early" d20s (ie in the 1970s) came printed with 0-9 twice and it was suggested you color half of them yourself, rather than being printed/cast with the numbers 1-20. The latter didn't become standard until the eighties.

Nobody in this thread has advocated rolling two d10s and adding them together (although several have thought others are suggesting that).


I still roll a d20 when a d10 is called for. Platonic solids FTW.

The wierd part for me is the d6 as a d2 which could be exploited a little bit...

One day you decide odds are 1 and even is 2, the next you decide 123 is 1 and 456 is 2...

(or in the OP's case odds are a leading zero, evens are a leading 1)

Like a d8 in place of a d4 is either cut in half round up, or the 1234 sequence repeated as 5678.

Make sure your dm knows the rule you're using and that you're consistant about it.


bookrat wrote:
Wait... How would adding them together result in a percentile? Designating one d10 as the tens place and the other for the 1s place is the only way to make 2d10 become 1d100.

The group in question were doing the usual 10s d10 and 1s d10, but they were treating a 10 on the 1s d10 as 'add 10' instead of 'add 0'. This generates a number between 1 and 100, and then you probably treat 100 as 0.


Bruunwald wrote:
thorin001 wrote:

...In fact the originals d20s were 0-9 twice, and you used different colors to determine 1-10 and 11-20.

You may be kidding, or being sarcastic. But it's worth noting, for historical reasons, that the d20 predates Roman times. And as far as I know, the game was always played with real d20s. I have never heard of there being a time when 2d10 was substituted (other than as a houserule).

Back in 1e, it was common to see a d20 with no numbers in the teens. It literally was 0-9 printed twice in two different colors. You would designate one color to be 1-10 and the other color to be 11-20. It was still a 20 sided die, it was just printed differently than the die we're used to seeing today.

Dark Archive

A recent study of dice rolling showed tbat d6 with curved corners and pips were actually twice as likely to roll a one then the other numbers. You would need d6 with flat straight edges and numbers instead of pips. Casino gambling dice should be the most likely trustworthy dice.


Quark Blast wrote:
Belafon wrote:
D10s are not Platonic solids and must be eradicated.

So true.

And, incidentally, that's the reason I hate soccer. Not only does it improperly marry hexagons and pentagons but purports to distort them into spherical geometry. Gah! Thales, Pythagoras, Euclid, Archimedes... all spinning in their graves.

so sad...

They really aren't hexagons and pentagons on the ball, as you say. Pffft.

What I find odd is that of the Platonic solids, the dodecahedron and the icosahedron match each other: Every corner on an inscribed of either will touch the middle of the faces of the other. It is the same with cubes and octahedrons.


If soccer players were kicking around what in effect was a stitched together d20, I'd probably watch it more. When you kick the ball through the goal, the face that ends face up is the score for the kick.


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Raymond Lambert wrote:
A recent study of dice rolling showed tbat d6 with curved corners and pips were actually twice as likely to roll a one then the other numbers. You would need d6 with flat straight edges and numbers instead of pips. Casino gambling dice should be the most likely trustworthy dice.

That study had serious issues.


Vincent Takeda wrote:
If soccer players were kicking around what in effect was a stitched together d20, I'd probably watch it more. When you kick the ball through the goal, the face that ends face up is the score for the kick.

Too random. Kicking 2d10 will average more goals than 1d20.

Seriously, unless you're outright missing some dice, go with the d20. No odds change.

And am I the only one who loves calling a 100 on percentiles 'double zero'? No-one else I've met does. (It hasn't come up enough to ever justify actually judging whether it's a 0 or a 100, for some reason.)

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