Fallacies of Die Probabilities

[Mouser13]

I'm happy that I'm not the only one insance logical here. Though I have to say Discrete Math was not my best math class. THough the section of this topic was ok.

[Natasha]

So. For to maximise damage:

Should I roll 3D6 once?

Or 1D6 three times?

[Natasha]

The probabilities say I should roll 1D6 three times if I want to maximise my chance to get maximum damage.

1. Chance to roll 18 on 3D6 is 0,463%
2. Chance to roll 6 on 1D6 is 16,667%

Each die has ~17% chance to roll six, while three, taken as a unit, has about half a percent chance of hitting maximum (eighteen).

Or is dice probabilities simply not useful in this scenario?

Or I am missing something blaringly obvious?

[Jesterzzn]

My head hurts.

[verdilak]

So. For to maximise damage:

Should I roll 3D6 once?

Or 1D6 three times?

It doesnt matter which way you roll, because rolling 3d6 or 1d6, 1d6, 1d6 and adding them up, is the exact same.

[Natasha]

I understand these things, but I seem to lack ability to explain myself. I'll think on it. Or find someone who can stay next to me with a whiteboard. Thanks

[Damian Magecraft]

Statistics was never my strong subject...equations of that sort may as well be Sanscrit as far as my comprehension goes...

broad based concepts and theories I get.
one question...do these equations take in to account chaos theory?

[bigbobsr6000]

Sometimes I have used 1d10+1d8 to roll stats for various RPGs. My thinking there is a less chance to get an 18 result (1/10 and 1/8) than 3d6 (1/6, 1/6, 1/6). I use this in games when I want a chance of lower stats. Am I correct?

Thanks, Big Bob.................

[Natasha]

I can appreciate the mathematical skill needed for this, and my son understands it, but my eyes glazed over in 2.3 seconds.

There was whopping 93% chance of that happening.
I, too, forgive you.

[bigbobsr6000]

Sometimes I have used 1d10+1d8 to roll stats for various RPGs. My thinking there is a less chance to get an 18 result (1/10 and 1/8) than 3d6 (1/6, 1/6, 1/6). I use this in games when I want a chance of lower stats. Am I correct?

Thanks, Big Bob.................

1d10+1d8

Will yield 80 diffrent results (8*10)
With
2 1/80 times
3 2/80
4 3/80
5 4/80
6 5/80
7 6/80
8 7/80
9 8/80
10 8/80
11 8/80
12 7/80
13 6/80
14 5/80
15 4/80
16 3/80
17 2/80
18 1/80

I think, but yes 1d8+1d10 will produce greater lower and higher stats.

Thanks for the comeback, Big bob................

[Damian Magecraft]

Statistics was never my strong subject...equations of that sort may as well be Sanscrit as far as my comprehension goes...

broad based concepts and theories I get.
one question...do these equations take in to account chaos theory?

Chaos theory doesn't play a roll in die probabilities.

I would think it would...
correct me if im wrong but the equations seem to make assumptions...
1. the die has no imperfections (an impossibility even if only on an atomic scale)
2.the surface the die is being rolled on also suffers no imperfections
3. the die is thrown in the exact same manner and with the same force every time

those are just the ones i can come up with off the top of my head...I am sure there are others

[sasha]

Yea if you threw the die under the same circumstances every time, it should roll the same.

But you can't roll like that. I don't care how cool you are.

Hail Random Chance.

[sasha]

Dice throwing is not chaotic or disorganized.

You've never seen me throw bones before.

[Damian Magecraft]

In craps (at least in vegas) for the toss to count the dice must strike the back board (a good 2 to 3 feet [sometimes more] from the shooter)

I have met those who can affect the result of a throw based on how they toss the dice... so to my mind that is a factor....

Related question: which is more random...tossing dice by hand or using a dice cup?

[sasha]

Surface matters. The way you hold the dice matters. It all matters. At least it does in reality.

I can roll the same number every time (or enough to blow probability out of the water) if I put the die in my palm the same way and let it roll off my fingers and land on a pillow or comparable soft surface.

When you let them fly, Random Chance takes over.

[sasha]

Put the die on your little finger and rest against the ring finger. Push your ring finger forward and your little finger back towards your ring finger. Let the dice drop on the soft surface. With a bit of practice you'll be rolling the same thing every time. It's not probability. It's physics.

[sasha]

Surface matters. The way you hold the dice matters. It all matters. At least it does in reality.

I can roll the same number every time (or enough to blow probability out of the water) if I put the die in my palm the same way and let it roll off my fingers and land on a pillow or comparable soft surface.

When you let them fly, Random Chance takes over.

great show on Breaking Vegas where a group of professional craps shooters learned to throw dice via the suggestions of a engineer on dynamics etc.

"the Dominator" as the guy was known, was doing outrageously well at times, even calling out numbers at certain points (rolling 2D6). Imagine playing craps and keeping your turn for like 80+ consecutive rolls, not to mention the money they won.

The Dominator doesn't let them fly. He's doing something intentionally.

[sasha]

Put the die on your little finger and rest against the ring finger. Push your ring finger forward and your little finger back towards your ring finger. Let the dice drop on the soft surface. With a bit of practice you'll be rolling the same thing every time. It's not probability. It's physics.

Yes as you are not rolling dice you are dropping them, D6's and D4's are too flat to be affected by wind resistance, if you actually roll the dice in anyway, you will not be able to produce repeatable outcomes.

It rolls off my finger. Or two fingers if you're dedicated to the practice of it. It's rolling the dice, technically speaking, and it's controlling the outcome. It demonstrates that there's more to rolling dice than the number of faces. Although D6 is easier than D4 to control.

[Killer Cyborg]

Put the die on your little finger and rest against the ring finger. Push your ring finger forward and your little finger back towards your ring finger. Let the dice drop on the soft surface. With a bit of practice you'll be rolling the same thing every time. It's not probability. It's physics.

Yes as you are not rolling dice you are dropping them, D6's and D4's are too flat to be affected by wind resistance, if you actually roll the dice in anyway, you will not be able to produce repeatable outcomes.

It rolls off my finger. Or two fingers if you're dedicated to the practice of it. It's rolling the dice, technically speaking, and it's controlling the outcome. It demonstrates that there's more to rolling dice than the number of faces. Although D6 is easier than D4 to control.

It may be "technically" "rolling", but it's not "rolling" in the sense that people normally use the term; it's just a cop-out method for cheaters.
Hell, I could take my d20, roll it along the table with two fingers until a 20 was showing, and that would "technically" be "rolling", but nobody in their right mind would actually consider it to be a legitimate roll.

[Damian Magecraft]

this discussion reminds me of a story a Math Professor I know tells at the start of every Statistics 101 course...

3 statisticians went deer hunting during bow season. They were out there in the cold dreary woods for several hours when they finally spotted the fabled 30 point buck. The first one takes aim and lets fly with a shot. His shot flies wide 10 feet to the left. The second one takes aim and lets fly with his shot. His shot flies wide 10 feet to the right. The third one starts jumping up and down shouting "We got him!"

[Killer Cyborg]

this discussion reminds me of a story a Math Professor I know tells at the start of every Statistics 101 course...

3 statisticians went deer hunting during bow season. They were out there in the cold dreary woods for several hours when they finally spotted the fabled 30 point buck. The first one takes aim and lets fly with a shot. His shot flies wide 10 feet to the left. The second one takes aim and lets fly with his shot. His shot flies wide 10 feet to the right. The third one starts jumping up and down shouting "We got him!"

[sasha]

Put the die on your little finger and rest against the ring finger. Push your ring finger forward and your little finger back towards your ring finger. Let the dice drop on the soft surface. With a bit of practice you'll be rolling the same thing every time. It's not probability. It's physics.

Yes as you are not rolling dice you are dropping them, D6's and D4's are too flat to be affected by wind resistance, if you actually roll the dice in anyway, you will not be able to produce repeatable outcomes.

It rolls off my finger. Or two fingers if you're dedicated to the practice of it. It's rolling the dice, technically speaking, and it's controlling the outcome. It demonstrates that there's more to rolling dice than the number of faces. Although D6 is easier than D4 to control.

It may be "technically" "rolling", but it's not "rolling" in the sense that people normally use the term; it's just a cop-out method for cheaters.
Hell, I could take my d20, roll it along the table with two fingers until a 20 was showing, and that would "technically" be "rolling", but nobody in their right mind would actually consider it to be a legitimate roll.

I am aware, of course; but it is a demonstration that there is more to dice rolling than the number of faces and the number of dice in your hand/cup. Normal rolling is chaotic. Probability plays out over time, over many of rolls. Probability does not help me determine what this roll is going to come up to be. Furthermore, if you do roll the same dice the exact same way on the exact same surface every time, it will come up the same every time. That is practically impossible, although a machine might be able to do it; or a person such as The Dominator who just practices repeating the same trajectory, force, and so on when throwing the dice.

[Damian Magecraft]

this discussion reminds me of a story a Math Professor I know tells at the start of every Statistics 101 course...

3 statisticians went deer hunting during bow season. They were out there in the cold dreary woods for several hours when they finally spotted the fabled 30 point buck. The first one takes aim and lets fly with a shot. His shot flies wide 10 feet to the left. The second one takes aim and lets fly with his shot. His shot flies wide 10 feet to the right. The third one starts jumping up and down shouting "We got him!"

and people wonder why some nerds get shoved into lockers.

dont like the tale? or is it the moral of the tale that bothers you?

[Jesterzzn]

Okay, I'll bite. What moral?

[Damian Magecraft]

numbers can say what ever a Statistician wishes them to say.

[Rallan]

Vegas has rules about card sharking, but not a single rule that says you can't hold the dice in the exact same manner over and over and over again.

Actually they sort of do. The reason the dice have to bounce off the far wall to be a valid Craps throw is specifically to stop people cheating by doing non-random rolls. It's possible (and apparently not that hard) to learn how to make a pair of dice come up exactly the way you want them to time after time. It's pretty much impossible to do that if you have to send the dice bounding along at high speed across three or four feet of felt and bounce them off a stepped wall, because teensy variations in the initial throw that are too small for you to have much control over can make a massive difference in the outcome of the throw.

Also (while we're on probability and things that people think you can't cheat at), anyone ever wonder why casinos don't let you record the results of the Roulette Wheel? It's because with enough data, you can cheat at roulette.

[Damian Magecraft]

Vegas has rules about card sharking, but not a single rule that says you can't hold the dice in the exact same manner over and over and over again.

Actually they sort of do. The reason the dice have to bounce off the far wall to be a valid Craps throw is specifically to stop people cheating by doing non-random rolls. It's possible (and apparently not that hard) to learn how to make a pair of dice come up exactly the way you want them to time after time. It's pretty much impossible to do that if you have to send the dice bounding along at high speed across three or four feet of felt and bounce them off a stepped wall, because teensy variations in the initial throw that are too small for you to have much control over can make a massive difference in the outcome of the throw.

Also (while we're on probability and things that people think you can't cheat at), anyone ever wonder why casinos don't let you record the results of the Roulette Wheel? It's because with enough data, you can cheat at roulette.

its more than just the results...
it also requires knowledge of the speed of the ball...
length of time the ball spins....
number of bounces the ball makes before stopping....
height of the croupier...
ambient temp in the room...
speed of the wheel...
weather the croupier is left or right handed...
etc...
roulette is harder to "cheat" (its not cheating if you do the math) there is even more chaos involved in roulette than craps.

do you know what vegas casino owners say to players who have a "system" at roulette?

















"welcome to vegas!"

[Rallan]

Vegas has rules about card sharking, but not a single rule that says you can't hold the dice in the exact same manner over and over and over again.

Actually they sort of do. The reason the dice have to bounce off the far wall to be a valid Craps throw is specifically to stop people cheating by doing non-random rolls. It's possible (and apparently not that hard) to learn how to make a pair of dice come up exactly the way you want them to time after time. It's pretty much impossible to do that if you have to send the dice bounding along at high speed across three or four feet of felt and bounce them off a stepped wall, because teensy variations in the initial throw that are too small for you to have much control over can make a massive difference in the outcome of the throw.

Also (while we're on probability and things that people think you can't cheat at), anyone ever wonder why casinos don't let you record the results of the Roulette Wheel? It's because with enough data, you can cheat at roulette.

its more than just the results...
it also requires knowledge of the speed of the ball...
length of time the ball spins....
number of bounces the ball makes before stopping....
height of the croupier...
ambient temp in the room...
speed of the wheel...
weather the croupier is left or right handed...
etc...
roulette is harder to "cheat" (its not cheating if you do the math) there is even more chaos involved in roulette than craps.

do you know what vegas casino owners say to players who have a "system" at roulette?

















"welcome to vegas!"

Ever heard of the Man Who Broke The Bank At Monte Carlo? He did it on the roulette tables, and he did it with *gasp*... a system.

He had this hunch that since roulette wheels aren't perfectly made, and since they suffer wear and tear over time, they'll have a bias. So he hired a bunch of clerks to spend all day every day recording all the results of each roulette wheel in the casino he was targetting. Once they'd identified the table that seemed to have the most pronounced bias, he went in with an load of cash and proceeded to beat the pants off the casino by going to that table and spending the whole night placing bets where he rather than the house had the advantage. None of the zillion and one variables you discussed particularly mattered to him, because he was just looking for the overall bias of the system over an extended period rather than attempting to do the impossible by predicting the outcome of individual spins.

Tragically that particular trick doesn't work any more, since casinos got wise after enough professional cheats had pulled similar tricks. Roulette wheels today have weights on them to artificially induce a bias, and the weights are regularly moved around (and replaced by new weights of a different mass) to ensure that any given wheel won't act the same way long enough to get a statistically useful set of results out of it. They also replace the whole dang roulette wheel fairly regularly so there's no chance of wear and tear gradually causing a bias distinct enough to be noticed by anyone who might be recording the results.

And finally of course, they'll kick you out if they catch you recording the results. It's more a formality than anything else since you can't cheat at roulette these days any more, but it makes the normal customers feel safer if they know that would-be cheats (even inept cheats using tricks that haven't worked in a hundred years or so) always get shown the door.

[Damian Magecraft]

the man at monte carlo had enough money to allow his system time (one of the things he needed) to "take effect" he also was extremely lucky. the wheel may have favored certain regions but he hit exact numbers (22 to 1 pay out) more often than even his system allowed. he admitted there was luck involved. but the big thing for him was time and enough money to allow time to play to his advantage.

the vegas casinos may not like it if you use math and physics to help increase your advantage but as long as you do not use mechanic or electronic assistance the law states its not cheating. (thats why card counters are frowned upon but cannot be prosecuted for cheating).

but anyway all of this is beside the point...

its true that there are fallicies surrounding dice where RPGs are concerned but simple statistics formulae assume Ideal conditions.
the worst assumption/fallacy I see surrounding dice is that the math of probabilities is dead on accurate. Its not. it mearly gives the most likly outcome based upon the data input.
so we must always remember the GIGO (Garbage In Garbage Out) rule when dealing with them.

[Rallan]

the vegas casinos may not like it if you use math and physics to help increase your advantage but as long as you do not use mechanic or electronic assistance the law states its not cheating. (thats why card counters are frowned upon but cannot be prosecuted for cheating).

They might not be able to prosecute you, but they'll still kick your ass the hell out of a casino if they realise you're counting cards or recording results. Just because there's ways for you to beat the house without breaking the law doesn't mean the house is dumb enough to let you play

its true that there are fallicies surrounding dice where RPGs are concerned but simple statistics formulae assume Ideal conditions.
the worst assumption/fallacy I see surrounding dice is that the math of probabilities is dead on accurate. Its not. it mearly gives the most likly outcome based upon the data input.
so we must always remember the GIGO (Garbage In Garbage Out) rule when dealing with them.

My personal favourite is when the game designers are the ones who don't understand probability. In the first edition of White Wolf's various World Of Darkness games, they accidentally screwed up so that when on rolls with higher difficulties, the less dice you had the better your average result.

[Damian Magecraft]

the vegas casinos may not like it if you use math and physics to help increase your advantage but as long as you do not use mechanic or electronic assistance the law states its not cheating. (thats why card counters are frowned upon but cannot be prosecuted for cheating).

They might not be able to prosecute you, but they'll still kick your ass the hell out of a casino if they realise you're counting cards or recording results. Just because there's ways for you to beat the house without breaking the law doesn't mean the house is dumb enough to let you play

actually now they welcome counters in with open arms...(they found a new method of running the game that ham strings counters) and recording results (with pen and paper) is considered mechanical assistance.