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Subject: How to simulate 100 to 1 odds with a D20 rss

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Joe Berger
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Just a little idle speculation on how one might, well, as the title suggests.

Two alternatives:

A) roll a d20 twice, and on the first roll must roll a 1 (20 to 1 odds), on the second a 1 to 4 (1 to 5 odds) - the combined odds are 100 to 1. Does that sound correct?

B) roll two d20s and require a double 1,2,3 or 4. Would this also be 100 to 1 odds?

B) seems preferable, since with A) it seems wrong to be eliminating players after a first roll. But is there a difference, and is my maths sound?
 
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Herb
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Mathematically that is correct.

Pragmatically I doubt it. I doubt that a d20 would actually yield equal odds on all its faces.
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Christopher Dearlove
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arnodestang wrote:
Just a little idle speculation on how one might, well, as the title suggests.

Two alternatives:

A) roll a d20 twice, and on the first roll must roll a 1 (20 to 1 odds), on the second a 1 to 4 (1 to 5 odds) - the combined odds are 100 to 1. Does that sound correct?


Actually that's 1 in 100, or 99 to 1 (against) rather than 100 to 1. But I'll assume that's what you meant.

Quote:
B) roll two d20s and require a double 1,2,3 or 4. Would this also be 100 to 1 odds?


It would be the same.

Quote:
B) seems preferable, since with A) it seems wrong to be eliminating players after a first roll. But is there a difference, and is my maths sound?


I really don't understand what your point is. Where did "eliminating players" come from?

Of course the usual case is rolling two dice numbered 0 to 9 (which may physically be d20s, but numbered as d10s) and looking for a double zero. Or in fact any two digit number you choose (assuming you know which die is first, and which is second).
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Christopher Dearlove
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herace wrote:
Pragmatically I doubt it. I doubt that a d20 would actually yield equal odd on all its faces.


I suspect a decent d20 isn't too bad. So even more pragmatically, I wouldn't worry about it, you are unlikely to roll enough times to be able to detect a bias. (I'm assuming we are playing a game here, not running a casino or a lottery.)
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Herb
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Dearlove wrote:
herace wrote:
Pragmatically I doubt it. I doubt that a d20 would actually yield equal odd on all its faces.


I suspect a decent d20 isn't too bad. So even more pragmatically, I wouldn't worry about it, you are unlikely to roll enough times to be able to detect a bias. (I'm assuming we are playing a game here, not running a casino or a lottery.)


I'm in violent agreement with your position.
 
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Ma Si
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Option C) roll two D20 and both have to be 1 or 2.
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Stephen Ashworth
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Rolling two D10's makes it a lot easier
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Chris Robbins
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I bought a d100 for exactly this reason.
 
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herace wrote:
Pragmatically I doubt it. I doubt that a d20 would actually yield equal odds on all its faces.


Do you believe a d6 can be produced that would yield equal odds across its faces?

Or is this specifically about a d20? Is it because you don't believe that an icosahedron can be properly machined? Or that a material exists that would be be evenly dense across the span of a die?

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Ryan McGuire
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Dearlove wrote:
Of course the usual case is rolling two dice numbered 0 to 9 (which may physically be d20s, but numbered as d10s) and looking for a double zero. Or in fact any two digit number you choose (assuming you know which die is first, and which is second).


Back in my D&D days, I just used D20 for D10s and D100s and just ignored the first digit. To get 1 out of 100, I'd use roll two D20s (or the same one twice) and require a roll of 10 or a 20 (i.e. zeros) on both.

This essentially boils down to requiring any one of four rolls out of the 400 possible. The OP's option B set of possibilities is 1-1, 2-2, 3-3 and 4-4. Ma Si, used 1-1, 1-2, 2-1 and 2-2. My way requires 10-10, 10-20, 20-10 or 20-20.

Tomayto - tomahto.
 
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Ryan McGuire
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bltzlfsk wrote:
I bought a d100 for exactly this reason.


Uggh... I hope you're using an antiprism or trapezohedron type of d100 instead of the Zocchihedron.

Don't get me wrong... Lou is a good guy. But I'm uncomfortable with any die where the stable faces are not all the same shape and size.
 
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Herb
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Ok, being an idiot I'll bite....

frumpish wrote:
herace wrote:
Pragmatically I doubt it. I doubt that a d20 would actually yield equal odds on all its faces.


Do you believe a d6 can be produced that would yield equal odds across its faces?


Los Vegas certainly does, but they spend a lot of money to machine a die rather than use mold cast ones. Even then I'm sure that the dice are not "perfect," but "good enough".

frumpish wrote:
Or is this specifically about a d20? Is it because you don't believe that an icosahedron can be properly machined? Or that a material exists that would be be evenly dense across the span of a die?


i think that most d20 die would have been mold cast, then painted, then ground to remove excess paint. With such a process the 20 faces won't come out the same. As you increase the number of faces I just think the probability that each face will be the same decreases.

I was really trying to point out if 1 in 100 probability was really critical (for instance you're gambling...) as compared to 1:75 or 1:125 (just a friendly game...) then using a d20 is probably not the way to do it. I have no idea if such variation would make a difference to the OP. No idea how throws are being used, or balanced against other aspects of the game.
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Christopher Dearlove
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herace wrote:
Even then I'm sure that the dice are not "perfect," but "good enough".


Always true. Even when using random (or pseudo-random) numbers in serious professional applications, they are never perfect.

Assuming even remotely competently programmed, a die rolling app on your phone should be pretty good.
 
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John "Omega" Williams
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Dearlove wrote:
herace wrote:
Even then I'm sure that the dice are not "perfect," but "good enough".


Always true. Even when using random (or pseudo-random) numbers in serious professional applications, they are never perfect.

Assuming even remotely competently programmed, a die rolling app on your phone should be pretty good.


Some PC RNG generators are notoriously NOT random. As for the mythical perfect physical dice. Even that is not perfect because it can be manipulated during the roll.
 
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Jake Staines
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Omega2064 wrote:

Some PC RNG generators are notoriously NOT random.


Point of order, but all PC random number generators are notoriously not-random. It's just not a feature of modern microprocessors to produce actually-random numbers... since nobody actually needs it (Mersenne twisters are good enough for nearly everybody) and nobody wants radioactive isotopes decaying in their computers just so gamers can get a higher quality of 'random' for their die-rolling applications!


Of course, if you want to be picky then your physical dice are pretty not-random, as well; theoretically their final number could be predicted from the moment they're dropped based on a heavy-duty simulation of their trajectory, the materials and shapes that they hit, local air pressure and so on. It's just not worth it, and we can't measure the relevant variables accurately enough yet anyway. ;-)
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Andy Holt
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Bichatse wrote:
It's just not a feature of modern microprocessors to produce actually-random numbers... since nobody actually needs it


Actually, some of the most produced micros do have hardware rng - for example many models of the Broadcom system-on-a-chip ARM machines as used in mobile phones and in the Raspberry Pi.

Why? For encryption technology when used in phones.

 
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Jake Staines
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andyholt wrote:

Actually, some of the most produced micros do have hardware rng


And most - not all, but most - hardware random number generators are still not actually random; they're just less predictable (and thus less likely to be vulnerable to attack) than software PRNG.
 
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Christopher Dearlove
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Omega2064 wrote:
Dearlove wrote:
herace wrote:
Even then I'm sure that the dice are not "perfect," but "good enough".


Always true. Even when using random (or pseudo-random) numbers in serious professional applications, they are never perfect.

Assuming even remotely competently programmed, a die rolling app on your phone should be pretty good.


Some PC RNG generators are notoriously NOT random.


Hence the reference to competently programmed. But barring the very worst cases described in the famous Park/Miller paper, even most poor ones are probably good enough for most casual game uses if you can ensure no seeding issues. Not good enough for a casino, but good enough if you just wanted to use it for e.g. a game of Settlers. But one that is really good is easy to find.
 
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Christopher Dearlove
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Bichatse wrote:
Mersenne twisters are good enough for nearly everybody


Actually, no. Not suitable for cryptographic use, and I therefore wouldn't trust a casino or online poker game that used one.

(My context for saying almost anything goes is for just you want to use as a dice substitute in a local game that I assume isn't being played for hard cash by computer hackers.)
 
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Jake Staines
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Dearlove wrote:

Actually, no. Not suitable for cryptographic use, and I therefore wouldn't trust a casino or online poker game that used one.


That's why I said "nearly everybody" instead of just "Mersenne twisters are good enough". :P
 
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Christopher Dearlove
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Bichatse wrote:
Dearlove wrote:

Actually, no. Not suitable for cryptographic use, and I therefore wouldn't trust a casino or online poker game that used one.


That's why I said "nearly everybody" instead of just "Mersenne twisters are good enough". :P


I was going to say that cryptographic use was enough to make it not nearly everybody. Then I thought that rather contradicted my earlier point.

I think the resolution is that something based on a Mersenne Twister (or something even simpler) is good enough for most users. But for a non-trivial proportion of programmers - those working on anything security related, i.e. anything subject to people trying to break things - it's not.

(Most users actually also use random numbers that need to be cryptographically secure. But they don't know about it, it's hidden from them, so doesn't count.)
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Chip Crawford
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Roll 2d20 setting Dice A's 1's digit as the Ten and Dice B's 1's digit as the One. (00 = 100)

Wouldn't that reduce to 1 to 100 odds just like rolling percentile?
 
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Dearlove wrote:
Bichatse wrote:
Dearlove wrote:

Actually, no. Not suitable for cryptographic use, and I therefore wouldn't trust a casino or online poker game that used one.


That's why I said "nearly everybody" instead of just "Mersenne twisters are good enough". :P


I was going to say that cryptographic use was enough to make it not nearly everybody. Then I thought that rather contradicted my earlier point.

I think the resolution is that something based on a Mersenne Twister (or something even simpler) is good enough for most users. But for a non-trivial proportion of programmers - those working on anything security related, i.e. anything subject to people trying to break things - it's not.

(Most users actually also use random numbers that need to be cryptographically secure. But they don't know about it, it's hidden from them, so doesn't count.)


Seriously, guys. Get a room.
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