05272022, 07:28 AM  #111  
Join Date: Apr 2022

Re: Gaming philosophy conundra
Quote:
Infinity is not, especially not math infinity since that's fake anyway. d∞ is probably just a d3 anyway, either you win or you lose or you draw. It's infinite so you either go below, above or the same. Why would the order matter unless this is some weird not really infinity thing? Kind of a rethorical question, I probably wouldn't understand the reasoning anyway because it's gonna be some math trick that humans have invented to think they can deal with infinity. Like the illusion of functional programming even though one cannot escape imperative programming in computing because that's just how computers work (at least the ones I know). It's all imperative in the end. 

05272022, 08:02 AM  #112  
Join Date: Jun 2005

Re: Gaming philosophy conundra
Quote:
As for "fake," in both mathematics and RPGs, we start out by making assumptions, which we agree to pretend are true. Within the context of the game, calling them "fake" is not a valid move; to do so is to refuse to play the game. In this case, the game is exploring the concept of a die in the shape of a regular polyhedron with infinitely many sides. One of my players likes to tell the story of a campaign he was in, where the GM said to the players that their characters had walked into a room whose floor was tiled in octahedra. One of the players said, "It's not possible to tile a surface in octahedra." And the GM said, "That's right. Roll for SAN loss."
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Bill Stoddard I don't think we're in Oz any more. 

05272022, 11:19 AM  #113 
Join Date: Feb 2005
Location: Berkeley, CA

Re: Gaming philosophy conundra
The problem is that you don't wind up with a fair die (where 'fair' is defined as 'equal probability for every result') doing that.

05272022, 01:08 PM  #114 
Join Date: Jun 2005

Re: Gaming philosophy conundra
It's not obvious to me that that's the case. It seems as if the probability of rolling any number is 0, and 0 = 0 = 0.
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Bill Stoddard I don't think we're in Oz any more. 
05272022, 01:13 PM  #115 
Join Date: Feb 2005
Location: Berkeley, CA

Re: Gaming philosophy conundra
You're talking about infinities now. 1/alephnull and 2/alephnull are both equivalent to zero, but nonequal.

05272022, 03:16 PM  #116 
Join Date: Jun 2005

Re: Gaming philosophy conundra
But is it necessary to assume that you would have such a case arise?
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Bill Stoddard I don't think we're in Oz any more. 
05272022, 05:41 PM  #117  
Join Date: Jun 2006

Re: Gaming philosophy conundra
Quote:
I more than half suspect it's going to get you back to the axiom of choice  you know the one that allows you to cut a sphere into two identical spheres.... The math joke is "the Axiom of Choice is obviously true, the wellordering principle obviously false, and who can tell about Zorn's lemma?"  the joke being that's pretty much true by inspection on the superficial definitions, and you can prove all three are restatements of each other.
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 MA Lloyd 

05272022, 07:38 PM  #118  
Join Date: Jan 2014

Re: Gaming philosophy conundra
Quote:
For example, consider a continuous uniform distribution from 0 to 1. The absolute likelihood of generating value 0.8 is zero, while the probability of rolling less than (or less than or equal to) is 0.8. This can be generalized to p(x)=(xa)/(ba), where a is the lower bound of the distribution, b is the upper bound, and x is the upper bound of values we're testing for. Plug in a=0, b=infinity, and you get p(x)=x/infinity=0. So if you know what the GM rolled, the chance you roll less than whatever the GM rolled is zero. Of course, this is probably wrong for two reasons: 1) Both die rolls are independent events, thus knowing what the GM rolled can have no effect as to whether you roll higher than what the GM rolls. 2) This is coming from arbitrarily plugging in infinity into a formula. So let's take it from a different angle of attack. Dice of the form 1dX have an average of (X+1)/2, a standard deviation of sqrt((X^21)/12)), and the odds 1dX>1dX is (X1)/(2X). As X approaches infinity, the average and stdev approach infinity, and the odds 1dX>1dX approaches 50%. So save yourself some time searching from your d∞ and toss a coin instead. 

05272022, 08:39 PM  #119 
Join Date: May 2005
Location: Oz

Re: Gaming philosophy conundra
And have done so at least since my freshman maths classes, forty years ago.
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Decay is inherent in all composite things. Nod head. Get treat. 
05282022, 01:35 AM  #120  
Join Date: Dec 2006
Location: Meifumado

Re: Gaming philosophy conundra
Quote:
3) There's a difference between probability and possibility. It might be infinitely improbable to roll below the GM's target, but it's not impossible. In other words, probability theory is a flawed model of reality.
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