Steve Jackson Games - Site Navigation
Home General Info Follow Us Search Illuminator Store Forums What's New Other Games Ogre GURPS Munchkin Our Games: Home

Go Back   Steve Jackson Games Forums > Roleplaying > Roleplaying in General

Thread Tools Display Modes
Prev Previous Post   Next Post Next
Old 05-26-2022, 10:13 AM   #11
Join Date: Jun 2005
Default Re: Gaming philosophy conundra

Originally Posted by malloyd View Post
Surely whoever rolls second always wins. The probability space between the first roll X and infinity is always infinitely larger than the space between 0 and X, right?
I didn't think of that one, but it sounds right, at least if you're rolling a die with countably infinite sides.

I'm not sure what happens if your die has continuous sides. If you give the south pole a value of 0 and the north pole a value of 1, and every point in between has some fractional value, then for example if you land on the point whose fractional value is exactly 0.5, your opponent has a 50% chance of beating you, right? There are no more points between 0.5 and 1 than there are between 0 and 0.5.

Can you treat the interval [0, 1] as isomorphic to the interval from 0 to infinity? I'm not sure you can. "Infinity" here probably means aleph sub null, the infinity of natural numbers, which can be visualized as a line; but I don't think the infinity of the continuum is on that line. So maybe there's a conceptual difference between a sphere and an infinite-sided polyhedron, or an apeirohedron (I just looked on Wiktionary and they say that word already exists, so I'm not the first to make it up)?

It seems as if you have said that when you throw an apeirohedral die, the number of sides with larger numbers must always exceed the number of sides with smaller numbers. Is that the same as saying that it must always land on the "bottom"?
Bill Stoddard

I don't think we're in Oz any more.
whswhs is offline   Reply With Quote

philosophy, sisyphus, theseus, trolley problem

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Fnords are Off
[IMG] code is Off
HTML code is Off

Forum Jump

All times are GMT -6. The time now is 02:12 PM.

Powered by vBulletin® Version 3.8.9
Copyright ©2000 - 2023, vBulletin Solutions, Inc.