peteroupc

This is a followup to my earlier post from 6 months ago.

There I announced two open-source articles on a specification and lean APIs for pre-2000 computer graphics that a new video game or game engine can adopt that wishes to run with very low resource requirements (say, 64 million bytes of memory or less). They are at:

• https://peteroupc.github.io/graphics.html#Graphics_Challenge_for_Classic_Style_Games (Specification where I seek to characterize pre-2000 computer graphics).
• https://peteroupc.github.io/graphicsapi.html (Suggestions on a minimal API for pre-2000 graphics)

I ha

I know there are many game situations where the intended behavior is apparently not covered well by the comprehensive rules. What are some of these?

Note: This post contains comments of mine to a post by another user that was automatically deleted. They are reproduced here to make them more discoverable.

Background

We're given a coin that shows heads with an unknown probability, λ. The goal is to use that coin (and possibly also a fair coin) to build a "new" coin that shows heads with a probability that depends on λ, call it f(λ). This is the Bernoulli factory problem (Keane and O'Brien 1994), and I catalog algorithms to solve it.

Main Question

Prove or disprove: Let f:(D⊆[0,1])→[0,1]. Given a coin that shows heads with probability λ (which can be 0 or 1), it is possible to toss heads with probability f(λ) using the coin and no other sources of randomness (and, thus, f is strongly simulable) if and only if—

• f is constant on its domain

Background

We're given a coin that shows heads with an unknown probability, λ. The goal is to use that coin (and possibly also a fair coin) to build a "new" coin that shows heads with a probability that depends on λ, call it f(λ). This is the Bernoulli factory problem (Keane and O'Brien 1994).

Main Question

Prove or disprove: Let f:(D⊆[0,1])→[0,1]. Given a coin that shows heads with probability λ (which can be 0 or 1), it is possible to toss heads with probability f(λ) using the coin and no other sources of randomness (and, thus, f is strongly simulable) if and only if—

• f is constant on its domain, or is continuous and polynomially bounded on its domain (polynomially bounded mean

I have written two open-source articles relating to classic graphics (graphics typical of pre-2000 video games for home computers, game consoles, and arcade machines, at a time before "shaders").

The articles are as follows.

• https://peteroupc.github.io/graphics.html#Graphics_Challenge_for_Classic_Style_Games (Specification where I seek to characterize pre-2000 computer graphics).
• https://peteroupc.github.io/graphicsapi.html (Suggestions on a minimal API for new game engines that support pre-2000 graphics)

So far, pre-2000 computer graphics generally involve a "frame buffer" of 640 × 480 or smaller, simple 3-D rendering (less than 12,800 triangles per frame for 640 × 480, fewer for s

Listing of pages containing requests and open questions that I have.

• For experts in mathematics and probability. Many of the questions on the following pages were also posted by me on MathOverflow and other Stack Exchange sites.
  • Open questions on the Bernoulli factory problem (the new-coins-from-old problem).
  • Other open questions on probability.
  • The sampling problem.
• Graphics and Music Challenges for Classic-Style Computer Applications. For anyone designing computer gr

These are suggestions for designing new core and supplemental instructional materials, for all school subjects, used in elementary and secondary schools, to improve the education of children. Among the notable suggestions is to implement learning science in the materials and to make them open source on a GitHub repository. The endnotes are also of interest.

Page: https://peteroupc.github.io/insmat.html

I have written two open-source articles relating to classic graphics (graphics typical of pre-2000 video games for home computers, game consoles, and arcade machines, at a time before "shaders").

The articles are intended to encourage the development of—

• modern video games that simulate pre-2000 graphics and run with very low resource requirements (say, 64 million bytes of memory or less) and even on very low-end computers (say, those that support Windows 7, XP, and/or 98), and
• graphics engines (especially open-source ones) devoted to pre-2000 computer graphics and meant for developing such modern video games.

The articles are as follows.

• https://peteroupc.github.io/graphic

I have written two open-source articles relating to classic graphics (graphics typical of pre-2000 video games for home computers, game consoles, and arcade machines, at a time before "shaders").

The articles are intended to encourage the development of—

• modern video games that simulate pre-2000 graphics and run with very low resource requirements (say, 64 million bytes of memory or less) and even on very low-end computers (say, those that support Windows 7, XP, and/or 98), and
• graphics engines (especially open-source ones) devoted to pre-2000 computer graphics and meant for developing such modern video games.

The articles are as follows.

• https://peteroupc.github.io/graphic