# Search Results

1. Post

### How many SOULS can God create ?

Demonstrate this.
Post by: rpenner, Jun 25, 2017 in forum: Religion
2. Post

### Probability — How many games to decide the best-of-N series

But it is given in the OP as "p". The expectation takes the largest value for p = 1/2, because as post #6 shows the expected number of games played...
Post by: rpenner, Jun 13, 2017 in forum: Physics & Math
3. Post

### Probability — How many games to decide the best-of-N series

Let n = \frac{N-1}{2} \geq 0 Then our expectation value goes like this: E = \sum_{i=0}^{2i -1 < N} \sum_{j=0}^{2j -1 < N} { {i+j} \choose i } p^i...
Post by: rpenner, Jun 6, 2017 in forum: Physics & Math
4. Post

### Probability — How many games to decide the best-of-N series

Thus to decide a best-of-1 series, exactly one game is played taking us from state (0,0) to (1,0) with probability p or to state(0,1) with...
Post by: rpenner, Jun 6, 2017 in forum: Physics & Math
5. Post

### Probability — How many games to decide the best-of-N series

Expansion of (p+(1-p))^n \begin{array}{c} & & & & & & & 1 & & & & & & & \\ & & & & & & p & & (1-p) & & & & & & \\ & & & & & p^2 & & 2 p (1-p) & &...
Post by: rpenner, Jun 6, 2017 in forum: Physics & Math

### Probability — How many games to decide the best-of-N series

Let N be an odd, positive number. A best-of-N series of games is played until one team has won a majority of the N maximum possible games in the...
Thread by: rpenner, Jun 5, 2017, 13 replies, in forum: Physics & Math
7. Post

### Does Common Descent Follow Logically From Darwin's Four Postulates?

This shows evidence of originating from a quote mine. First Edition was published circa 1998...
Post by: rpenner, May 11, 2017 in forum: Biology & Genetics
8. Post

### Quest to settle riddle over Einstein's theory may soon be over

My flourless chocolate torte says you are wrong.
Post by: rpenner, May 11, 2017 in forum: Astronomy, Exobiology, & Cosmology
9. Post

### Over-thinking the stochastic painting of spheres withdrawn from a box

Not quite. The essential thing different with n>2 is that it is possible that the lead color changes. So as the number of colors goes down, so does...
Post by: rpenner, May 7, 2017 in forum: Physics & Math
10. Post

### Over-thinking the stochastic painting of spheres withdrawn from a box

Wrong. It's not a problem about how to paint the balls the same color. It's a question about how long a given description of the process is expected...
Post by: rpenner, May 6, 2017 in forum: Physics & Math
11. Post

### Over-thinking the stochastic painting of spheres withdrawn from a box

That's not actually the same problem. Here the balls are actually changing colors and nothing prevents any of the remaining colors from overtaking...
Post by: rpenner, May 6, 2017 in forum: Physics & Math
12. Post

### Over-thinking the stochastic painting of spheres withdrawn from a box

Excellent blog post by Laurent Lessard on this: http://www.laurentlessard.com/bookproofs/colorful-balls-puzzle/ A PDF by Tim Black:...
Post by: rpenner, May 5, 2017 in forum: Physics & Math
13. Post

### Over-thinking the stochastic painting of spheres withdrawn from a box

A Simpler Model nColors=15; transitions = DiagonalMatrix[1 - Table[Binomial[nColors + 1 - k,2]/Binomial[nColors,2],{k,1,nColors}]] +...
Post by: rpenner, May 5, 2017 in forum: Physics & Math
14. Post

### Over-thinking the stochastic painting of spheres withdrawn from a box

Automation All of the above can be coded and run for different numbers of balls from 1..15. Maybe higher if you don't use a free-to-use cloud...
Post by: rpenner, May 5, 2017 in forum: Physics & Math
15. Post

### Over-thinking the stochastic painting of spheres withdrawn from a box

Uh oh, where in simulation, each simulation individually came to an end, the state vector always has a non-zero component not yet in the final state....
Post by: rpenner, May 5, 2017 in forum: Physics & Math
16. Post

### Over-thinking the stochastic painting of spheres withdrawn from a box

Tricks with Matrices In addition to the five state transition matrix, lets have it automatically add 1 to a counter for the portion of our state...
Post by: rpenner, May 5, 2017 in forum: Physics & Math
17. Post

### Over-thinking the stochastic painting of spheres withdrawn from a box

Stochastic Matrixes and Simulation Instead of having sampling error, we could simulate the probability of outcomes. First we need to enumerate all...
Post by: rpenner, May 5, 2017 in forum: Physics & Math
18. Post

### Over-thinking the stochastic painting of spheres withdrawn from a box

Underthinking I predict a number of people will attempt simulation to attempt to model this. Simulation is reasonably fast to code, fast to run, and...
Post by: rpenner, May 5, 2017 in forum: Physics & Math