## ODE,problem:division by zero, why?...

Asked by:

I want to solve an ODE from Game Theory, the Cournot competition.

It says

p(q1+r2(q1))+p'(q1+r2(q1))*r2(q1)-c2'(r2(q1))=0

where, I think,

' means diff(,q1),

c2(q2)=c*q2 for a fixed c in [0,1]

and

p(q)=max(0,1-q).

So c2,p and r2 are functions.r2 goes from [0,inf) to [0,inf).

I look for r2, which should be r2(q1)=(1-q1-c)/2 when correctly solved.

However, the command dsolve says Error in dsolve (divison by 0).

What is wrong? How do I obtain the solution for r2 in Maple?

Asked by:

## How to identify whether biased game is changed bas...

Asked by:

How to identify whether biased game is changed based on the latest toss from a sequence

can HMM identify this?

for example

if

fair fair fair biased biased fair fair biased

## Solitaire Numbers

This is a little more than a new game it potentially uncovers a new class of numbers -- though determining membership might become a hard problem.

A number that possesses the solitaire property can be written in as ...,0,...1,...2,...etc, or ...,0,...1,...10...11,...etc,(where the "0" is the first zero in the number), with a radix point anywhere. We are free to pick the base and say it is solitaire with respect to that base. After the initial 0, the subsequent ordinals (the 1,2, etc or the 1,10,11, etc) used to write the solitaire number don't have to be the first ones. For example:

pi=3.1415926535897932384626433832795
0 2884
1 971693993751058
2 0974944592
3 078163860
4 ...
etc.,

or

pi=3.1415926535897932384626433832795

0 2884197

1 6939937510582 097494459

2 3 07816

3 860
4 ...
etc.,are both acceptable. (If the number can be written as  ...,0,...1,...2,...etc, or ...,0,...1,...10...11,...etc. it is solitaire.)

The Champernowne constant with respect to base 10 has only one representation:

0.

1

2

3

4

5

6

7

8

9

10

11...

etc. .

I know Base 10 Champernowne constant is base 10 solitaire. I can not say the same with certainty for Pi.

I also propose we can measure the solitude of a number by the average amount of numbers between the 0,1,2,3..., and give a perfect solitude score to Base 10 Champernowne constant. Other constants can be given additional credit, of some kind, if the amounts of numbers between the 1,2,3... follow a specific preset pattern.

marvinrayburns.com

## question: roll the bones...

Asked by:

my_sol.mw

Leonhard is playing a casino game. He places his bet and then rolls a
pair of dice: if the dice sum to 7, 8 or 9 then Leonhard wins the amount of his
bet, and otherwise Leonhard loses his money. Leonhard begins with \$100 and
decides to bet \$50 at time, until he has either won \$100 or has gone broke. What
are the chances that Leonhard leaves the casino a winner?

My soln doesn't agree with the stated answer..25/74

## Maple SOKOBAN game

by: Maple

I made 3 years ago a SOKOBAN game using Maple for my Math/Programming class.

Here is a video of the application:

http://www.youtube.com/watch?v=l00l82_LK2Y

Have a nice day!

## Optimal Stopping in a Stochastic Game...

Asked by:

Does any one know how to derive this model in Maple?

The_Price_is_Righ.pdf

## Poker Probabilities

by: Maple 13

I have below outlined the different probabilities for different poker hands given
5 cards from a 52 cards deck. The frequencies are from wikipedia
http://en.wikipedia.org/wiki/Poker_probability

These frequencies are quite interesting....I wonder if they found them by "brute fource"

## Exponential Growth - Game Theory...

Asked by:

One thing I have always found interesting is that exponential growth/decay
is not symmetrical hence:

100*(1+0.01)^2+100*(1-0.01)^2-200 = 0.0200

For example:

If you start with 100 and bet 1% and you win and then again bet 1% of your portfolio value
and you win again your portfolio value will be PW=100*(1+0.01)^2.

If you start with 100 and bet 1% and you lose and then again bet 1% of your portfolio value
and you lose again your portfolio value will be PL=100*(1-0.01)^2. ...

## Does there exist a list of chosen numbers by 649 p...

Asked by:

Sorry that this may not belong here but I thought I would ask, it is interesting.

Now I'm not asking for the winning numbers list but rather the numbers chosen by people (the thousands of non winning ticket numbers per game)  Is there a database somewhere we can access that stores the list of picked numbers?  It would be interesting to find out how randomly people pick numbers, do people flock to certain numbers more often than others?

I...

## How may I obtain 2-simplex and 3-simplex?...

Asked by:

Good morning,

I want to  to show the 2-simplex (in R^2) obtained from the inequality

x+ y+ z < = 12*a

with a:=1;

x, y, z  >= 0.

(the angles of the triangle are (12,0,0), (0,12,0) and (0,0,12) )

The CORE of a cooperative game, is the set points that additionally satisfy the system

x+ y >= 6

x+ z >= 6

y + z >= 6

## How to simulate the card game war...

Asked by:

Just for fun last night I thought I'd try to whip up a simulation of the simple card game war.  The hoyle rulebook - evenly divide the cards up between 2 players facedown, turn over top card, highest card wins.  In the event of a tie the higher of the next overturned card wins (the more common variant is to play 3 facedown cards and turn up the 4th) - but that introduces more complexity to the programming ... I thought I'd tackle that later, but first ...

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