No I think the speed is ok now :-) Which is good!  I guess I was referring to the pre-server-change period.

thanx for explaining that :-)  That is quite interesting....humm

"I've never learned anything in a class - why should you?"

Ha, ha that is a good alec ! Yes there is definitely some inherit bitterness in the system for sure. The "eye for an eye a tooth for a tooth" mentality definitely creates feedback loops through many generations. Another thing I thought about is the source of financing. The source of financing for some strange reason seem to be critical. When the government finance education the relationship between the buyer ( ie student) and seller ( ie university represented by lecturer ) is in many ways lost or at best fuzzy which I think have a negative impact on the educational quality. USA has many problems such as social injustices ie income inequality, healthcare but they have also got some of the best universities in the world. Coincidence ?!

I agree with more or less what you are saying however I also acknowledge that everyone has different experiences so I don’t expect everyone to have the same opinions as me. In my experience students can be lazy, unmotivated and selfish but so can "professors". The main problem is however that professors and lecturers are supposed to be better than that ie knowledgeable, supportive, sharing knowledge (not selfish) etc which is not always the case. There exist a principle agent problem here where the university is the principle i.e. paying salary and the lecturer is the agent i.e. receiving salary. The student which in this case is the consumer has very limited input into such a process. The incentives to provide good teaching, ie the reward compared to journal publication etc that might give you a better job, are very low. All though I have noticed that some American universities seem to be better on this. One explanation might be that they can’t get away with neglecting students interests due to extremely high tuition fees paid by students (however this is not always a guarantee). Another problem is the way some universities allocate teaching responsibilities to save money or from a lecturer’s perspective make money. The teaching workload for some lecturers can in some cases be extreme. This should never be allowed because the teaching quality goes down extremely fast. Another problem is that once someone has reached professorship very few (if any) are going to questioning your authority i.e. teaching methods, supervision methods etc. Everything becomes the Wild West i.e. as long as the surface is clean (i.e. journal publications) anything goes. Institutional theory calls this “shadow places” where no questions are asked. To conclude I think too much focus is put on formal knowledge (i.e. journal publications, titles i.e. professorship etc etc) rather than answering basic questions such as: Is this person willing to share?!

"and my students perform better on the common departmental exams than students in other sections"

Alec I have no doubt !  Based upon your posting history on this site it is clear that you have a genuine interest
in helping and supporting people by sharing your knowledge which in my world make you an excellent teacher ! 
This can however not be said about many lectureres. I spent my last 10 years in lectures and some of these
lecturers are so competitive that they dont want to share any useful information. They see students and teaching
as a necessary evil (compared to journal publication) and they spend probably an equal amount of time preparing
for an lecture as they spend on the toilet. Some of them even go so far to point you in the wrong direction.
Sorry if I spam your blog with bitterness but I just cant help it :-)

ha ha that was funny !  Can you sing a song he he. I feel sorry for the students :-)

Do you LOVE calculus ?  Yes we LOVE it but please give us a good grade...

or wait it does make sense if you use the previous expected value ( for a fair game)

E(x) = 1/2*(x-1) + 1/2*(x+1) = 1/2*x-1/2+1/2x+1/2 = x

Then it kind of make sense that for an unfair game it should be

E(f(x)) = p*f(x+W) + q*f(x-W) = f(x)

Yes, I feel reasonably comfortable with that :-)

or wait it does make sense if you use the previous expected value ( for a fair game)

E(x) = 1/2*(x-1) + 1/2*(x+1) = 1/2*x-1/2+1/2x+1/2 = x

Then it kind of make sense that for an unfair game it should be

E(f(x)) = p*f(x+W) + q*f(x-W) = f(x)

Yes, I feel reasonably comfortable with that :-)

Yes, I was thinking of that extention to the problem ( with unequal probabilities)

I initially thought I could simply extend your logic but it appears that it might not be possible

because the solution expressions are a litle bit more complicated (wikipedia)

P1= [1 - (q/p)^n1 ] /  [ 1 - (q/p) ^ (n1+n2) ]

P2= [ (q/p)^n1  - (q/p) ^ (n1+n2) ] /  [ 1 - (q/p) ^ (n1+n2) ]

" There is a nifty technique that permits easily computing the result when the winning probability of each player for any

hand is constant but unequal."
 

I would be very greatful if you could please explain such a method as well ? 

I am note sure my weak brain can managed to solve it ....:-)   

Not that I had to work though your above solution myself to see it but the two expected value are

basically the same. The only thing that is different is the notation (score terms and probability

of winning terms ) . Your logic is simple and elegant !  Which cannot be said about some of

the "solutions" on the internet

Yes, I was thinking of that extention to the problem ( with unequal probabilities)

I initially thought I could simply extend your logic but it appears that it might not be possible

because the solution expressions are a litle bit more complicated (wikipedia)

P1= [1 - (q/p)^n1 ] /  [ 1 - (q/p) ^ (n1+n2) ]

P2= [ (q/p)^n1  - (q/p) ^ (n1+n2) ] /  [ 1 - (q/p) ^ (n1+n2) ]

" There is a nifty technique that permits easily computing the result when the winning probability of each player for any

hand is constant but unequal."
 

I would be very greatful if you could please explain such a method as well ? 

I am note sure my weak brain can managed to solve it ....:-)   

Not that I had to work though your above solution myself to see it but the two expected value are

basically the same. The only thing that is different is the notation (score terms and probability

of winning terms ) . Your logic is simple and elegant !  Which cannot be said about some of

the "solutions" on the internet

It appears that Maple had a simplex algorithm then hummm. I initially thought that the simplex

algorithm = Generalize Reduced Gradient (excel solver)  but it appears they are different.

I have been struggling with this myself. I dont think Maple has a Generalize Reduced Gradient solver

It appears that Maple had a simplex algorithm then hummm. I initially thought that the simplex

algorithm = Generalize Reduced Gradient (excel solver)  but it appears they are different.

I have been struggling with this myself. I dont think Maple has a Generalize Reduced Gradient solver

Excellent Joe , I think I might have to start paying you soon ha ha 

Two good solutions within 2- 3 hours nice ! That is a months work for me :-)

However, I dont really understand why  "But from the previous observation, this equals his current score"

Is this because you said the first expected score is constant throughout the game so even if he

is winning ( which is the case here) or losing for that mather such an expected score would still hold ?!

and then you simply calculate the expected score when he is winning and argue that such an expected

winning score must be equal to the first expected score since by definition it is constant throught the game...ok

I think I understand. Very nice indeed..... I wish I had your mathematical problem solving abilities my

life would have been much easier then :-) 

Excellent Joe , I think I might have to start paying you soon ha ha 

Two good solutions within 2- 3 hours nice ! That is a months work for me :-)

However, I dont really understand why  "But from the previous observation, this equals his current score"

Is this because you said the first expected score is constant throughout the game so even if he

is winning ( which is the case here) or losing for that mather such an expected score would still hold ?!

and then you simply calculate the expected score when he is winning and argue that such an expected

winning score must be equal to the first expected score since by definition it is constant throught the game...ok

I think I understand. Very nice indeed..... I wish I had your mathematical problem solving abilities my

life would have been much easier then :-) 

all right thanx for explaining that,

Yes I think the probability of ruin is P(Ruin Player B ) = b / (a+b) = 7/ (7+13) =0.35 and

P (Ruin Player A ) = a / (a+b) = 13/ (7+13) =0.65.  As outlined here

algo.inria.fr/csolve/ruin.pdf

The problem is how I can prove that ?!