11176 - Winning Streak

All about problems in Volume 111. If there is a thread about your problem, please use it. If not, create one with its number in the subject.

Moderator: Board moderators

Robert Gerbicz
Experienced poster
Posts: 196
Joined: Wed May 02, 2007 10:12 pm
Location: Hungary, Pest county, Halasztelek
Contact:

Post by Robert Gerbicz » Sat Aug 18, 2007 4:30 pm

little joey wrote:If my hand calculations are right, the first four polynomials are:

Code: Select all

    A(1) =   p
    A(2) =  2p
    A(3) =  3p - p^2 +2p^3 - p^4
    A(4) =  4p -3p^2 +7p^3 -6p^4 +3p^5 - p^6
There are some errors, the degree of A(k) is at most k. By a program the correct computed polynomials:

Code: Select all

A(1)=p
A(2)=2*p
A(3)=p^3 - p^2 + 3*p
A(4)=-p^4 + 4*p^3 - 3*p^2 + 4*p
A(5)=2*p^5 - 6*p^4 + 10*p^3 - 6*p^2 + 5*p
A(6)=-2*p^6 + 10*p^5 - 18*p^4 + 20*p^3 - 10*p^2 + 6*p
A(7)=2*p^7 - 11*p^6 + 30*p^5 - 41*p^4 + 35*p^3 - 15*p^2 + 7*p
A(8)=-p^8 + 10*p^7 - 36*p^6 + 72*p^5 - 80*p^4 + 56*p^3 - 21*p^2 + 8*p
A(9)=p^9 - 7*p^8 + 36*p^7 - 96*p^6 + 151*p^5 - 141*p^4 + 84*p^3 - 28*p^2 + 9*p
A(10)=-2*p^10 + 10*p^9 - 36*p^8 + 112*p^7 - 225*p^6 + 288*p^5 - 231*p^4 + 120*p^3 - 36*p^2 + 10*p

User avatar
little joey
Guru
Posts: 1080
Joined: Thu Dec 19, 2002 7:37 pm

Post by little joey » Mon Aug 20, 2007 10:18 am

Yes, my polynomials are wrong. Thanks for pointing that out.
The biggest problem with most problems is not how to solve the problem, but how to not solve what is not the problem.

tkcn
New poster
Posts: 5
Joined: Wed Apr 02, 2008 3:42 pm

Re: 11176 - Winning Streak

Post by tkcn » Fri Jun 04, 2010 9:04 am

Hello.
I am trying to solve this problem.
I already used DP to calculate the number of "from i consecutive games you get no more than j consecutive wins", just like Ivan said.
But I still confused how to derive the correct answer from this DP table.

My biggest problem is, for example i=3 and j=1, there are 4 cases: LLW, LWL, WLL, WLW.
The final case "WLW" has a different probabillity with orthers and I don't know how to separate them.
Can somebody give me a hint?

Thanks in advance.

tkcn
New poster
Posts: 5
Joined: Wed Apr 02, 2008 3:42 pm

Re: 11176 - Winning Streak

Post by tkcn » Tue Jun 08, 2010 8:08 am

Hi.
Finally, I was solved this problem.
I was misunderstanding Ivan said, try to calculate the "count" of "from i consecutive games you get no more than j consecutive wins",
but what we need is the "probability".

Thanks.

Post Reply

Return to “Volume 111 (11100-11199)”