In the problem Optimal Card Drawing Strategy, an optimal strategy was determined for a card game. Give a closed expression for the expected score when using the optimal strategy.

(In reply to C = 19, R = 6 by Steve Herman)

I have to apologized, I logged on with the intention of using my equation to confirm/deny your calculations (which appear to be correct).  However my hard drive corrupted and I have lost the pdf files which stored my solutions for this problem.  So now I am having to start from scratch which is going to take some time and more white board space than I have available at the moment.  I intend on reworking the equation as soon as I can.  In the meantime, I will leave you with this hint.  Try writting nested summations which determine the expected score if you stop at round N, find a pattern in the summations and find a closed form for this called F(N),  then the exptected score is the sum of F(N) with N=1 to R.  This is how I worked out the problem, however as you can imagine the equations get rather tricky and require a large space to work it out, which will have to wait until later in the week when I have access to my larger white board at home.

Posted by Daniel on 2010-10-03 09:43:16