Neil G
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 Feb4 comment Probability problem of dice game Feb4 comment Probability problem of dice game @joriki: Yes, it's solving a system of linear equations. You could have written it as a dynamic program that memoizes the transition probabilities and the probability of return for every state, which would be more efficient for a sparse transition matrix. Feb4 awarded Popular Question Feb3 comment Probability problem of dice game @joriki: I think you could turn all of the loops into self-loops first, and then you would have a traversal order. Anyway, I calculated the transition matrix. Perhaps you can finish it from there? Feb3 comment Probability problem of dice game @joriki: I was thinking of doing something like this: stats.stackexchange.com/questions/48396/… I see your point that you can get the transition matrix and decompose it, which might give an easier solution. I have some time now to give it a shot. Feb3 comment Probability problem of dice game It's not hard to use dynamic programming to find an exact solution. The state space is the last number rolled cross the run length (1 or 2). So, there are 22 states plus 2 finish states. The start space can be $(12, 1)$. What happens if they both simultaneously win? Feb2 accepted Trace of a matrix times outer product Feb2 comment Trace of a matrix times outer product Thanks for your answer so far. Is there an intuitive explanation of why someone would prefer to write the first expression? Does it reveal some mathematical structure? The second one seems clearer to me. Feb2 asked Trace of a matrix times outer product Nov26 awarded Popular Question Nov24 comment Convex function plus $v e^{-x}$ @coffeemath: I meant $w$, but I don't think it makes any difference? Nov24 revised Convex function plus $v e^{-x}$ giving the function a name Nov24 comment Convex function plus $v e^{-x}$ Yes, thanks for the correction. Nov24 asked Convex function plus $v e^{-x}$ Sep23 revised Sufficient statistic for product of $\Gamma(x + a_i)$ added 77 characters in body Aug4 awarded Yearling Aug2 comment What are the practical uses of $e$? Interesting. Note that the "information contribution" is often called the "surprisal" or "self-information". Aug1 answered What are the practical uses of $e$? Jul13 comment General nonatomic measure that cannot be expressed as an integral Thanks! (Now, I wonder if there are any real-world Poisson processes whose intensity varies as the cantor set ;) ) Jul13 accepted General nonatomic measure that cannot be expressed as an integral