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I'm having trouble thinking of the correct way to pose the following problem: Say a dice game (like Yahtzee) involves throwing up to 5 6-sided die in three rounds. After three rounds, a score is awarded based on which pattern the die conform to. In the first round, all five dice are thrown. In subsequent rounds, some dice may be held back and the remainder thrown in an effort to confirm to a higher scoring pattern. (Eg - You roll 3 of a kind and now you want to roll the remaining two to get 4 or 5 of a kind.)

I'd like to create a machine learning model (for fun) to train and determine which dice to hold back and which dice to roll in a given round to improve the pattern. As input variables, the state S (1-6) of each of five dice is given, a decision D to roll or not constructed of (0 or 1) for each of the five dice (encoded binary from 0-31), and I can generate a training set comprising the above information plus simulated results R. So in summary, each observation in the training set will contain a vector of initial dice values S, a bitmask of which dice to roll D, a simulated vector of final dice values R, and +1 if this improved the pattern and -1 if it did not improve.

What is the best way to pose this problem? If I'm predicting D, it seems like the model should be D~S, but this ignores R. If I include R, and train on D~S+R, how to I predict results knowing only D?

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    $\begingroup$ In an answer at stats.stackexchange.com/a/155402, I describe a framework for doing this. I don't really understand why you would approach this as a machine learning problem when you can (in principle) fully analyze it. To make the analysis practicable you might want to approximate the solution with sampling, but it still doesn't seem fruitful to conceive of that as a machine learning situation. $\endgroup$ – whuber Oct 6 '15 at 20:22
  • $\begingroup$ I'm new to the subject and I'm using it to learn about applicability of machine learning algorithms in different situations. I intended to compare the results to what I got from a full analysis. $\endgroup$ – Greg Graham Oct 7 '15 at 2:06
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After researching different approaches of machine learning, I think that reinforced learning and Markov Decision Processes are appropriate to apply to decision making in a dice game like Yahtzee. Previously I had only been exposed to supervised and unsupervised learning.

I've written up my approach here (http://rpubs.com/ggraham412/117575) and created a toy implementation in Python here (https://github.com/ggraham-412/RLDiceGame).

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