TODO

generalise minimax to mcts: sample k moves without replacement (using gumbel-max trick?) with the distribution determined by a softmax of equities, and choose l die rolls
do this using async calls to the neural network?
do this with multiple different values of k (and l? maybe just use l = 1) and average them all with some weights
could reduce k as depth increases
consider how to tune the many different hyperparameters - online cross-validation? there is a bias-variance trade-off
note this bias-variance trade-off in the write-up, and add to the point about the stronger convergence property that it is related to the fact that it is unbiased
rethink regularisation parameter, especially if using a biased method (could incorporate into the online cross-validation)
use clustering to select die rolls?
probability of move has something to do with stability of likelihood of winning as well as the likelihood itself?
impelement parallelisability to make training a much deeper net more realistic
add a convolutional layer?
add an epsilon chance of playing randomly (and possiblye using an old version for smoothness) - do this some proportion of the time
for gammons and backgammons, pass an Outcome.t and a Player.t to equities and a (payoff : Outcome.t -> Player.t -> float) to games
give the network 5 output nodes (or possibly 3 if you want to ignore backgammons)
for a gammon pip count ratio, use pip count to point 6 plus 1 if nothing borne off, divided by sum of that plus opponent ordinary pip count
use the repeat variant now that the memory leak is fixed
consider batching tensorflow calls in minimax
consider just using 1-ply search and updating using the best move
general doubling algorithm as a function of payoff and equity - use analytic solution for continuous games to begin with (possibly with a 1-ply lookahead)
(technically doubling state should be an input into the game equity function)
doubling: http://www.bkgm.com/articles/ZadehKobliska/OnOptimalDoublingInBackgammon/index.html
games: first to or number of
consider also alpha-beta pruning / negascout / mcts / transposition table