Google scholar: game of Nim [since 2016], Hex game, Knight's Tour, Tower of Hanoi, Texas holdem research,
Games, because they follow well-defined rules,
represent good laboratories for testing our predictive skills. They help us
to a better understanding of randomness and uncertainty and provide insight
about how we might forge information into knowledge [Nate Silver, The Signal and the Noise: Why So Many Predictions Fail--but Some Don't].
John Nash proved in 1952 that a game of Hex cannot end in a tie, and that
for a symmetric board there exists a winning strategy for the player who
makes the first move (by the strategy-stealing argument). However, the
argument is non-constructive: it only shows the existence of a winning
strategy, without describing it explicitly. Finding an explicit strategy has
been the main subject of research since then.
Knight's: 3x3 middle square, circuits and
4x4 and graph theory
(start at P, never get back, start elsewhere
to go through P then stuck at A (or miss it)),
Tower of Hanoi
The minimum number of moves required to
solve a Tower of Hanoi puzzle is 2^n - 1, where n is the number of disks.