  Challenges for physical solitaire puzzle games are typically designed in
advance by humans and limited in number. Alternatively, some games incorporate
rules for stochastic setup, where the human solver randomly sets up the game
board before solving the challenge. These setup rules greatly increase the
number of possible challenges, but can often generate unsolvable or
uninteresting challenges. To better understand the compromises involved in
minimizing undesirable challenges, we examine three games where component
design choices can influence the stochastic nature of the resulting challenge
generation algorithms. We evaluate the effect of these components and
algorithms on challenge solvability and challenge engagement. We find that
algorithms which control randomness through entangling components based on
sub-elements of the puzzle mechanics can generate interesting challenges with a
high probability of being solvable.
