  Understanding the properties of games played under computational constraints
remains challenging. For example, how do we expect rational (but
computationally bounded) players to play games with a prohibitively large
number of states, such as chess? This paper presents a novel model for the
precomputation (preparing moves in advance) aspect of computationally
constrained games. A fundamental trade-off is shown between randomness of play,
and susceptibility to precomputation, suggesting that randomization is
necessary in games with computational constraints. We present efficient
algorithms for computing how susceptible a strategy is to precomputation, and
computing an $\epsilon$-Nash equilibrium of our model. Numerical experiments
measuring the trade-off between randomness and precomputation are provided for
Stockfish (a well-known chess playing algorithm).
