Monte Carlo algorithms are developed to calculate the ensemble-average particle leakage through the boundaries of a two-dimensional binary stochastic material. The mixture is specified within a rectangular area and consists of a fixed number of disks of constant radius randomly embedded in a matrix material. The algorithms are extensions of the proposal of Zimmerman et al., using chord-length sampling (CLS) to eliminate the need to explicitly model the geometry of the mixture. Two variations are considered. The first algorithm uses CLS for both material regions. The second algorithm employs limited CLS (LCLS), using only CLS in the matrix material. Ensemble-average leakage results are computed for a range of material interaction coefficients and compared against benchmark results for both accuracy and efficiency. Both algorithms are exact for purely absorbing materials and provide decreasing accuracy as scattering is increased in the matrix material. The LCLS algorithm shows a better accuracy than the CLS algorithm for all cases while maintaining an equivalent or better efficiency. Accuracy and efficiency problems with the CLS algorithm are due principally to assumptions made in determining the chord-length distribution within the disks.