  We continue the study of restricted Monte Carlo algorithms in a general
setting. Here we show a lower bound for minimal errors in the setting with
finite restriction in terms of deterministic minimal errors. This generalizes a
result of Heinrich, Novak, and Pfeiffer, 2004 to the adaptive setting. As a
consequence, the lower bounds on the number of random bits from that paper also
hold in this setting. We also derive a lower bound on the number of needed bits
for integration of Lipschitz functions over the Wiener space, complementing a
result of Giles, Hefter, Mayer, and Ritter, arXiv:1808.10623.
