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We study the problem of deterministically predicting boolean values by combining the boolean predictions of several experts. Previous on-line algorithms for this problem predict with the weighted majority of the experts'' predictions. These algorithms give each expert an exponential weight beta^m where beta is a constant in [0,1) and m is the number of mistakes made by the expert in the past. We show that it is better to use sums of binomials as weights. In particular, we present a deterministic algorithm using binomial weights that has a better worst case mistake bound than the best deterministic algorithm using exponential weights. The binomial weights naturally arise from a version space argument. We also show how both exponential and binomial weighting schemes can be used to make prediction algorithms robust against noise.