  Toehold purchase, defined here as purchase of one share in a firm by an
investor preparing a tender offer to acquire majority of shares in it, reduces
by one the number of shares this investor needs for majority. In the paper we
construct mathematical models for the toehold and no-toehold strategies and
compare the expected profits of the investor and the probabilities of takeover
the firm in both strategies. It turns out that the expected profits of the
investor in both strategies coincide. On the other hand, the probability of
takeover the firm using the toehold strategy is considerably higher comparing
to the no-toehold strategy. In the analysis of the models we apply the
apparatus of incomplete Beta functions and some refined bounds for central
binomial coefficients.
