  We correct the double spend race analysis given in Nakamoto's foundational
Bitcoin article and give a closed-form formula for the probability of success
of a double spend attack using the Regularized Incomplete Beta Function. We
give a proof of the exponential decay on the number of confirmations, often
cited in the literature, and find an asymptotic formula. Larger number of
confirmations are necessary compared to those given by Nakamoto. We also
compute the probability conditional to the known validation time of the blocks.
This provides a finer risk analysis than the classical one.
