It is said that Napoleon assessed probabilities at the battle of waterloo in 1815. His hopes for victory depended on keeping the English and Prussian armies separated. Believing that they had not joined forces on the morning of the faithful battle, he indicated his belief that he had a 90% chance of defeating the English; P (Napoleon Wins = 0.90). When told later that the elements of the Prussian force had joined the English, Napoleon revised his opinion downward on the basis of this information, but his posterior probability was still at 60%; P(Napoleon Wins │ Prussian and English join Forces) = 0.60. Suppose Napoleon was using Bayes’ theorem to revise this information. To do so, he would have to make some judgment about P(Prussian and English join Forces │ Napoleon Wins) and P(Prussian and English join Forces │Napoleon Loses). In particular, he would have had to make judgment about the ratio of these two probabilities. What is that ratio?