monte carlo simulation def playhand(self)#an alternativefasterimplementation of playhand pointsdict { : : : : : :throw rolldie(rolldie(if throw = or throw = self passwins + self dplosses + elif throw = or throw = or throw = self passlosses + if throw = self dppushes + elseself dpwins + elseif random random(<pointsdict[throw]point before self passwins + self dplosses + else before point self passlosses + self dpwins + figure using table lookup to improve performance finding it is easy to see how monte carlo simulation is useful for tackling problems in which nondeterminism plays role interestinglyhowevermonte carlo simulation (and randomized algorithms in generalcan be used to solve problems that are not inherently stochastici for which there is no uncertainty about outcomes consider for thousands of yearspeople have known that there is constantcalled (pisince the th centurysuch that the circumference of circle is equal to *diameter and the area of the circle equal to *radius what they did not know was the value of this constant one of the earliest estimates *( / ) can found in the egyptian rhind papyruscirca bc more than thousand years laterthe old testament implied different value for when giving the specifications of one of king solomon' construction projectsand he made molten seaten cubits from the one brim to the otherit was round all aboutand his height was five cubitsand line of thirty cubits did compass it round about solving for so perhaps the bible is simply wrongor perhaps the molten sea wasn' perfectly circularor perhaps the circumference was king james bible kings