I determined to... investigate how closely the runs, that is, successions of numbers of the same colour were in accord with theory. ...The chance of … - Karl Pearson

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I determined to... investigate how closely the runs, that is, successions of numbers of the same colour were in accord with theory. ...The chance of a head<math>=\frac{1}{2}</math>, of two heads succeeding each other <math>\frac{1}{2}\times\frac{1}{2} = \frac{1}{4}</math>, of three heads <math>\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2} = \frac{1}{8}</math>, and so on. Calling a "set" the run of tosses or the throws of the roulette ball till a change of face or of colour comes, the chance of a change<math>=\frac{1}{2}</math>, of a persistence followed by a change <math>\frac{1}{2}\times\frac{1}{2} = \frac{1}{4}</math>, and so on. ...[I]n the case of the roulette on one occasion the actual deviation is nearly ten times the standard.... The odds are thousand millions to one against such a deviation as nine or ten times the standard. ..My pupil... tabulated... the runs in a second fortnight's play with the result... so improbable that it was only to be expected once in 5000 years of continuous roulette. ...Finally, Mr. de Whalley investigated 7976 throws of the ball, forming a fortnight's play, at a slightly later date... There resulted deviations 4.63, 4.62, and 4.44 times the standard deviation, or odds of upwards of 263,000 to 1... That one such fortnight of runs should have occurred in the year 1892 might be looked upon as a veritable miracle, that three should have occurred is absolutely conclusive. Roulette as played at Monte Carlo is not a scientific game of chance.