one
after three
`` The odds against ' 17 ' appearing four consecutive times are some millions , '' he went on , `` and yet , having appeared three times , it is just as likely to appear again as before . It is the usual practice to avoid a number that has had a run , on the theory that some other number is more likely to come up than it is . That would be the case if it were drawing balls from a bag full of red and black balls -- the more red ones drawn the smaller the chance of drawing another red one . But if the balls are put back in the bag after being drawn the chances of drawing a red one after three have been drawn are exactly the same as ever . If we toss a cent and heads appear twelve times , that does not have the slightest effect on the thirteenth toss -- there is still an even chance that it , too , will be heads . So if ' 17 ' had come up five times to-night , it would be just as likely to come the sixth as if the previous five had not occurred , and that despite the fact that before it has appeared at all odds against a run of the same number six times in succession are about two billion , four hundred and ninety-six million , and some thousands . Most systems are based on the old persistent belief that occurrences of chance are affected in some way by occurrences immediately preceding , but disconnected physically .