Raymond Tallis thinks about probability and the frozen world of quantum mechanics.
When you toss a coin, there are two possible outcomes – heads (H) or tails (T). No outcome should influence its successor: there is no causal pressure exerted by Toss 1 on Toss 2, as there is, say, from the movement of the thumb to the movement of the coin, so the chances of H on a particular occasion are the same irrespective of whether its predecessor was H or T. Improbable sequences – such as 100 straight Hs – do not defy or even bend the laws of mechanics. But if the outcome of Toss 1 does not influence the outcome of Toss 2, such that there is no gathering causal pressure for a T to follow a long run of Hs, why don’t we easily accept that the series H, H, H… could be extended indefinitely? Why would an unbroken sequence of 100 Hs raise our suspicion of a bent or even two-headed coin?
Let us look a bit closer at the properties of a genuinely random sequence. As we extend the series of tosses, the number of possible patterns increases enormously, but the proportion of those that are significant runs of Hs or Ts are vanishingly small. There is a 1:4 chance of HH (the other possibilities being HT, TH, and TT), but 25 Hs in succession would be expected to occur by chance only once in 33,554,432 throws. The longer any run of Hs or Ts, the less frequently it will occur; so the most likely outcomes will be those in which runs of Hs or Ts are soon broken up. This is how we reconcile the 50/50 chance of getting H on a particular toss, irrespective of what has gone before, with the growing suspicion that appropriately greets a very long series of Hs and the mounting expectation of a T.