The gambler's fallacy 81
Many so-called 'systems' of gambling are based on the gam-
bler's fallacy. If betting on a 1 in 2 chance, you double the stake
after each loss, then when you do win you will recover your losses
and make a modest gain. The trouble with this is that the rules of
maximum stake, if not your own resources, will soon stop you
doubling up. (Try the trick of doubling up ears of wheat on each
square of a chessboard, and see how quickly you reach the world's
total harvest.) Furthermore, the odds are that the sequence which
it takes to beat such a system will occur with a frequency sufficient
to wipe out all of the winnings you made waiting for it. Only one
rule is worth betting on: the house always wins.
You can use the gambler's fallacy by appealing to a quite
unfounded general belief that the universe is somehow fair.
My argument for avoiding the west of Scotland is that it has rained there
on about half the summers this century. Since it was fine for the last two
years, the odds are that it will rain this year.
(Things change, even in the west of Scotland.)You may find the gambler's fallacy particularly useful in per-
suading people to go along with you, despite a previous record
which indicates that luck was not involved.
/ propose this candidate for our new secretary. I know that the last three I
chose were pretty useless, but that's all the more reason to suppose I've
had my share of the bad luck and will be right this time.
(This sounds like bad judgement disguised as bad luck. The odds are
that the new choice will be both pretty and useless.)The last four lawyers I had dealings with were all crooks. Surely this one
must be better.
(No chance.)