## Oddities

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Humans and not very good at calculating odds and how probabilities work. For instance, if we are tossing coins and we get six heads in a row, the probability of getting yet another head is still fifty-fifty. Yet people feel that after a series of heads that it is more likely that more tails than heads will turn up for a while, so that the ratio of heads to tails returns to the expected one to one ratio.

But the expected ratio of heads to tails for all subsequent tests is one to one. It’s as if a new set of tests is being started, and so any lead that has already built up is, in all probability, not going to be reduced.

This seems odd. If we have done one thousand trials and have turned up 550 heads to 450 tails, the ratio of heads to tails is about 0.818 and the ratio of heads to the number of tests is 0.55. Surely more tests will take the ratios closer to the expected values of 1.0 and 0.5? Surely that means that there will be more tails than heads in the future?

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Well, the answer to both questions is no, of course. The ratios for the whole test may move closer to 1.0 and 0.5, but equally, they may move further away. In the extreme case, there may never be a tail again. Or all the rest of the throws may result in tails.

Interestingly, if the subsequent tests produce a series of heads and tails, the difference between the number of heads and tails stays at around 100, but the ratio of tails to heads for the whole test slowly creeps closer to 1.0 and the ratio of heads to the total number of tests closes in on 0.5 as more and more trials are done. By the time we reach two million tests, the two numbers are not very far from the expected values, being 0.9999 and 0.5000 respectively.

So, if you think to yourself, as you buy a lotto ticket “Well I must eventually win, if I keep buying the tickets”, it doesn’t work like that. You could buy a lotto ticket forever, literally, and never ever win. Sorry.

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Lotto and sweepstakes are, I believe, a different type of gambling from other forms, such as betting on horses or poker and other gambling card games. Lotto, sweepstakes and raffles involve no element of skill, and the gambler’s only involvement is buying the ticket. Betting on horses or cards involves skill to some extent, and that skill comes down to things like working out the probabilities of a particular card coming up and the probabilities of other players having certain cards in their hands.

Both types of gambling encourage the gambler to gamble more. If a gambler doesn’t win on the Lotto he or she might say to his or herself “Better luck next time.” Of course, luck does not exist, but probabilities do, and this is a mild form of the Gambler’s Fallacy described above. Nevertheless, people do win and the winners appear on television for us all to see and emulate.

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There’s two sorts of strategy for winning the Lotto. First there’s the “always use the same numbers” strategy, and then there’s the “random numbers” strategy. If you always use the same numbers, goes the theory, then eventually there must be a match. That’s wrong of course, since the number combination may not appear before the end of the universe.

The random number strategy argues that there is no pattern to results so it is silly to expect a particular pattern to eventuate. This strategy acknowledges the random nature of the draw, but doesn’t give the gambler any advantage over any other strategy, even the same numbers strategy. It is certainly easier to buy a randomly generated ticket than to fill in a form to purchase the same numbers every time.

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Some people experience a run of luck. They might have three things happen to them, so go and buy a lotto ticket while their luck holds. Then is they win they attribute it to their lucky streak. It’s all nonsense of course. They conveniently forget the many, many times that they bought a ticket because of a lucky streak, only for the ticket to be a loser.

The proceeds from the sales of lotto tickets don’t normally all go to holders of winning tickets. Firstly the operators of the system need to recoup their costs. It’s not cheap to own and operate those fancy machines with the tumbling balls and it also costs to employ the people to check that the machines are fair.

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If one of the balls is dented, will that affect the probability of that ball being selected? Maybe, just a little, but the draw should be fair so those providing the lotto equipment spend a large amount of effort to ensure that they are fair, and the costs of that effort must come out of the prize funds.

Secondly, the state or maybe the lotto organisation itself will often withhold part of the lotto sales takings for local or national causes, such as cancer research, or societal things, like the fight against teen suicide. The money for humanitarian causes is deducted from the prize funds.

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One of the humanitarian causes is often the fight against problem gambling. It’s ironic and somewhat appropriate that funds from gambling are used to combat problem gambling. It seems that some people get such a thrill from gambling that they use all their, then borrow or steal from others to continue to gamble.

They invoke the Gambler’s Fallacy. They suggest that their luck must change sooner or later. It doesn’t have to, and may never change, but they continue to spend money on their gambling. They also don’t take account of the fact that they might win, eventually, by sheer chance, but it is unlikely that their winnings will cover what they have already gambled away. They have a tendency to believe that one big win will sort things out for them. It won’t of course.

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So, the only true fact about Lotto and similar draw is that you have to be in to win. But just because you are in doesn’t mean that you will win. You probably won’t. The best way to treat Lotto and other similar games is that you are donating to a good cause and you might, but probably won’t get something back. So, I’m off to buy a lotto ticket. I might win thirty million dollars, but I won’t cry if I don’t.

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## Gambling

Gambling has probably been a human activity since two cavemen had a bet over their respective hunting prowess. Or maybe it was over which of them could stay upright longest after sampling the newly invented alcoholic grog. Gambling games generally have probabilistic component, though the contestants generally try to remove or circumvent it, usually by such techniques as remembering the order that cards come out or ‘card counting’. This latter technique involves keeping track of the high cards that come into play.

For some people gambling can become a problem. Sometimes susceptible individuals can become ‘addicted’ to gambling to the extent that they embezzle and steal so that they can continue to gamble. They may rationalise this by claiming that they are only trying to regain what they lost, or repay the people who they have stolen from, and indeed, because of the probabilistic nature  there is a chance that they might be able to do that. However the chance is very very small.

When a gambler starts gambling the reason that they gamble is the thrill of the possibility of winning big. Once the gambler has used up all his or her resources and has borrowed or stolen to keep gambling then the fear of losing and the fear of people finding out would be the predominant emotions, especially the fear of being found out.

They probably think to themselves that their luck must turn sooner or later and they must start winning, however this is just not true. Suppose the gambler is \$100,000 in debt and chooses odds of evens. Then to win \$100,000 he or she must wager \$100,000 and to do that he or she would have to steal another \$100,000. Such a theft is more likely to be noticed than a smaller amount and there is an even chance of losing and being \$200,000 in the hole.

As a result, it is likely that a ‘problem gambler’ would choose to go for longer odds and therefore smaller amounts of stake money, but with less chance of winning.

Statistically, over a large number of gamblers and a large number of wagers on something like a horse race, if all the money taken on wagers is paid back to punters then the average return, over all punters taking into account the stakes and the winnings paid out, is exactly zero! Of course, not all the money taken in in bets is paid to the punters. If the bets are on a totalizator system then the organisation running the ‘tote’ takes out taxes and administration costs so the payout will be less than the amount taken in.

If the system is a ‘bookmaker’ run system then the bookie needs to cover his costs so he (or she) arranges his books so that not all the money taken in bets is returned to the punters. There is a very small chance that under some circumstances he cannot cover all the bets made, but it is rare for this to happen. A bookie will sometimes ‘lay off’ a bet somewhere else if he feels exposed as a result of a large bet.

What this means to the gambler is that, on average, he is going to get back from the system less than he puts in. What a gambler hopes is that his personal return is positive, and he will in fact beat the odds. It is highly likely that he won’t though. A ‘problem gambler’ is unlikely to be a clever gambler and is likely to continue to lose.

Lotteries are different. Although Lotto is referred to as gambling, it is different from card games like poker or betting on horses. Again the average return is going to be zero or negative. However, with a lottery, the only way to increase your chance of winning is to buy more tickets. There is no real or illusory skill involved. As a result the lottery is unlikely to attract the ‘problem gambler’.

Of those who do take part in the lottery there are some who fall foul of the “Gambler’s Fallacy”. Some people use the same numbers draw after draw after draw in the belief that their particular set of numbers must come up sometime. This is not so at all. It doesn’t do any harm, though, as their particular numbers are just as likely to come up in one draw as any other. In fact, if their numbers do come up, they are equally as likely as any set of numbers to come up the next week too.

I confess that I don’t see much sense in betting on horses or dogs or whatever. I don’t have the skills necessary to increase the odds in my favour, though the so-called ‘professional gamblers’ appear to have those skills, and ‘problem gamblers’ definitely don’t.  I do buy lotto tickets, though, but I’m not too upset when I lose and the rare small win is fun.