The Art of Bookmaking.

Thames Star, Volume X, Issue 3142, 14 March 1879, Page 1

The Art of Bookmaking.

A Lisbon pob^matbcjw.

The object of the present piper is to Bhow that there is a science of betting, and that this it wholly mathematical in its nature. We shall first explain what the market price of a horse is, and then illustrate a few of the mathematical laws exempified m the transactions which hare been going on in Dunedin during race week. Let us ask this question:—Suppose there is a lottery with one prize say of £5, and four blanks. You* hold a ticket. Has your chance any market Talue of a precisely calculable nature? Very few will be found to d*ny that the Talue of such a chance can be expressed in money. Mathematicallj»ion»-"<'c>«i<i- — say '.hat tho holders ehfttiee wtfs "one-, fifth, and that as the prize was £5, the cash Talue of the ticket was £1. It is not difficult to see that the betting would be 4 to 1 against the ticket 'drawing the prize. We can now say generally that if a horse is at 4 to 1 his chance is l-stb. Suppose a horse is 6 to 1, 'think of a lottery -with one prize and six blanks; The chance is one-seventh; and if the, prize is a guinea, the market value of one ticket is three shillings. Similarly, if a, horse is at 100 to 8, you have to imagine a lottery with one prize and 108 tickets, of which you hold eight. Your chance, then, is as 8 against 100, or, expressed fractionally, eight one-hundred arideighths. The next step is the hardest to make. Suppose there is a lottery with" three tickets. The chance of each ticket is -g; the chance of a man who holds two is f; the chance of a man who holds three w 3-3rds, or 1. Take this, then, as an established mode of expression, that when an event is certain, as in the above instance, a man holding three tickets is certain of the prize; his chance is said to be 1. Now let~ us ask, suppose a horse's " chance to be 3-7th,sj what is the betting ? Well, you must imagine a lottery with seven . tickets, and three of them in your possession. Your chance is as .3 against 4; in other words, the betting is 4 to 3 against you^_We can now attempt a problem of the highest practical importance. Suppose the odds are 5 to 1 against one horse and 8 to 1 against another, what is the betting against the pair P The chance of the first horse is l-6th, of the' second l-9th. Add these fractions, and you find the chance of the pair to be 518ths. Now we know that certainty is expressed %y-'■■.!,■" and 1 that the chance of the whole field must therefore be 1. Subtract 5-18ths from 1, and we get 11-18tbs as the chance of all the field, bar the two whose chance is 5-18ths. The chance of the two then against the field is as 5-18ths against 11-18ths, or as 6 againßt 11, and the betting is 11 to 5 against the pair. Take another oate. Three horses are at 2to 1,3 to 1, and 4to 1 respectively. Find odds against the field. As before, the horses' chances are respectively |; i, andl-Sth.Add: 'these fractions, and you get 47-60ths. Snttnpt this from 1, and you hare 13-60ths. ; ; This is the chance of the field, and the betting is 47 to 13 against the field ; or, roughly,, about 4 to 1. ; jlt?will haTe occurred tot our readers by now that if what we say is true, and if certainty can be legitimately represented by 1, we must, if we add up ■^c chances of all the horses in a race, fet f m -+ as total a fraction equal to 1. We .ill wTi vii * «nKle experiment. On Tues. J A- W v of February, the bettingcorrespondent "Beaco. > ; . £,i fA9'TiH Templeton 5 to 1, Ohanoeliu * -iM? tk $ t '< : nia 8 to 1, Oamballo.B toli JS^ 9e^g^ Fishhook 100 to 8, Mata 100 to 8, - — 3Fund 100 to 6, Maritana 100 to 5, ,„ 100 to 4 against the rest. It may fnirij be assumed that after Maritana at 100 to 5 there certainly were not more than two horses about whom any legitimate business was done- at 100 to 4 ■ The chances of the lot, expressed fractionally, are l-6th + 2-l3ths + l-9th + 1 9th + 1-llth + 8-108ths + 8-ICBLhs -f 6 106ths + 6105ths 4- 410<lths -f 4-104ths. These fractions then ought, when added, to amount to exactly 1. There are several ways of ado!io£ them. The best is, to very slightly alter all the awkward denominators in such a, way that the' slight"errors thus introduced correct each other. Another way is, to copy out a table of reciprocals and work by decimals. Howevor, we will suppose our readers .willing to find out and use some method- The exact result is fsllHl, if we have done our sum correctly. Let us take |g>as a near enough approximation for our purpose, and inquire why it.does not come out exactly unity, and what conclusions we may" draw therefrom. There are 1 many reasons why,wedonot get unity in every case. Speaking loosely, one may say that the - market is continually fluctuating, and that all bets have to be put down in - round numbers. No one would book a bet of 47 to 18. There would be a little ' haggling, and eventually either 4 to 1 or 7to 2 would probably be accepted. The really important matter is, what ought a man to do if he wishes to place some money, when he adds up the chances and finds them less than unity P 'Well, any , boy will see how the cat jumps if we take a simple .case. Suppose < there are .three horses in a race, and the betting is 5 to 1 all round. Add up their chances, And we have 1 6th + l-6th -f- l;6A t » i. It is tolerably clear that in this state "of ihe> ; market backers must win if thej• back all horses, and spread their money pretty ■■>. equally over the field. Now take another simple case. Three horses are entered, and the betting is 2to 1 all round. Adi ; the chances and you have -5 4- 4 -f" iV== 1. We see that our result is uriity.aud a few exprriments will show anyone '■>■ whoi ' cares to try that on auoh a race'as the above, a- man who either backed : the . horses ,or laid against them, operating systematically, and distributing his money ° evenly,: would neither gain nor' lose. ' Lastly, imagine three horses entered, and '

the odds 7 to 4 all round. Adding chances, we have 4-llths -j- 4-llths -j--4-llths = 12 llths. Our result is greater than unity, and the safe line is to lay against all the horses, and you are certain to win. We shall now recapitulate our conclusions, and then divulge the one and only secret of bookmaking. We have seen that if the added chances of the horses come to unity, yon may as well leave it all alone; that if they are less than unity, you win as a backer; that if they exceed unity, you win ai a layer. Professional bookmakers are perfectly acquainted with all this; but their phraseology is so different from oum that they probably will not understand a word of this article. The way they work the thing practically will, we think, be intelligible to our least mathematical readers. "To win as layers they must operate in a market where the added chances are greater than unity." All they have to do is to make a fnir shot at the values, or prices, of the different horses, express these prices in the usual way, and "invariably bet a po nt or so shorter odds than the estimated price of the horse." Nobody need ask where they will find backers. Every city clerk was hungering after sport last week, and he regarded very little such an apparently trifling matter us whether he got 4t010r7 to 2. Suppose, however, that a bookmaker wants to come out as a backer, does it not follow naturally that " he has nothing to do but to insist ob getting a point or two longer odds" thnn current prices? He is then operating in a market where the added chances are less than unity; and if he distributes his money — spreads his " sugar "—evenly, he is sure to win. It must now be pretty plain that it is not necessary to resort to the tricks about which we hear so much as to horses being pulled, or drugged, or dishonestly scratched. The ring can make plenty of money without resorting to. absolutely illegal means. And, in conclusion, we may ask why, if it is all so simple, should not our readers start their books, and make sure of winning a pot on the next race meeting. We see no reason at all. If they like "the amount of dirty work they will have to do; if they do not shrink from the innumerable lies they will have to tell in order to get always longer odds than the current prices, and to lay always shorter, let them go in. They will certainly make some money. But for ourselves we think even so valuable a commodity as money may be bought too dear. The countenances of some of the gentlemen who crowd the Empire during the Cup week warn the amateur of what he may expect to become if he attempts to rival.tjjtie professionals.— Pablo, in the Otago Dlily Times.