New York joined the ranks of all the other racing states and legalized betting in the mutuels to the exclusion of bookmakers. J Although certain tracks in various states became war casualties, nevertheless in 1947 over $1,500,000,000 were poured through the mutuel windows in straight, place, show or daily double betting on thousands of horses in thousands of races. A reader of course should understand that for every dollar wagered legally in the machines at the tracks possibly $5 to $10 are wagered on the same horse with illegal handbooks away from the tracks. If the ratio of illegal off-course to legal on-course betting is 5/1 to 10/1, it follows that approximately $5:000,000.000 to $10,000,000,000 are wagered each year in the United States on horses. No one conversant with the general facts will dispute the figure, and it is sufficiently romantic and impressive even in this era.]

So far as I know, the laws of no state make it a crime to bet with a bookmaker, although the laws of all, specifi­cally or through anti-gambling statutes, prohibit the book­ing of a bet. I am not concerned with the ethics of betting at the track or away from the track; my only interest is to give direction as to how to make money through wagering on horses, whether the attempt be made in a dingy poolroom or out in the sunshine of the lawn before the roaring thousands in the grandstand.

A prerequisite to a player's making money is a thor­ough knowledge of what happens to his dollars when shoved into the hungry maw of the "iron men" (mutuel machines), how mutuel prices are computed for all bet-table finishing positions of horses, what adverse percent­ages are involved, and just how a particular track may be checked to determine whether proper percentages are be­ing taken from the three mutuel pools on each race.

Of course the approximate odds against each horse's chances of winning are posted on the odds board during the betting on the race. All players know that a heavily backed horse will pay a short price for all positions, win, place and show, and that a lightly backed horse may pay a relatively long price for any position. But such general­ized knowledge is not enough for one who would become really expert in selecting his horses. The machines can develop some appalling percentages against a player who goes up against them in ignorance, and no citizen of the United States has any business wandering about mutuel windows with money in his hand unless he thoroughly understands what will be developed in this chapter and in Chapter 7, Section III, entitled How to Bet.

The first thing to be understood is how mutuel prices are computed, whether straight (win) prices, place (sec­ond) prices, or show (third) prices.

Assume the horses in the following table represent
a straight pool, the amounts indicated having been bet on
each animal to win.

Horse                      Amount bet Mutuel          Odds to 1

A.... $5,000            $ 4.30                               1.15
B.... 3,000                 7.20                               2.60
C.... 2,000                10.80                               4.40-
D.... 1,000               21.60                               9.80
E.... 1,000               21.60                               9.80

Here the total bet on all the horses to win is $12,000, establishing the gross straight pool at that figure. To get the mutuel that will be paid by any one of the horses it is necessary to go through the following steps. (1) From the gross pool deduct the legal "take" in the particular state. Say that the race is in a state where 10% is the authorized take of state and track. Ten per cent of $12,000 is $1,200, so with that out of the pool $10,800 is left as the net straight pool. (2) From the net pool deduct the amount bet on the horse whose mutuel is to be figured. (3) Divide the remainder by the amount bet on the horse. (4) Mul­tiply the result of this division by 2. (5) From the prod­uct subtract or strike out any cents above the last even dime. (6) To the dollars and cents figure (in even dimes) thus resulting add the $2 paid for the mutuel ticket. This final figure will be the mutuel price. To determine the horse's odds to 1, deduct $2 from the mutuel price and divide the remainder by 2. (All mutuel prices posted on the board or printed in the newspapers are in terms of what is paid for a $2 ticket, and include the amount staked.) The elimination of cents above the last dime [step (5)] is called "breakage to the dime," and adds about 2% to the authorized take deducted in step (1), This extra tax is imposed on the bland assumption that the player does not want to be bothered with nickels and pennies in getting his pay-offs, but it amounts to millions of dollars a year extracted from the public and going not only to states and tracks but also to the bookies that han­dle much more money than the tracks themselves.

The arithmetic involved in figuring the straight mutuel of any horse is so simple that it is unnecessary to work out the mutuel or odds to 1 price of A, B or any other horse in the table.

Place prices are computed in much the same way, but there is a difference, since two horses share in the place pool, the animal that ran first and the one that finished second.

The first point to note is that no horse goes to post at a fixed price to place, because what he will pay depends not only on how much is bet on him but also on how much is bet on the animal that happens to run first or second with him. Consequently I cannot show a fixed price to place for every horse in the race in the table above, as­suming the same amounts were bet on each. For instance .;i —on the betting shown in the table if to place—if A runs first and B places, B will pay a place mutuel of only $2.90. But if E wins and B places, B will pay a place mutuel of $4.20. In the first eventuality the profits of a place bet on B will be at the rate of 45c on the dollar; in the sec­ond case at the rate of $1.10.

The rules for computing place prices should be intelli­gible without working out the price of any single horse in the table. (1) From the gross place pool—total of money bet on all the horses to place—deduct the au­thorized take of track and state, as 10%. (2) From the remainder deduct the total of money bet to place on the horses which finished first and second. (3) Divide this remainder by 2, since half the net place pool goes to the holders of place tickets on the winner and half to the holders of similar tickets on the second horse. (4) Divide the half of the net place pool thus established by the amount bet to place on the horse whose place price is be­ing figured. (5) Multiply the result of this division, a dol­lars and cents figure, by 2. (6) From the product sub' tract the cents above the last even dime. (7) Add $2 to the remainder, this being the amount paid for a mutuel ticket and therefore included in the pay-off. The figure thus secured will be the mutuel price. To convert such a price into odds to 1 proceed exactly as in the case of straight prices by subtracting $2 and dividing the re­mainder by 2.

It will be noted that total moneys bet on both the first and second horses to place are deducted from the net place pool before it is divided 50-50 between the holders of place tickets on these animals. A much fairer way would be to divide the net place pool between the two before the sub­traction of amounts bet on each, and then to award as winnings to the holders of place tickets on either the excess in the particular horse's half of the pool over what was bet on him to place. But to do so would tend to increase the number of minus pools, so-called—pools where the track has to dip into its own pockets to pay off on a horse the statutory minimum profit of 10c on each $2 bet—with the result that the procedure is not followed. To get ahead of the story for a moment, the same thing should be done in the case of show pools; they should be divided three ways between the three money horses before and not after deduction of all money bet on such horses. That also would increase the number of minus pools radically, and it is not done.

A reader interested in checking his own figuring of place prices for horses in the table assumed to run first and second will find a number of such prices given in Chapter 7, Section III, where they illustrate the fallacy of place and show betting in comparison with straight or win betting.

No horse goes to post at a fixed price to show any more than he does at a fixed price to place. What he will pay, to show depends not only on his running in the money— first, second or third—but also on the amounts bet on the two horses that run in the money with him. The pro­cedures for computing show prices are similar to those employed in computing place prices. (1) From the total of all money bet on all the horses in a race to run third deduct the legal percentage of take in the particular state, thus establishing the net show pool. (2) From the net pool deduct the total of all money bet to show on the three horses which finished first, second arid third. (3) Divide the resulting remainder by 3. (4) Divide the result by the amount of money bet to show on the horse whose price is being figured. (5) Multiply the result, a dollars and cents figure, by 2. (6) From the product subtract the cents above the last even dime. (7) Add $2 to the re­mainder, the amount paid for a ticket. The figure secured will be the show mutuel for the particular horse.

I have indicated how mutuel prices for the three bet-table finishing positions are computed merely to explain how the mutuel system works.

I will now set out the same table printed above to repre­sent a race in a state authorizing a 10% take from the pools. There are, however, two changes. The mutuel prices are not given, only the odds to 1 against each horse to win, and the booking percentages developed from the odds have been added.

Horse Amount bet Odds to 1 Booking %

A....                 $5,000              1.15     .4651
B                      3,000              2.60     .2777
C                      2,000              4.40     .1851
D                      1,000              9.80     .0925'
E                ...... 1,000              9.80     .0925

Mathematical explanation of a booking percentage need not be given here, although I will explain how to develop the figures from any price to 1 against a horse. The point is that the booking percentages in the case of the race set forth above total 1.1129, and the excess over an even 1.00, or .1129 expressed decimally, 11.29, as a percentage, ac­curately shows what track and state are taking from the pools as their percentage, plus breakage to the last dime. Normally, in a state where the take is 10%, the booking percentages on a race would total closer to 1.12, but in the case of the race assumed in the table the round amounts bet on each horse have minimized breakage and reduced the total of percentages to 1.1129.

Developing booking percentages is a very simple procedure. In the first place, the result chart on any race not mutuels gives the price against all horses to win, in terms of odds to 1. And to convert any odds to 1 to the corresponding booking percentage the only necessity is to add 1 to the figure expressing the odds and to divide 1 by the total so secured.

In the case of a horse at even money, 1 to 1, conven­tionally written as 1/1 and shown in a result chart as 1.00, merely add 1 to the 1.00 and divide 1 by the result. One plus 1 is 2, and 1 divided by 2 is .50, the booking per­centage representing odds of even money. If the result chart shows a horse went to post at 16.45 to one, go through the same procedure to develop the corresponding booking percentage, being careful to get the decimal point in the right place. One divided by 16.45 plus 1 is 1/17.45, or, expressed decimally, .0573, worked out to the nearest fourth point like the percentages in the table above.

If the excess over an even 1.00 in the total of booking percentages on an actual race as shown in the result chart measures what has been taken by track and state by way of take and breakage, it follows that any track can be checked on whether it is dipping too deeply into the pools. If the booking percentages representing the odds to 1 against all horses in a race are developed in the way outlined above, and if the total of these percentages ex­ceeds the statutory rate of take plus 2% for breakage to the last dime, then there is something exceedingly rotten in Denmark and a wise player will shun that track and confine his betting to a course satisfied with the take that is authorized by that particular state—preferably one that permits 10% rather than 15%.

Up to this point I have set out no actual races, only an assumed one, but now I will show a few races at specified tracks, giving odds to 1 as shown by result charts and de­veloping corresponding percentages, as well as exhibiting their totals in comparison with the take authorized in the particular state. Here is a race in New York.

Horse   Odds to 1     Booking %
Dansation..    8.70                .103
Still Life.....    7.50                .118
Play Grier..    1.05                .488
Stuhldreher... 2.20                .312
One Look. 11.45                .080
James T.R. 54.60                .018
Total percentages............... 1.119

In New York a 10% take is authorized.6 It will be noted that the booking percentages representing the odds to 1 against the horses (carried out to three points) total just a shade short of 1.12, as they should with 10% take plus nearly 2% for breakage to the last dime. In other words, the tracks in New York confine themselves scrupu­lously to the exactions from pools to which they and the state are entitled. Only one New York race is shown, but I never have checked a race in the state under the mutuels without finding everything in order as regards percentages exacted.

But there are other tracks in other states. Here, for in­stance, is the same showing for a race at a southern track.

Horse         Odds to 1       Booking %

Air Transit.                       3.80 .20833
Lord Bart 1.70                .37037
Ancipital.... 6.05               .14184

6 The New York State Legislature for the years 1946, '47 and '48 authorized a temporary 5% increase in the 10% take for the benefit of local municipalities where the tracks are situated.

Horse      Odds to 1       Booking %

Golden Message .....         7.35 .11976
Valdina Troth                    4.10 .19607
Gaykis...... 37.85              .02574
Astraea...      7.25              .12121
Viejo ........        ..              69.10           .01427
Total percentages........ „ . 1.19759

The authorized take was 15%, to which breakage to the last dime would add about 2%. But .15 plus .02 is not .19759, the excess about 1.00 developed by the booking percentages on this race. Over 2.7% (.02759) disappeared Irom the straight pool without explanation, apology or-legal warrant. Who got it I do not know. But I do know that each state has inspectors in the mutuel department, checking on what is taken from the pools and on the cal­culations of prices. Just what they did to earn their sal­aries is something of a mystery.

Here is another race at the same track.

Horse          Odds to 1       Booking e/o

Peace Eagle                         1.95         .33898
Panbroom... 6.55             .13245
One Shen    1.20             .45455
Alaflag.....    4.15             .19417
Cyrus P.... 11.90             .07751
Total percentages........... 1.19766

The percentages on both these races have been run out to five decimal points in an effort to be quite exact. And it will be noted that the excess over a proper 1.17 in the percentages is greater even than in the other event at the same track.7

7 Odds to 1 against each horse printed in a result chart "show the price of each after breakage to the last dime has been eliminated in the case of all. But breakage actually has been eliminated in paying off only from the winner's price. Therefore the total of booking percentages, computed as directed here, is slightly in excess of the correct figure of exaction. But this fact does not explain the difference between a correct total of 1.17 (about) and the figures developed from the result chart odds to one in the case of the two races analyzed.

A player will be wise to develop occasionally the book­ing percentages on races in order to ascertain whether the proper percentages are being taken from the pools, plus 2% for breakage to the last dime. This precaution should not be necessary, but it is. Of course one is at liberty to make wagers at any track he chooses. But the game is hard enough to beat without going up against excessive takes that cut down the price on every winner, or turn profits into a loss.

Perhaps this is not the place to refer to the matter, but there is no other place for it in the book. I am referring to. betting two, three, four or even more apparent con­tenders in a single race, each to win, in an effort to beat it for a percentage profit provided that some one horse of the group bet on does win.

If enough horses can be ignored as non-contenders and not bet, so that the total of booking percentages represent­ing the odds against them is materially in excess of the percentage exacted by track and state through take and breakage, then all the other horses in the race, all the real contenders, can be bet straight (to win only) in amounts proportionate to the booking percentages representing the odds against each of them, and a profit realized if any one of them wins. If the betting has been on the scale of $1 for 1%, profit on the race in the event of success will be roughly the difference between $100 and the total bet on the contenders. A player using this method has gotten rid of the mutuel percentage by rejecting non-con­tenders, putting up less than $100 to win the difference between that amount and what is bet.

Take the race set up in the last table. If Panbroom, Alaflag and Cyrus P. could have been excluded from bet­ting, a player would have gotten rid of the percentages representing their odds, or, in even figures, 13, 19 and 7, which total 39, or about 20% in excess of the take and breakage of 19% plus. By betting $33 on Peace Eagle and $45 on One Shen, both to win, a total of $78—at the scale of $1 for 1%—would have been wagered to win about .$22, the difference between what was bet and $100. When Peace Eagle won, the return from $33 bet on him at $1.95 to 1 (winnings at that rate, plus stake returned) would have been $97.35, which represents $19.35 winnings over a.nd above the total of $78 bet. The profit would have been slightly less than the difference between $100 and the amount bet (see statement above as to that constant margin of profit in the event of success) because in bet­ting an even $33 on Peace Eagle the actual percentage representing his price was rounded down somewhat from .33898 as shown in the table.

Obviously play of this type can be made a very power­ful weapon by a player who is a first-class handicapper in his own right and is able to use fairly substantial amounts of money. Contention play cannot be conducted with ac­curacy, betting 25c or less for 1%, because one gets into trouble through too much rounding of percentages in turning them into amounts bettable in the mutuels, where $2 is the least that can be wagered. Again let me say that in play of this type a bettor must be a first-class handi­capper in his own right. In other words, he cannot elim­inate non-contenders on the opinions of public selectors. Such people simply are riot good enough, since, as I've already pointed out, horses they do not like win too often. And of course in play of this type a single loss eliminates the profits from four, five or six successful transactions. Also, it must be operated at the track, where one can buy tickets at closing odds.

I have suggested that tracks occasionally milk the mu-tuel pools by taking from them more than is permitted by the legal take plus breakage. And I have shown how a player can detect when this is being done by developing the booking percentages representing the odds to 1 against all the horses in a race, by totaling the percentages, and by noting whether the total exceeds an even 1.00 by more than the legal rate of take in the particular state plus about 2% for paying off winning tickets only to the last dime of winnings on each $2 staked. But more need be said about the real mutuel take, whether it be legal or larcenous.

Sportswriters on newspapers are constantly gabbling about the mutuel machines' chewing up 10%—or other authorized fraction—of each dollar bet. This is a mis-statement, because losers of bets pay no part of the take on a particular race. Each has lost his whole wager, and lost it irrevocably. The take is paid by the holders of win­ning tickets on the event, who receive not their full profit —the amount the losers have lost—but this sum dimin­ished by the authorized rate of take and breakage includ­ing the winners' own money. A reader will see at once that this means that winners' profits are diminished by more than the legal rate of take and breakage even when the track is entirely honest.

Here is another table showing the real take against the holders of winning tickets.

Mutuel                   Mutuel        %

Horse Amount bet if no take   with take diminution

A       $5,000          $4.80        $4.30    17.8
B         3,000            8.00        7.20      13.3
C         2,000          12.00        10.80    12.0
D        1,000          24.00        21.60    10.9
E ..... 1,000 24.00    21.60        10.9

? Percentages in this column show diminution of natural profits involved in mutuel prices. In the case of horse A, $1 bet on him would win $1.40 if there were no take, but only $1.15 under a take of 10% with breakage to the last dime on $2 bets. Reduction of $1.40 profit by 25c to $1.15 is equivalent to a cut of 17.8%, not 10%. It must be remembered that I am speaking of the re­ductions of profit in the mutuels. Each mutuel price as quoted in­cludes the stake of $2, and only the excess of the mutuel over that amount is the profit. Thus, in the case of horse A, reduction of the natural mutuel without take of $4.80 to $4.30 involves a cut of winnings from $2.80 to $2.30, which is equivalent to 17.8%, as shown in the table.

In computing the mutuel prices for all the horses in the event each wins, the assumption has been that the legal take is 10%, with breakage to the last dime. When a win­ner's profits are diminished, as they always are, by opera­tion of the take, and the extent of that diminution is re­garded as the real mutuel take, two basic conditions be­come apparent. (1) The real take, paid only by the hold­ers of winning tickets and paid in diminution of the price they would have received had it not been for the take, is always in excess of the legal rate of take. (2) The more money bet on a single horse, in relation to the total bet on all, the greater the legal take against the holders of tickets on him if he wins.

Favorites win only thirty-two or thirty-three races in a hundred, on an average. But still the distribution of money means something. It is the concrete opinion of the horse world on the chances of the several horses—the com­bined opinion of selectors, informed and uninformed pub­lic, individual betting stables and individual heavy bettors. Nevertheless a player who follows the money instead of betting against it—when his independent analysis of the chances permits—is constantly losing to the take its ex­aggerated share of the wagers on well-backed horses. A player who normally bets favorites puts himself in" the position of a man who matches quarters and agrees to ac­cept 15c or 20c whenever he does match, and will pay over the full quarter when he fails. Well-backed horses are simply well-backed horses; a heavy proportion of all the money bet is on them. Selectors have chosen them to win; the public has followed the selectors, and the prices of such favored animals are odds-on, even money or a little more. To judge merely from the odds, the race is over before it is run. But favorites do not win 40% of their starts, only 32 or 33. Even odds-on favorites usually manage to lose at least half the time. In New York, for instance, in a recent year, 169 odds-on favorites went to post and only 82 managed to win. If a handicapper can get as many as 40% winners he must secure an average mutuel on them of $6 (which is 2/1) if he is to make the reasonable percentage profit of twenty on all amounts bet. A chronic backer of favorites, with an occasional short-priced second or third choice mixed in, probably will not get 40% winners (unless he is a first-class handicapper and picks his own horses without reliance on selectors). He cer­tainly will not realize an average price on winners of 2/1. There is too much money with his on the type of horse specified. On top of that, his small natural winnings of what the lightly backed horses have lost will be cut down by the exaggerated mutuel take that develops from the legal rate on animals carrying a great deal of the money.

These matters should be plain as a pikestaff to one who knows simple arithmetic and will read such an analysis as I have just made. If half the money in the straight pool is on the favorite, then even without any take at all the return is only even money, or a mutuel of $4. And a mere 10% take will consume 20c of each dollar in the natural profits of winning tickets on the favorite, not just 10c. No one can take profits so seriously diminished and hope to balance the sixty to seventy bets out of each hundred lost through the mere accidents of racing, the secret in­tentions of stables, and one's own mistakes of judgment.

No one can deny these statements. And yet a player betting at or away from the course is always straining to get an impossibly high percentage of winning transactions, instead of wagering coolly in a pattern planned to take care of the price-factor as well as the percentage of bets won. The player who has made up his mind in advance that he is bound to lose 50% more bets than he wins is not going to be shaken by a few losses in a line. And if he is wagering at least part of the time on horses really solid as he sees them, going to post at 3/1 or more, he need not worry about the price-factor in the long run if he has made himself a first-class handicapper by study and experiment.

A player who is a good handicapper can maintain, over prolonged periods, an average of 40% winning bets. And, while doing this, he can maintain an average price on winners of 2/1, $6 mutuel, if he is not afraid to wager on a horse that he likes for definite reasons even though none of the selectors picks the animal which goes to post at five, ten or even twenty to one. It is the occasional good-priced winner secured by a player strictly on his own that will compensate for the short prices he is often forced to accept on favorites.

The first problem a player must lick is to train himself to find horses really solid, horses that really do figure to win quite apart from the prices they will pay, whether short or long. The second problem for a player is to de­velop such confidence in his own judgment that he will not be afraid to back his independently selected horses on occasions when they are going at good prices. All his profits over a period will be found on later analysis to have come from such horses. On the short-priced favorites that he had to take because he could find nothing else worth a bet he will have made nothing material, will have broken about even, or will have sustained a loss.

If you want to make money by betting horses (1) for­get the newspaper and scratch-sheet experts and concentrate on learning how to figure a field for yourself; (2) back your own opinions when you have attained a degree of expertness that warrants it; (3) of two bets, where you figure two horses in different races to win and by satisfactory margins, always take the one offering the longer price. The profits yielded by lightly backed horses are diminished only triflingly by the mutuel take, which is impossibly severe in the case of heavily backed animals-

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