Edgar and Clyde

PARTENT EN VACANCES!

In which the favorite pastime of two public servants is discussed and explained with emphasis on the underlying science and mathematics of a popular American recreation.

(Click on the image to zoom in.)

There is, of course, much debate and many volumes written about Edgar and many of these tomes mention Clyde as well. Admittedly the sources are often secondhand and at times unverifiable. For instance, you might have one source tell a historian that he had seen a most interesting photograph of Edgar. But, alas, he didn't have the photo himself, so you'll just have to take his word for it.

But here the discussion will be limited to the known and verifiable facts about Edgar and his good friend Clyde. And indeed there are photographs of Edgar and Clyde engaged in particular activities. Nothing untoward, of course: going to dinner, attending nightclubs or parties (sometimes meeting a celebrity or two), or just going about and doing their jobs.

And some photographs are of Edgar and Clyde taking vacations together. There was nothing clandestine about these getaways and they didn't mind having their pictures taken and having them published in the newspapers. After all, as the #1 and #2 men at the FBI, Edgar and Clyde were entitled to some relaxation.

Among their verifiable and documented relaxations while on holiday (as the British say) was a day at the races. And like most racetrack visitors, Edgar and Clyde enjoyed laying down a bet.

Of course, during their lifetimes off-track betting - or OTB to the cognoscenti - was only permitted in New York and then at properly licensed sports offices. So we read that Edgar and Clyde, as men of law, made sure that when they placed their bets they did so at the tracks where it was legal. Their favorite bet, we read, was the $2 minimum.

Obviously such stakes were scarcely designed to make Edgar and Clyde wealthy. But exactly how much could they hope to make? We've always wanted to know that.

Captain Mephisto
We understand.

No doubt you have, as Captain Mephisto said to Sidney Brand. But to understand what the races would pay off, you must first know about the Paris mutuel betting system or as it's usually written, parimutuel betting.

Parimutuel betting was first introduced in 1865 in Paris by Pierre Oller.¹ It was adopted by the Jockey Club for the first Kentucky Derby in 1875 on the instructions of Colonel Lewis Clark (you know in Kentucky he had to be "Colonel" Lewis Clark). Parimutuel betting had the effect of driving the bookies away from the track but was also to make sure that the track got a profit.

x

Footnote

A popular informational website states that it was Joseph Oller, the co-founder of the Moulin Rouge cabaret, that invented the parimutuel system. But all other sources say it was Pierre.

Close Footnote

But why, you ask, couldn't the tracks simply pay off at the odds calculated by knowledgeable handicappers? Well, the disadvantage of simply setting odds will be clear if we run through a simple example of horse betting. And all that's needed before you can say "I understand" (as did Sidney) is a bit of grade school math.

Suppose there's a race with five horses and each horse is just as likely to win as any other. That means you have odds that look like:

Horse	Odds
Dobbin	4/1
Black Beauty	4/1
Gunpowder	4/1
Trigger	4/1
Buttermilk	4/1

The odds shown here are known as fractional odds and are sometimes called British odds. They can also be written as 4-1 or 4:1 but are always read as "four to one".

The first number (call it the numerator) is the amount of the Winnings you receive if you bet the amount on the right (the denominator). That is, if you bet on any of these horses and it wins, you will win $4 for every $1 bet. But since $2 is the lowest bet allowed, your minimum Winnings will be $8.

But when you do win, you get both the Winnings and your original $2 bet back. So the Payout from the track is:

Total Payout ($) = Total Winnings Paid + Total Bets Wagered

... and the Payout to a bettor who wagers $2 on the winner is:

Total Payout ($2 Bet #@ 4/1 Odds)	=	Total Winnings Paid + Total Bets Wagered
	=	$8 + $2
	=	$10

One nice thing about fractional odds is that as long as they are accurate, you can easily calculate the probability that any horse will win. If you have fractional odds of W/B (here we abbreviate W is the Winnings and B is the bet), the probability the horse will win is:

Probability (W/B)

=

B W + B

So for fractional odds of 4/1, the probability would be:

Probability (W/B)	=	B W + B
	=	1 4 + 1
	=	1 5
	=	0.20

So the probability that any horse will win is 0.20 or as it's often put, 20%.

We see then that if a horse has 4/1 odds, that means that on the average if you run five races the horse is expected to win one race. So if you have 4/1 odds, the probability of winning is 1 out of 5.

Using probabilities can sometimes simplify the calculations. For instance, you can calculate the total Payout by simple division:

Payout ($)	=	Bet ($) Probability
	=	$2 0.2
	=	$10

Even so, such math may seem unnecessarily complex. After all, the first number of the 4/1 odds is the Winnings for each dollar. So you already know your Payout is $5 without any division by the probability. Why bother with all the multiplying and dividing?

The reason you need the math is that odds aren't always given based on a $1 bet. You'll see odds like 7/2, 11/10, and you could have weirdo odds like 35/11. Fortunately, putting any odds on a $1 basis is simple. You just divide the two numbers by the denominator. So:

35/11 Odds	=	(35 ÷ 11)/(11 ÷ 11)
	=	3.182/1 Odds

So for 35/11 odds the Winnings are $3.182 for each $1 bet.

But the formulas still work whether you use 35/11 or 3.182/1. So if you have 35/11 odds, the total Payout per $1 is:

Payout Per Each $1 Bet	=	W + B B
	=	35 + 11 11
	=	46 11
	=	$4.182

The Winnings per $1 are just:

Winnings per $1	=	Payout per $1 - $1
	=	$4.182 - $1
	=	$3.182

... as we saw before.

And the probability is still calculated by:

Probability (W/B)	=	B W + B
	=	11 35 + 11
	=	11 46
	=	0.239

... or 23.9%. You get the same number if you use the 3.182/1 odds.

Probability (W/B)	=	B W + B
	=	1 3.182 + 1
	=	1 4.182
	=	0.239
	=	23.9%

Knowing how to convert the posted odds to Payout per $1 makes it easy to calculate your total Payout no matter what you bet. Say you bet $14 instead of $2. If our Payout per Dollar is $5 (that is 4/1 odds) then the Total Payout is:

Total Payout	=	Payout per Dollar Bet × Total Bet
	=	$5 per $1 Bet × $14 Bet
	=	$70

Which is the same as dividing the bet by the probability.

Total Payout ($)	=	Total Bet Probability
	=	14 0.20
	=	$70

[Note: In the olden days, the race tracks would generally round down to the nearest nickel or dime. This is called breaking. Suppose the odds were 12/7 for a horse to Win and you bet $12. Using the formulas, you would calculate your Payout as $32.57. At a track where Payouts broke to a nickel, you would get paid $32.55 and if the track broke to a dime you'd get $32.50. Naturally, the extra 2¢ or 7¢ would be kept by the track. Because the breakage (as it's called) was in effect keeping money that should be paid to the winners, the practice has never been popular with the bettors. Today, though, with electronic payments many tracks no longer use breakage or rather the breakage is now to the nearest penny.]

It is also possible you might see odds like 2/3. That is, the Winnings are less than the bet. Again this simply means you win $2 for a $3 bet or $0.66 for $1 which gives a Payout of $1.66 per $1 or $3.33 for a $2 bet. If you see the odds are 1/1 this is called an even money bet and you'd win $1 for each $1 bet or a $4 Payout for a $2 bet.

Odds where the Winnings are more than the bet is generally the rule in horse racing because there are so many horses in each race. However, what can be called inverted odds are sometimes seen when a particularly good horse is in the field.

For instance when Secretariat was racing in Saratoga in August 1973 he had already won the Triple Crown by finishing up at the Belmont Stakes by 31 lengths. So the odds were 1/10. Therefore the Winnings would be only 10¢ per each $1 bet or a total Payout of $2.20 for a $2 bet.

However, in this case Onion, the horse ridden by jockey Jacinto Vasquez, won the race by a length. Onion's odds were 5/1 and so his bettors made a nice profit. The longest odds ever posted for a winner in the Kentucky Derby were in 1913 when Donerail had odds of 91/1. So a $2 bet would give you a $184 Payout.

Although calculating the Payout and Winnings from the odds is easy, actually calculating the odds - that is, the true odds - that a horse will win is tough. Ultimately the odds are based on the past performance of each horse and whether the horse is "in form", but also who the jockey is, which track the race is at, and things like weather and track conditions. These opening odds are determined by expert handicappers who, you may not be surprised to hear, don't always agree.

At best the opening odds can only be an approximation of the true odds. But regardless of the odds - whether true or opening - the parimutuel system makes the final odds - or at least the Payouts - easy to calculate.

OK. What if we don't use parimutuel betting but just pay out based on the initial odds? This is called fixed odds betting and is sometimes used.

For simplicity we'll assume the attendance is pretty rotten and only five people show up at the track. And we'll have each person bet on a different horse and play the minimum $2.

And we also assume the handicappers have determined each horse has an equal chance of winning. With five horses the probability is 0.20 and the odds are 4/1 to win. The situation before the race is summarized as:

Horse	Odds	Probability	Bets
Dobbin	4/1	0.2	$2
Black Beauty	4/1	0.2	$2
Gunpowder	4/1	0.2	$2
Trigger	4/1	0.2	$2
Buttermilk	4/1	0.2	$2

So a total of $10 has been bet on the race. The track has to use this $10 Handle to pay off the winners.

However, only one horse will win.² Let's say the winner was Gunpowder. With a $2 bet at 4/1 odds, the Payout is:

x

Footnote

Of course, a race can end in a tie - a "dead heat" - where two horses cross the finish line together. But with cameras recording the finish, dead heats are rare and in most races there is only one winner.

Close Footnote

The track has taken in $10 from the tickets and has to pay $10 to the winner who bet on Gunpowder. So the track's profit is a whopping.

... which we can summarize as:

Hm. Something seems amiss. The track has to make money or it can't stay in business. So what to do?

Before the parimutuel system, the way out was for the track to not pay quite what it should. That is, the posted odds are deliberately not the true odds. If the handicappers figured the true odds on a horse were 4/1, the track would not post those odds. Instead they would give the odds as something like 7/2 which would give a "probability" (note quotes) of 0.22 or 22%.

If all five horses get equal "action" (as the bookies call it), at 7/2 odds a $2 bet could only win $7, not $8. But the losers would still fork over their $2 apiece. So the track's total Payout would be:

... and the track's profit is:

And the situation becomes:

So the track makes money.

At this point, it's useful to add up the probabilities. As anyone who has studied probability theory knows, probabilities should add up to 1. And when we had the 4/1 odds for each of five horses - or 0.2 probability - that was the case.

But at 7/2 odds, which is 0.22 probability, we have:

This extra 0.1 probability represents the profit the track will make by shorting the winner. At the true odds of 4/1 they should make a $10 Payout for a $2 bet. But by using 7/2 odds, they only pay off $9. Taking in more than they pay, the track makes $1 for a $10 handle which is 10% profit.

This extra profit by using odds tilted in the track's favor is called the house percentage, the house advantage, the rake, the juice, the cagnotte, or the vigorish ("vig" for short, a great Scrabble word). All commercial gambling has the vigorish built in to its Payouts. Of course, the casino and race track owners point out this is both fair and reasonable. They have expenses they need to pay to keep in business. But the vigorish also means that in the long run the gamblers will lose.

OK. But at least now we can sit back and smile with satisfaction. With the advantage, the juice, the rake, and the vig, the track will make a profit. So there is no problem in keeping the track open and running.

Someone Else

But hold on there, pilgrim, as someone else said. Suppose we have two people who bet on Gunpowder and none on Buttermilk. So with our 10% vig, the winners would have to be paid off at the 7/2 odds. That's $7 Winnings for a $2 bet and a total Payout of $9 for each bettor.

But remember! There are now two bettors. Each wins $9 and so that's a total of $18 that the track has to fork over.

But the total amount paid out has to be taken from the bets - the Handle - and here it's only $10! So we have the most lamentable situation as shown below:

Ha? (To quote Shakespeare). So the track would actually lose money? Even with the vigorish?

Yep. Even with a 10% house advantage, there are situations where the track would lose. This sad scenario is well known to casino and track owners and is why these establishments sometimes go out of business.³

Clearly the racetrack is still in a precarious position. If the bets are spread out and it offers less than the true odds, it could turn a profit. But if the betting is lopsided or a longshot wins, the track could still loose their shirts.

So wouldn't it be nice (to quote Brian Wilson) if there was a way for the track to always turn a profit? Certainly we've always wanted to know that.

Here comes parimutuel betting. Let's try this. The track takes its profit - the vigorish - after the bets are laid down but before the race is run. We'll take a modest vig of 15% which is fairly typical for a racetrack:

So we'll be content with a buck and a half.

What's left over, the Prize Money, is called the Parimutuel Win Pool or just the Win Pool. This Win Pool is what will be divvied up among the winners.

Of course, the bettors still want to see the odds. But instead of odds based on the actual probabilities that the horse will win, the - quote - "odds" - unquote - are calculated simply from the Payout. So you have to convert the Win Pool to look like odds and probabilities.

For a simple example, we'll again have the five bettors each bet $2 on a separate horse. With the 15% vigorish deducted from the handle, we have $8.50 left over to pay to the winner.

This, though, is the total Payout with the original bet included. So the parimutuel Winnings are calculated as:

Then from the formula relating the Winnings and the bets to the odds, we can write the parimutuel odds as:

So with these odds, the bettors know the track will pay out $6.50 to the winner plus the original $2 bet.

There is also a parimutuel probability calculated as:

Of course, we can put the new 6.50/2 "odds" in terms of each $1 bet and get:

So we have:

Parimutuel "Odds":      3.25/1

... and summarize the original race with each person betting on a separate horse but using parimutuel payoffs:

And not surprisingly, we see the track gets its $1.50 profit - some prefer the word "commission" - we took out of the handle before the race.

Because the parimutuel odds and probabilities are based only on the amount bet on the specific horses, they may have absolutely nothing to do with the true odds. Therefore parimutuel odds and probabilities are sometimes referred to as the implied odds and the implied probabilities.

At this point we can now look at the second scenario using parimutuel odds. That is, we have two people bet on Gunpowder and none on Buttermilk. Remember using the true odds - and even the odds with added vigorish - the track lost its shirt.

First of all, as long as only one person bets on a horse, the Payout would be as before. The Win Pool is still $8.50 ($10 minus the $1.50 vigorish). The Winnings are still $3.25 per every $1 bet or $6.50 for each $2 bet. So the odds on Dobbin, Black Beauty, and Trigger are still 3.25 to 1.

And remember we say no one bets on Buttermilk. So there is no defined odds and no Payout. So we now have:

But Gunpowder?

With two people betting on Gunpowder, they both have to share the Win Pool and get their bets back. So if Gunpowder wins, we have:

Now this Payout includes their original bet. That's $2. So the Winnings are now:

But since this $2.25 is for a $2 bet, to calculate the Winnings per $1, you divide by $2:

But remember the Winnings per $1 Bet also give us the odds - the implied odds - which are are:

... and the race is summarized as:

... and, hey presto!, the track gets its 15% no matter what. But because the winners have to share the Win Pool, the more people who bet on a horse the less they get paid.

Honesty compels the admission that the derivation just given is a bit more laborious than needed but was made so to emphasize the effects of multiple bettors on the same horse. Of course in the real world you can have hundreds or thousands of bettors on each horse and they can bet different amounts. Fortunately, the calculations of the parimutuel odds and payout is actually quite simple.

All you have to do is divide the total payout on a particular horse by the total bets and so convert to payout per every dollar bet. In our example given above then:

Since this is the total Payout, to get the Winnings per each $1 dollar bet you just subtract 1.

... and so the parimutuel odds are:

... exactly as the longer derivation.

This formula works for any number of bets and any amount of money. For instance, suppose that there are 12750 attendees - not unusual for a large track - and on a particular race they bet a total of $152,082 dollars for the various horses to Win. So the 15% vigorish is:

... and the Win Pool is therefore:

So if $25,804 is bet on Gunpowder and Gunpowder wins, the Payout per $1 is:

And the Winnings per $1 for Gunpowder are:

And the posted parimutel odds on Gunpowder would have been:

So just multiply the amount you bet on Gunpowder by 4 and you'll get your Winnings.

Remember that the parimutuel - quote - "odds" - unquote - are based only on the amount bet. They may have nothing to do with the true odds or the opening odds. Failing to understand this important point can cause quite a surprise to the uninitiated bettor.

Now there is a book about a British Secret Service agent who sometimes drinks four double bourbons, two double vodka martinis, and a pint of pink champagne in one evening who is trying to trace down a smuggling ring. You'll remember as part of his undercover work James smuggles in some diamonds to New York. There he gives them to a gangster named "Shady" Tree who is supposed to handover $5000 to James for smuggling in the diamonds.⁴

James

Shady, though, says they pay indirectly. This is to provide James with an alibi for suddenly being flush with cash. Shady gives James $1000 which is an amount that he can claim he won in a card game. Then he goes to Saratoga, New York, with its famous race track. There he bets his $1000 to win on a horse named Shy Smile whose odds will be at least 4:1.

But the horse is actually a ringer named Pickapepper who the gangsters have substituted for the real Shy Smile. Pickapepper is so fast that there's no doubt he'll win. So James will earn at least his $5,000. Naturally the gangsters will also bet heavily on the race and acquire much ill gotten gains.

So James goes up to Saratoga but the jockey - a less than savory character named Tingaling Bell - has been bribed to throw the race by Felix Leiter who is James's old friend from the CIA. Shy Smile will still win, but Tingaling agreed to commit an infraction by crowding out the favorite - either Come Again or Pray Action or whichever horse is coming in second. So Tingaling will be disqualified but can tell his bosses the loss wasn't his fault. Felix agreed to pay Tingaling $3000 for his perfidy.

James gets to the track and waits for the race to begin. Shy Smile - that is Pickapepper - was No. 10 and had initial odds of 15/1. But then the gangsters start betting and so the parimutuel odds change. As the story tells it:

Bond went on watching the board. In a minute the big money would go on (all except the remains of Bond's $1000 which would stay in his pocket) and the price would come down with a run. The loudspeaker was announcing the race. Away to the left the horses were being marshalled [British sic] behind the starting-gate. Ping, ping, ping, the lights opposite No. 10 on the board started to wink and flash - 15, 14, 12, 11, and finally 9 to 1. Then the lights stopped talking and the tote was closed.

So with parimutuel betting, the odds are updated as soon as the bets are laid. This way once the betting is closed, everyone knows how much they stand to make.

But if you're not familiar with the parimutuel system, imagine your surprise if you inherit $35,000 from a rich uncle and get a tip that Gunpowder - originally a long shot - is really likely to win. Figuring to increase your assets, you hie off to the track and see the opening odds are:

Following Shady's advice you wait to lay down your money before the betting closes. You stand around waiting for everyone else to make their bets and see on the toteboard that all the other bets have shifted the odds to be:

... which isn't all that far from the opening odds.

So it looks like if Gunpowder wins - remember you've gotten a tip that he will - you'll win $980,000. So with your $35,000 bet returned, you'll have $1,015,000 - over a million - in your pocket.

So just before the windows close, you go and lay down your bet. Then you happily go back to the stands and look at the toteboard. There you loudly express surprise when you see the odds are now:

But since we know the Payout is just the Win Pool, it's a bit more informative if you look at the Winnings:

Horse	Opening Odds	Opening Probability	Total Bets	Potential Winnings
Dobbin	13.35/1	0.07	$2452	$32749.04
Black Beauty	23.44/1	0.04	$1440	$33761.04
Gunpowder	0.00003/1	0.99997	$35200	$1.04
Trigger	41.9/1	0.023	$35200	34381.04
Buttermilk	16.65/1	0.057	$1994	$33207.04
			Total: $41906 (Handle) $35201.04 (Win Pool with 15% Vigorish)

Indeed. (Again quoting Shakespeare). If you go by the math, you'll find the total per dollar Payout is:

So with your $35,000 you glean a Payout of:

And your Winnings are:

... and you make a whopping $1.03.

And the other bettors on Gunpowder? Since their total bets were $200, their Payout is:

... which we'll generously round up to $200.01.

So their total Winnings are:

So the other bettors on Gunpowder have 1¢ to divide amongst themselves.

Clearly there's little reason to bet such a huge amount on a horse race. After all if you put up most of the bet handle, then the Win Pool would be mostly just your own dough. So all you're doing is getting your money returned and you royally goober up the Payout to the other bettors.

This example, though, is somewhat simplified as many state laws require a winner to be paid at least a dime for a $2 bet. In that case, if someone bet $35,000 the track would have to pay out Winnings of at least $1750. After paying the other bettors as well, the track's vig would be only about 4%.

Of course, the Win bet isn't the only way to lay down your money. In addition, to the Win, there are Place and Show bets. If you bet Place, you win if the horse comes in 1st or 2nd. If you bet Show, you win if the horse comes in 1st, 2nd, or 3rd. Each of these bets has its own pool and the Payouts are calculated after the track takes out its vigorish.

It may seem that the best bet - the one most likely to pay out - is to bet the favorite to Show. Surely the horse most likely to win will come in 1st, 2nd, or 3rd. And in fact, a lot of people - including James - like this type of bet.

The trouble, of course, is there are times the favorite comes in fourth and even if it does Show, the money has to be divided with all the bettors who bet on the other horses who Showed. For instance, suppose in a race Gunpowder came 1st, Trigger was 2nd, and Buttermilk was 3rd. So if you bet Gunpowder to Show, you win your bet, yes. But everyone who bet on Trigger and Buttermilk to Show also wins their bets and you all have to share the Show Pool.

OK. Since there are five spots for Gunpowder to finish the race, he will Show only if he comes in at one of the first three spots. So if all our horses are of equal ability, the probability for Gunpowder - or any other horse - to Show is simply calculated by:

... or 60%.⁵

With a little more grade school arithmetic and our formulas, we easily calculate that a probability of 60% means the odds are 2/3 and we can fill in the table:

Remember that these are the opening odds. It will be left as an exercise for the reader to prove that with these odds and if the final results are as shown, then anyone who bet on Gunpowder, Trigger, or Buttermilk to Show has Winnings of $1.33 and the track makes no - that's NO! KEINS! NICHTS! - profit.

OK. But what about if we go by the parimutuel odds for Show?

Well, since Gunpowder came in first, Show is a paying bet. But anyone who bet on Trigger or Buttermilk to Show also gets paid. So the Show Pool has to be shared with them.

But two of the betters also bet for Dobbin and Black Beauty to Show. They loose their money and this gives the track a total Show Handle of $10.

As before to calculate the parimutuel odds for the Show, the track takes the total Show bets and removes their 15%. As we saw above, taking 15% from $10 leaves the Show Pool with $8.50.

But three horses Show. So to calculate the odds and probabilities, we divide the $8.50 Pool by 3.

Since this is for a $2 bet, the Winnings per Horse is:

And the Winnings per $1 per horse are:

Using the formulas for calculating the odds and probabilities from the Payouts, we get the table:

Once the race is run, the table then becomes:

So with breakage to a penny, the Show bet gives the track an extra penny.

And as you may guess, this derivation just given was more laborious than needed in order to emphasize the point that the Show Payout is shared over three horses. But again all you need to do is calculate the Payout for Show per $1 Bet.

... and the Winnings to Show per $1 bet:

With the resultant odds being:

But to cover a final scenario, suppose that the only Show bets are on Gunpowder, Trigger, and Buttermilk. No one bets on Dobbin and Black Beauty to Show.

Well, the parimutuel table once the bets are down is:

The race finishes with Gunpowder #1, Trigger #2, Buttermilk #3, Dobbin #4, and Black Beauty #5. As the total Payout is equal to the Show Pool and it's divided amongst the three horses, each of our bettors receives a Payout of:

... and the table summary is:

So everything balances out, yes?

Uh, no.

The discerning reader may remember that the Payouts include the original $2 bet, and the Winnings are the difference between the Payout and the original bet. So the Winnings for each bettor are:

Payout per Bettor (Show)	=	$1.70 - $2
	=	-$0.30

Yes, the - quote - "Winnings" - unquote - for each Show horse is 30¢ in the hole.

And a -$0.30 Payout gives us the following odds and probabilities:

... and is seems the bettors owe the track money.

[Note: The proof that these numbers can again be calculated simply based on Payout per $1 Bet will be left as an exercise to the reader.]

But here's the rub (to misquote Will). We mentioned that most of the states that permit horse betting have the rule that horse races must pay out a minimum of 10¢ for a $2 bet, regardless of the betting pool. So if we go by that rule, we have a new table:

... and it's the track that loses money.

Now all this may seem to be ridiculous number fiddling. But the examples do show - no pun intended - that the parimutuel system does not - that's NOT! NOT! NOT! - guarantee a profit for the track.

The resolution for this rather unsatisfactory situation - which sometimes does happen in the real racing world - is that any betting pool with a negative Payout is simply canceled for that race and the bets are refunded. This situation occurs more often in the Show Pool but it sometimes will happen for the Place bets. Naturally such occurrences are not popular with the bettors who will grump that the track is happy to let the bettors lose money, but don't accept such a risk for themselves.

Of course, there are a lot of other bets than Win, Place, and Show. You have Across the Board where you bet on a horse to Win, Place, and Show. Then if the horse comes in first you collect the money from all three bets: Win, Place, and Show. If it comes in second, you only collect the Place and Show Winnings but loose your Win bet. Then if the horse comes in third, you only can collect the Show Winnings and loose your Win and Place bets. The Across the Board bet is actually three bets and if you bet $2 on Across the Board, you have to fork over $6.

Some bettors think Across the Board doesn't make much sense because you can easily loose money and the payback is relatively modest. For instance, in our example if you bet Gunpowder Across the Board and he came in third, you would have paid out $6, but only win $0.83 plus your $2 bet back. So you would have lost $3.17.

More popular bets are the Daily Double, Pick 3, Pick 4, Pick 5, Pick 6, Double, Treble, Accumulator, Trixie, Lucky 15, Lucky 31, Lucky 63, Forecast, Tricast, Exacta, Quinella, Trifecta, and the Superfecta. These are pretty long shot bets. For instance the Superfecta for a race means you have to pick the first, second, third, and fourth horses in the correct order to win.

The Daily Double is a bet on predicting the winners of two specified consecutive races. The Pick races are similar to the Daily Double but you pick the horses that will win the designated number of consecutive races. For instance, Pick 3 means you have to correctly select the horses that win a set of 3 consecutive races. Pick 5 means you have to select the horses that win 5 consecutive races.

The longest shot is the Pick 6 but it's also one of the most popular bets. The odds are usually so long that if there is no winner, some tracks let the Pick 6 bettors who correctly picked 5 consecutive winners split 30% of the Pick 6 Pool. The rest of the Pool carries over to the next day's race. This continues until someone picks all six winners.

As to why people like these bets is that there is the potential to win a large amount with a small bet. The Daily Double can have payoffs of $100 to $500 to $1. An average Payout of a Trifecta is about $7000 for a $2 bet but there have been cases where the Payout was over $100,000. Some tracks allow bets lower than $2 for these exotic wagers. One Trifecta winner won over $4000 in Payout for a 20¢ bet and a Pick 6 winner once received nearly $190,000 for a 50¢ wager.

Well, at least we now know much would Edgar and Clyde would make with their $2 bets.

Edgar
Senior Citizen

Maybe a lot. Maybe not much.

Most books about Edgar mention how he and Clyde liked the races. Some of the historians like to point the irony that the #1 and #2 men in the FBI enjoyed visiting establishments that were at that time a source of considerable revenue for well, let's just say some of America's (alleged) less than savory citizens. Some writers like to connect Edgar's horse betting with the fact that he himself long denied there was such thing as "The Mafia". But when the Mafia meeting in the town of Appalachin, New York, was raided in 1957 by the state highway patrol, it was hard to deny that the mob bosses did get together to talk business. However as late as the 1970's Edgar's friend, the magician, gambling consultant, and author John Scarne referred to the "non-existent Mafia".

It is possible that Edgar may have really believed that there was no Mafia per se. The (alleged) gangsters themselves, though, said that Edgar's ignorance of their organization let them indulge in mischievous pleasures at his expense. Whenever Edgar was visiting one of the tracks run by some (alleged) mobsters, they liked to come up and introduce themselves as fellow horse fans and admirers of the nation's Top G-man. They would join Edgar in the stands and have their pictures taken with him. But then someone tipped Edgar off who his new fans and racing aficionados really were, he ordered a raid on a number of gambling joints in the area. Edgar, it seems, could always get the last laugh.

Nevertheless, there were stories that Edgar would ask these - ah - "knowledgeable gentlemen" - for advice. That they passed on racing information was denied by the men themselves. A protégé to gambling czar Meyer Lansky named Phil "The Stick" Kovolick was asked if he ever gave Edgar information. Phil replied rather ungrammatically "[!] no, I didn't give him nothing. Wouldn't give him the sweat off my [!]".

The official FBI press releases readily admitted that Edgar played the horses but only at the $2 minimum and at the track. Others - unofficial but supposedly knowledgeable sources - claim Edgar upped that amount by a factor of 100. But since a $200 bet might look conspicuous, Edgar would have others place the bets for him. Clyde we learn would would often advise him against the riskier wagers.

The reliability of the sources of the various stories remains a largely unresolved question. Sometimes they do seem pretty good. Once one of the assistant attorney generals who was friendly to Edgar said Edgar didn't limit his bets to the track and remembered Edgar used to tell a story on himself. He liked to visit a fancy off-track racing office where you could have drinks and dinner while laying down your bets. Suddenly in burst the local police in a raid. Edgar laughed when he remembered how fast the officers cleared out once they saw who was the favored customer.

So it seems that Edgar did have a sense of humor. And surely he wouldn't have objected to gentle tweakings of the monologists.

A family was on vacation in the Rocky Mountains and set up camp right at the border of California and Nevada. They got out their sleeping bags and one of the children though it would be fun to have his bag so he could put his head in California and his feet in Nevada.

The next morning the FBI showed up. The parents asked what the problem was. The agents replied the were investigating a kid napping across state lines.

J. Edgar Hoover was a great pet lover. One day in addition to his dogs he decided to buy some sheep. He bought a family with the male, female, and baby sheep.

When his friend came over they only saw the ram and the lambs. Naturally they asked where the female sheep was.

Edgar told them she was on a farm near Las Vegas. His friends asked him why she was there. Edgar told them that was the best place possible.

After all, Edgar said, everyone knows that Nevada was the only place to go to see Hoover's dam.

And of course there's:

J. Edgar Hoover was sitting in his office when he got a phone call. It was the chief security officer from an art museum. Someone, he said, had come in and defaced an ancient Babylonian sculpture.

"Can you describe the sculpture in more detail and exactly what the perpetrators did?" Edgar asked.

"Certainly" the officer said. "The sculpture is of a lion in the style from the reign of King Nebuchadnezzar II from around 600 BC. It is carved in black basalt. Evidently two people came in and played a game of tic-tac-toe on it.

"Well, sir" Edgar said. "I'm afraid the Federal Bureau of Investigation does not have the jurisdiction in this case. For one thing we normally would only be able to arrest the player who was making the 'X' marks. And in this case we can't even arrest him because the statue is made of basalt."

"What?" the officer exclaimed. "You could only arrest the player making the 'X' marks and you can't even do that because the statue is made of basalt?"

"I'm afraid so," Edgar replied. "The FBI can investigate the case only if it involves crossing slate lions."

Geddit?

Crossing slate lions?

Crossing state lines?

Geddit?

NyeahahaHAHAH
!!!!!!!!!!!

References and Further Reading

J. Edgar Hoover, Kevin Cunningham, Compass Point Books, 2006.

J. Edgar Hoover, Harry Messick, David McKay Company, 1972.

Scarne's Complete Guide to Gambling, John Scarne, Simon and Schuster, 1961.

Diamonds Are Forever, Ian Fleming, Jonathan Cape, 1959.

Goldfinger, Ian Fleming, Jonathan Cape, 1956.

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