In my previous post I explained the basic math behind calculating the payouts for Win wagers; which, in turn, is the same basic formula for calculating payouts for any other single winner result at the track. So if you know how to figure out how much the Number 7 horse will pay to Win in Race 5 at Emerald Downs, you can use those same steps to calculate, for example, how much the 7-1 Exacta or the 7-3 Double will pay.
In this post, I will try to explain how payouts are calculated for multi-winner results; specifically, Place (which, typically, will have two "winners") and Show (which, typically, will have three "winners"; exceptions coming when there is a tie for one of the top spots, officially referred to as a Dead Heat). We'll begin by making sure that we all understand what each wager represents.
When you bet a horse to Place, your horse must finish either first or second in order for you to collect.
When you bet a horse to Show, your horse much finish either first, or second, or third in order for you to collect.
As with all other wagers, Place and Show bets form their own pools; meaning that payouts are determined solely by the amount bet into those specific pools. So, for example, the amount bet on the Number 7 horse to Win is totally irrelevant to how much the Number 7 horse will pay for Place; which, in turn, is totally irrelevant to how much the Number 7 horse will pay for Show.
OK; let's work out a few examples. Suppose Happy Day and It Figures finish one-two in Race 5 at Laurel Park. $25,000 was bet into the Place Pool. What are the payouts?
First Step: Deduct the track take out
First things first; just as with all the other wagers, the race track makes sure that it gets its cut of the money. Let’s again pretend that FDR is still President of the United States, and the track takeout is a mere ten percent. So we’ll deduct ten percent out of our Gross Place Pool of $25k, giving us a Net Place Pool of $22,500.
Next Step: Determine how much was wagered on the two Place horses
A review of the tote board shows that $6,500 was bet on Happy Day to Place, while It Figures was backed by $12,750 in the Place Pool.
Net Step: Determine the profit amount to be divided among the winning bettors
Simple enough; we just subtract the amount wagered on Happy Day and It Figures from our Net Place Pool. So $22,500 minus $19,250 ($6,500 plus $12,750) gives us $3,250, which is the amount of profit to be split up among the winners.
Net Step: Divide the total profit amount into two prize funds
This is a step we don't have in the single winner pools. Since there are two Place horses, the profits get divided in half. $3,250 split down the middle gives us $1,625. So $1,625 will be divided among those who made a Place bet on Happy Day, while $1,625 will be divided among those who made a Place bet on It Figures.
Next Step: Divide each prize fund equally among all winning tickets for each horse
For Happy Day, this means $1,625 gets divided by $6,500, giving us $0.25. The $1,625 prize fund for It Figures gets divided by $12,750, giving us $0.13.
Next Step: Remove breakage
Time for the track to double-dip, which it does by rounding both of those amounts down to the nearest dime (though it should be mentioned that New York, for one, does give the bettors a break in the breakage by only rounding down to the nearest nickel). So Happy Day bettors see their profits shrink from $0.25 to $0.20, while It Figures goes from $0.13 to $0.10.
Final Step: Double each amount and add two dollars to determine payouts
Our calculations have computed the profits for each dollar wagered. Since race tracks, traditionally, display Win, Place, and Show wagers per every two dollars bet, we double the profit and add in the initial two dollar wager. That gives us Place payouts of:
Happy Day $2.40 (($0.20 x 2) + $2)
It Figures $2.20 (($0.10 x 2) + $2)
Alright, let's do another one. We'll use the same race, except this time It Figures runs third, getting nosed out at the wire by Unexpected. How does that change the payouts? Well, for starters, those who wagered on It Figures to Place are now losers, collecting nothing but an unpleasant memory. As for Happy Day and Unexpected:
First Step: Deduct the track take out
There's no change in this step; ten percent comes off the top of our Gross Place Pool of $25k, giving us a Net Place Pool of $22,500.
Next Step: Determine how much was wagered on the two Place horses
We still have the same $6,500 bet on Happy Day to Place, while Unexpected was backed by just $2,200 in the Place Pool.
Net Step: Determine the profit amount to be divided among the winning bettors
As before, we're subtracting the amount wagered on Happy Day and Unexpected from our Net Place Pool. So $22,500 minus $8,700 ($6,500 plus $2,200) gives us $13,800, which is the amount of profit to be split up among the winners.
Net Step: Divide the total profit amount into two prize funds
$13,800 divided by two gives us $6,900. So $6,900 will be divided among those who made a Place bet on Happy Day, while $6,900 will be divided among those who made a Place bet on Unexpected.
Next Step: Divide each prize fund equally among all winning tickets for each horse
Those who wagered on Happy Day now have $6,900 to split up among their $6,500 in tickets, which makes for $1.06 . Meanwhile, the $6,900 prize fund for Unexpected gets divided by $2,200, giving us $3.14.
Next Step: Remove breakage
It's good to be the house, as the track takes again, knocking the $1.06 for Happy Day down to an even dollar, while the $3.14 for Unexpected shrinks down to $3.10.
Final Step: Double each amount and add two dollars to determine payouts
As before, our calculations have computed the profits for each dollar wagered. Doubling the profit and adding in the initial two dollar wager gives us Place payouts of:
Happy Day $4.00 (($1.00 x 2) + $2)
Unexpected $8.20 (($3.10 x 2) + $2)
Notice the increase in payout for Happy Day just by virtue of It Figures not finishing in the other Top Two spot. Lesson to be learned: Place bets (and, as we'll see later, Show bets) are more desirable when you have a strong opinion that a well backed horse will not be getting a share of the pool.
Calculating Show payouts follow the same basic steps as above, except there's now three "winners" to be taken care of, instead of just two. So let's work out an example, using the same race as above, with Happy Day, Unexpected, and It Figures crossing the wire in that order. There's $20,000 in the Show pool; let's go!
First Step: Deduct the track take out
$20,000 reduced by ten percent leaves us $18,000.
Next Step: Determine how much was wagered on the three Show horses
Per the tote board, the amounts bet on each horse to Show:
Happy Day: $4,800
Unexpected: $1,400
It Figures: $10,000
Net Step: Determine the profit amount to be divided among the winning bettors
$18,000 minus $16,200 ($4,800 plus $1,400 plus $10,000) gives us $1,800, which is the amount of profit to be split up among the winners.
Net Step: Divide the total profit amount into three prize funds
Since there are three Show horses, the profits get divided three ways. $1,800 divided by three is $600.
Next Step: Divide each prize fund equally among all winning tickets for each horse
Happy Day: $600 / $4,800 = $0.125
Unexpected: $600 / $1,400 = $0.43
It Figures: $600 / $10,000 = $0.06
Next Step: Remove breakage
Happy Day drops to $0.10; Unexpected shrinks to $0.40; WAIT! What do we do about It Figures? If we round down to the nearest dime, the wager has no profit.
Well, for It Figures, the track can only round down to $0.05. This is because race tracks must pay out a minimum of five cents to the dollar for winning wagers, regardless of how much is in the pool (more on this momentarily).
Final Step: Double each amount and add two dollars to determine payouts
Happy Day $2.20 (($0.10 x 2) + $2)
Unexpected $2.80 (($0.40 x 2) + $2)
It Figures $2.10 (($0.05 x 2) + $2)
And there you go.
I mentioned a few lines ago that race tracks must pay out at least five percent (five cents on the dollar) for every winning wager. Sometimes so much is wagered on a specific horse in a pool (almost always the Show pool) that there isn't enough in the pool to cover all the winning tickets. This is a situation known as a minus pool, meaning that the track is going to lose money on the race, because it will have to dip into its reserves to pay all bettors the amounts that are due.
Let's work out an example of a minus Show pool. We'll use the same race as above, except this time It Figures really figures with the bettors, to the point where the big plungers have wagered heavily on It Figures to finish either first, second, or third. We'll tweak our pool so that, instead of having a Show pool of $20k with $10k of that wagered on It Figures, we now have a Show pool of $50k, with all of the additional $30k having been put down on It Figures.
First Step: Deduct the track take out
$50,000 reduced by ten percent leaves us $45,000.
Next Step: Determine how much was wagered on the three Show horses
Our adjusted tote board now shows the following amounts bet on each horse to Show:
Happy Day: $4,800
Unexpected: $1,400
It Figures: $40,000
Net Step: Determine the profit amount to be divided among the winning bettors
$45,000 minus $46,200 ($4,800 plus $1,400 plus $40,000) gives us, well, it doesn't give us anything. Actually, it gives us less than anything, as the result is a negative $1,200. But, profits or no profits, the track must pay the minimum of five percent, or $0.05 for every winning dollar wagered. So we can just skip the remaining steps and cut to the chase:
Final Step: Double each amount and add two dollars to determine payouts
Happy Day $2.10 (($0.05 x 2) + $2)
Unexpected $2.10 (($0.05 x 2) + $2)
It Figures $2.10 (($0.05 x 2) + $2)
Almost all the money was bet on It Figures; but because there were no profits in the pool left to distribute to backers of Happy Day and Unexpected, all three horses pay the same amount for Show, the $2.10 minimum.
Did it make sense to bet on Happy Day and/or Unexpected to Show when there's a minus pool? Well, when deciding upon your answer, keep in mind that in racing, as in real life, things that figure to happen don't always come to pass. Sometimes events that can't miss do, in fact, miss. Sometimes horses like It Figures finish out of the money; and then what? Well, for one thing, it causes those who wagered heavily on It Figures to rethink their life choices. As for the Show payouts:
First Step: Deduct the track take out
$50,000 reduced by ten percent still leaves us $45,000.
Next Step: Determine how much was wagered on the three Show horses
The amounts on Happy Day and Unexpected remain the same; but Nondescript replaces It Figures:
Happy Day: $4,800
Unexpected: $1,400
Nondescript: $800
Net Step: Determine the profit amount to be divided among the winning bettors
$45,000 minus $7,000 ($4,800 plus $1,400 plus $800) gives us $38,000, which is the amount of profit to be split up among the winners.
Net Step: Divide the total profit amount into three prize funds
$38,000 divided by three is $12,666.67.
Next Step: Divide each prize fund equally among all winning tickets for each horse
Happy Day: $12,666.67 / $4,800 = $2.64
Unexpected: $12,666.67/ $1,400 = $9.05
Nondescript: $12,666.67/ $800 = $15.83
Next Step: Remove breakage
Happy Day drops to $2.60; Unexpected shrinks to $9.00; Nondescript falls to $15.80.
Final Step: Double each amount and add two dollars to determine payouts
Happy Day $7.20 (($2.60 x 2) + $2)
Unexpected $20.00 (($9.00 x 2) + $2)
It Figures $33.60 (($15.80 x 2) + $2)
Real life examples of such occurrences include last Saturday's Hollywood Starlet Stakes, July's Victory Ride Stakes at Belmont Park, this 2010 Allowance Race at Calder, and 2009's Desert Stormer Handicap. There are many other examples, but these help illustrate how such Show payouts can happen, while reminding us all that there's no such thing as a sure thing.
The steps for calculating Place and Show payouts above work with any payout that involves multiple "winners". For example, if there's a Dead Heat for Win, then Win payouts and the resulting exotic payouts (because there are now two winning Exactas, Trifectas, etc.) are determined using the Place payout steps; the Show payout steps are used when three horses finish in a Dead Heat for Place; and so on.
So now you know all you need to know about how to calculate payouts at the track (well, almost all; we didn't cover consolation Doubles and Pick Threes; that will have to wait for another day). If you have any questions, or if you see (or think you see) an error in my work, please LET ME KNOW and leave a comment below.
Peace and Love,
Jimbo
Showing posts with label Payouts. Show all posts
Showing posts with label Payouts. Show all posts
Friday, December 14, 2012
Monday, December 10, 2012
Jumping Into the Pool - How Payouts Are Calculated
When I began this blog, I figured that I would primarily be communicating with my friends and buds, especially my fellow members of what is affectionately known as The Derby Crew; seasoned horse players all. But as I look at the various search terms that lead others here, I see that there are many that are relatively new to the game that are searching for some basic information as to how it all works. With that in mind, I thought it might be a good idea to have a post describing one the most basic aspects of the game: how payouts are calculated.
Let's start here: nearly all wagering on horse racing in North America (and many other parts of the world) is parimutuel - a nice French word that basically means that we're betting among ourselves, rather than against the house (as with, say, casino games like Blackjack). Parimutuel wagering means that the odds (and, therefore, the payouts) on any given wager on the menu is determined by the amount of money that has been bet on that occurrence. For example, the amount that a horse pays to win in any given race is determined by the amount of money bet on that particular horse to win compared to all the money bet on each of the other horses in the race to win. Likewise, a Pick Four payout is determined by the amount of money wagered on that specific Pick Four combination compared to the total amount wagered on all the other possible Pick Four combinations.
Basically, parimutuel wagering means that the more money that is wagered on a specific outcome, the less that outcome will pay, should it occur. A horse with a lot of money bet on it to win will pay much less than a horse with only a small amount of money wagered on it.
Since payouts are based upon the percentage of money bet on a specific occurrence (i.e., Horse A will win) versus the total amount bet on all occurrences, parimutuel odds are in a constant state of flux, from the moment wagering begins right up until the betting is officially closed. And since math takes time (even with computers) that's why you'll often see odds change while the race is being run. It doesn't mean that folks are still betting; but rather that the final calculations can't be made until the total amount in the pool is known, and that can't be known until betting has closed (an event that is simultaneous with the gates opening and the race beginning).
The next concept to understand is that all wager types (i.e., Win, Place, Show, Exacta, Pick Three, etc., etc.) all form their own totally independent pools. That means that the odds on Horse A to Win is totally meaningless to the odds that Horse A will Place; which, in turn, is totally meaningless to how much the Horse A and Horse B Exacta will pay.
OK; not totally meaningless. Humans being human, it stands to reason that if a large percentage of the money in the Win Pool is wagered on Horse A, then a large percentage of the money in, say, the Exacta Pool will be wagered on combinations that have Horse A on top. But the main point holds true: each pool is totally independent; no pool payout is used to determine the payout in any other pool. And, of course, humans don't always behave logically; so every once in a while you'll see something like what happened in Race 7 at Calder on August 18, when Daddys Jewel paid $3.80 to Place; the same amount that she paid to Win.
Let's see if working out some examples help make everything clear. Let's say that Race 3 at the no longer in existence Sportsman's Park is won by Some Colt. There was $100,000 bet into the Win Pool. How do we determine how much Some Colt paid to Win?
First Step: Deduct the track take out
The Take Out is the amount that the track keeps for itself out of each of the pools; this is the money that the racetrack uses to pay its bills, chief of which is the purse money that gets paid out to the victors in each event. Let’s pretend that FDR is still President of the United States, and the track takeout is a mere ten percent (here's a more recent accounting of current track take out rates at various racetracks throughout the U.S. While the chart is somewhat out of date, it will at least give you an idea of how much of the wagering money the racing facilities keep for themselves). So we’ll deduct ten percent out of our Gross Win Pool of $100k, giving us a Net Win Pool of $90,000.
Next Step: Determine how much was wagered on the Winner
A review of the tote board shows that $23,000 was bet on Some Colt to Win.
Net Step: Determine the profit amount to be divided among the winning bettors
Simple enough; we just subtract the amount wagered on Some Colt from our Net Win Pool. Removing $23k from $90k gives us $67k, which is the amount of profit to be split up among the winners.
Next Step: Divide the profits equally among all winning tickets
We've got $67k in profits to be split among $23k worth of winning tickets. Dividing $67,000 by $23,000 gives us $2.91.
Next Step: Remove breakage
Oh, you thought the track was done dipping its hand in the till, did you? No, not yet; now the track will round each winning share down to the nearest dime (some tracks, such as New York, will give the players a break and just round down to the nearest nickel). With that, the $2.91 profit becomes $2.90.
Next Step: Double the amount and add two dollars to determine payouts
Since it's traditional to state Win (and most other) payouts in terms of each $2 bet, we'll double our one dollar profit calculations, and then add in the original $2.00 wagered (since that gets returned to the winners; after all, their bets didn't lose). $2.90 doubled is $5.80; plus $2.00 gives us $7.80, which is what Some Colt pays to Win.
The steps for determining Win payouts are the same steps used for all other single-winner wagers; that is to say, every payout except Place (which has two "winning" wagers) and Show (which has three "winning" wagers) is determined the same way as above.
Let's work another example to demonstrate. Let's say the Race 3 Trifecta was Some Colt / Second Best / Third in the Bunch. If Race 3 had a total of ten horses entered, then the winning Trifecta was one out of 720 possible Trifecta combinations (10 x 9 x 8). An interesting piece of information, but meaningless to what we want to know: What did it pay?
We'll start our calculations by stating that $50,000 was bet into the Trifecta Pool
First Step: Deduct the track take out
For this example, let's use a more realistic 25% track take out. Removing twenty-five percent from the Gross Trifecta Pool of $50,000 gives us a Net Trifecta Pool of $37,500.
Next Step: Determine how much was wagered on the winning Trifecta combination
The Some Colt / Second Best / Third in the Bunch Trifecta combination (in that order; Trifecta bets with those horses in any other order are as much losers as those combinations containing other horses) had a grand total of $725 bet on it to come to pass.
Net Step: Determine the profit amount to be divided among the winning bettors
Deducting the $725 bet by the winners from the Net Trifecta Pool of $37,500 gives us $36,775 to be divided among the winners.
Next Step: Divide the profits equally among all winning tickets
$36,775 divided by $725 is $50.72.
Next Step: Remove breakage
Once again the race track double dips, in this case making the profit per dollar $50.70.
Next Step: Double the amount and add two dollars to determine payouts
That is, if we want to state the payout in terms of $2 bets. While traditional to do so for Win, Place, and Show wagers, it's quite common for exotic wagers, such as Trifectas, to be stated in terms of $1 bets. To be consistent, we'll state the $2 payout of $103.40 ($50.70 + $50.70 + $2.00), though giving the $1 payout of $51.70 ($50.70 + $1.00) is perfectly acceptable.
And there you go. As I mentioned above, calculating Pick Six, Pick Four, Pick Three, Daily Double, Exacta, Quinella, etc., etc., payouts follow these same basic steps. The exceptions are Place and Show wagers, which I'll cover in my next post sometime later this week.
If you have any questions, or if you see (or think you see) someplace where I messed up, or if everything above is clear as mud LET ME KNOW and post a comment below.
Peace and Love,
Jimbo
Let's start here: nearly all wagering on horse racing in North America (and many other parts of the world) is parimutuel - a nice French word that basically means that we're betting among ourselves, rather than against the house (as with, say, casino games like Blackjack). Parimutuel wagering means that the odds (and, therefore, the payouts) on any given wager on the menu is determined by the amount of money that has been bet on that occurrence. For example, the amount that a horse pays to win in any given race is determined by the amount of money bet on that particular horse to win compared to all the money bet on each of the other horses in the race to win. Likewise, a Pick Four payout is determined by the amount of money wagered on that specific Pick Four combination compared to the total amount wagered on all the other possible Pick Four combinations.
Basically, parimutuel wagering means that the more money that is wagered on a specific outcome, the less that outcome will pay, should it occur. A horse with a lot of money bet on it to win will pay much less than a horse with only a small amount of money wagered on it.
Since payouts are based upon the percentage of money bet on a specific occurrence (i.e., Horse A will win) versus the total amount bet on all occurrences, parimutuel odds are in a constant state of flux, from the moment wagering begins right up until the betting is officially closed. And since math takes time (even with computers) that's why you'll often see odds change while the race is being run. It doesn't mean that folks are still betting; but rather that the final calculations can't be made until the total amount in the pool is known, and that can't be known until betting has closed (an event that is simultaneous with the gates opening and the race beginning).
The next concept to understand is that all wager types (i.e., Win, Place, Show, Exacta, Pick Three, etc., etc.) all form their own totally independent pools. That means that the odds on Horse A to Win is totally meaningless to the odds that Horse A will Place; which, in turn, is totally meaningless to how much the Horse A and Horse B Exacta will pay.
OK; not totally meaningless. Humans being human, it stands to reason that if a large percentage of the money in the Win Pool is wagered on Horse A, then a large percentage of the money in, say, the Exacta Pool will be wagered on combinations that have Horse A on top. But the main point holds true: each pool is totally independent; no pool payout is used to determine the payout in any other pool. And, of course, humans don't always behave logically; so every once in a while you'll see something like what happened in Race 7 at Calder on August 18, when Daddys Jewel paid $3.80 to Place; the same amount that she paid to Win.
Let's see if working out some examples help make everything clear. Let's say that Race 3 at the no longer in existence Sportsman's Park is won by Some Colt. There was $100,000 bet into the Win Pool. How do we determine how much Some Colt paid to Win?
First Step: Deduct the track take out
The Take Out is the amount that the track keeps for itself out of each of the pools; this is the money that the racetrack uses to pay its bills, chief of which is the purse money that gets paid out to the victors in each event. Let’s pretend that FDR is still President of the United States, and the track takeout is a mere ten percent (here's a more recent accounting of current track take out rates at various racetracks throughout the U.S. While the chart is somewhat out of date, it will at least give you an idea of how much of the wagering money the racing facilities keep for themselves). So we’ll deduct ten percent out of our Gross Win Pool of $100k, giving us a Net Win Pool of $90,000.
Next Step: Determine how much was wagered on the Winner
A review of the tote board shows that $23,000 was bet on Some Colt to Win.
Net Step: Determine the profit amount to be divided among the winning bettors
Simple enough; we just subtract the amount wagered on Some Colt from our Net Win Pool. Removing $23k from $90k gives us $67k, which is the amount of profit to be split up among the winners.
Next Step: Divide the profits equally among all winning tickets
We've got $67k in profits to be split among $23k worth of winning tickets. Dividing $67,000 by $23,000 gives us $2.91.
Next Step: Remove breakage
Oh, you thought the track was done dipping its hand in the till, did you? No, not yet; now the track will round each winning share down to the nearest dime (some tracks, such as New York, will give the players a break and just round down to the nearest nickel). With that, the $2.91 profit becomes $2.90.
Next Step: Double the amount and add two dollars to determine payouts
Since it's traditional to state Win (and most other) payouts in terms of each $2 bet, we'll double our one dollar profit calculations, and then add in the original $2.00 wagered (since that gets returned to the winners; after all, their bets didn't lose). $2.90 doubled is $5.80; plus $2.00 gives us $7.80, which is what Some Colt pays to Win.
The steps for determining Win payouts are the same steps used for all other single-winner wagers; that is to say, every payout except Place (which has two "winning" wagers) and Show (which has three "winning" wagers) is determined the same way as above.
Let's work another example to demonstrate. Let's say the Race 3 Trifecta was Some Colt / Second Best / Third in the Bunch. If Race 3 had a total of ten horses entered, then the winning Trifecta was one out of 720 possible Trifecta combinations (10 x 9 x 8). An interesting piece of information, but meaningless to what we want to know: What did it pay?
We'll start our calculations by stating that $50,000 was bet into the Trifecta Pool
First Step: Deduct the track take out
For this example, let's use a more realistic 25% track take out. Removing twenty-five percent from the Gross Trifecta Pool of $50,000 gives us a Net Trifecta Pool of $37,500.
Next Step: Determine how much was wagered on the winning Trifecta combination
The Some Colt / Second Best / Third in the Bunch Trifecta combination (in that order; Trifecta bets with those horses in any other order are as much losers as those combinations containing other horses) had a grand total of $725 bet on it to come to pass.
Net Step: Determine the profit amount to be divided among the winning bettors
Deducting the $725 bet by the winners from the Net Trifecta Pool of $37,500 gives us $36,775 to be divided among the winners.
Next Step: Divide the profits equally among all winning tickets
$36,775 divided by $725 is $50.72.
Next Step: Remove breakage
Once again the race track double dips, in this case making the profit per dollar $50.70.
Next Step: Double the amount and add two dollars to determine payouts
That is, if we want to state the payout in terms of $2 bets. While traditional to do so for Win, Place, and Show wagers, it's quite common for exotic wagers, such as Trifectas, to be stated in terms of $1 bets. To be consistent, we'll state the $2 payout of $103.40 ($50.70 + $50.70 + $2.00), though giving the $1 payout of $51.70 ($50.70 + $1.00) is perfectly acceptable.
And there you go. As I mentioned above, calculating Pick Six, Pick Four, Pick Three, Daily Double, Exacta, Quinella, etc., etc., payouts follow these same basic steps. The exceptions are Place and Show wagers, which I'll cover in my next post sometime later this week.
If you have any questions, or if you see (or think you see) someplace where I messed up, or if everything above is clear as mud LET ME KNOW and post a comment below.
Peace and Love,
Jimbo
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