How does betting/bookies/odds work?

Factual Questions
1

I was remidned of my complete ignorance of this fact while watching an episode of Futuram in which Bender takes bets on a fight wherin he gives 9-2 odds on Dr. Zoidberg, “The Crab with the Jab.”

So…how do bookies make money off of people betting in sporting events? He gave 9-2 odds…so if I in theory bet $2 and Dr. Z won, I would get $9 from the Bender, yes? A few minutes later, Bender tells Fry that he wants him to take a dive (in a fight to the death, no less.) But if Fry took a dive, that means that Bender would lose money to everyone who betted on Zoidberg. So in theory that means more people must have bet on Fry. And not just more, but enough so that even after paying at at 9-2, he would still come out ahead.

So how do bookies:

  1. Decide the odds? Obviously, they give higher odds to the underdog, in the hopes the high odds entice more people to place bets on the underdog. Yet he of course wants the favored one to win, assuming he gets enough money from the higher odds bet, so that he only has to pay out a small amount.

  2. Decide when to even accept bets? Let’s say Evander Holeyfield fought some 90 year old grandma. There is no chance for the grandma to win. Even with 1000-1 odds, I seriously doubt any bookie would get enough bets from that to cover everyone betting $1000 on Holryfield (especially since everyone who bet on grandman would only need to bet like $1 to still get a good return.)

2

How do bookmakers make money?

vigorish

How do they determine the proper odds? Experience. The ones who can do so successfully are the ones who last in the business. And the odds also change as the money comes in so that each side has approximately equal bet on it.

3

The vigorish aspect is correct - odds and point spreads are adjusted to encourage equal betting on both participants, with the booking collecting a 5-10% fee on all bets.

As for Bender giving 9-2 on Zoidberg, the implication is that a $9 bet on Zoidberg wins only $2, i.e. Zoidberg is considered far more likely to win. To turn a profit, Bender should, for example, take bets on Zoidberg at 9-2 and bets on Fry at, say, 3-8. Thus if he gets one person to bet on each fighter:

Bets on Z: 9
Bets on F: 3
Total income: 12

Outcome if Z wins: Payout of 11, profit 1
Outcome if F wins: Payout of 11, profit 1

If he gets a large imbalance, with many times more bets on one fighter, he has to adjust the odds to encourage more bets on the unfavoured fighter. If he asks Fry to take a dive, it means he got more bets on Fry and will lose if Zoidberg wins.

4

The basic concept is called “overround”. I now see that that is another word for “vigorish”, although I have never come across that term. (I assume vigorish is an Americanism).

A bookmaker is called a bookmaker because he makes a book. Simple, yes? The overround of the book is expressed as a percentage. a “100% book” is one in which the payout is excatly “fair” - if you back every outcome with appropriate stakes, you will come out exactly level. Most real bookies’ odds are around 115% - 120%, at least on sports such as horse racing where there are lots of runners. A 120% book is one in which you would have to stake £120 in order to get back £100, assuming you divided your stake correctly.

E.g. if I was taking bets on the roll of a fair die, I could offer 5/1 about each of the six numbers coming up. A punter could bet £10 on each number, making a total stake of £60. Obviously only one of these numbers could win, and that winning number would pay out £50 plus the stake on that number, making £60. The bookie has taken £60 and paid out £60. That is a 100% book.

That is not much use to me as a bookmaker, as I don’t make any money, so instead I offer, say, 9/2 (which is the same as 4.5/1) on each number.

Now, if the punter backs all the numbers for £10 each, he has paid £60, but will only win £55 back. I make £5 profit on every £60 staked, assuming the stakes are evenly spread.

To calculate the overround, convert the odds to decimal odds (evens = 2.0, 2/1 = 3.0 and so on) then simply sum the reciprocals.

e.g. 5/1 on each of 6 numbers, overround = (1/6) x 6 = 100%

9/2 on each of 6 numbers (9/2 = 4.5/1 = decimal odds 5.5). Overround = (1/5.5) x 6 = 109.09%.
In the real world of sports, obviously the odds are not usually equal and calculable as in the case of a die. Bookies have “odds compilers” whose job it is to work out the odds using stats and a good dose of intuition.

Typically they will work out the “true odds”, which should add up to 100%, and will then reduce the odds on each slightly in order to give themselves an overround.

But it is certainly incorrect to assume that the bookies will make a profit on every match or every race no matter who wins. Even with the help of the overround, if 90% of punters are backing the 1/3 favourite, the bookies will take a hammering if it wins. If a strong favourite wins, that is usually a bad result for the bookies - OK, the payout is not huge, comparatively, but it means that the majority of bets they have taken were winners. What thw bookies want to see is that strong favourite falling at the first fence and a 100/1 outsider romp home. They’ll happily return a few grand to some speculative £10 punters, while trousering the thousands and thousands wagered on the fav.

A bookie will always keep track of what his exposure is on each runner. If he is too exposed on one, then he will either cut the odds on it, and hope that punters will go elsewhere where they can get better odds, or even stop taking bets altogether.

5

Another interesting feature of the bookie arts comes into play in sports where the betting is influenced by point spreads instead of odds. In these situations it may sometimes be possible to play a “cross”.

Given that there will be variation in the spreads offered by different bookies, it is sometimes possible to set up a situation where you have 2 possible outcomes, (1) you loose the vig only or (2) you win your bets (minus vig).

Lets say bookie A (bA) says the Bears will beat the Packers by 7-1/2 and Bookie B (bB) says the Bears will win by 10-1/2. Assume a 10% vig.

Place a $1,000 bet with bA on the Bears and a $1,000 bet with bB on the Packers.

If the Bears win by 7 or less pay bA with your winnings from bB and your out the vig on both bets. Net result: -$200
If the Bears win by 10 or more pay bB with your winnings from bA and your out the vig on both bets. Net result: -$200
If the Bears win by 8, 9, or 10, collect both bets. Net Result +$1,800

6

Please elaborate. I’ve played casino games and poker for years and have a pretty good handle on odds and payouts, but I’ve only been betting football a couple of years.

I use a bookie through a friend. I give him the game and he gives me his spread. Ok. Let’s say I take the favorite to cover for $100. If I win, he gives me $100. If I lose, I owe him $110. All his bets are like this. It’s not like the spread changes based on whether I pick the favorite to cover or the dog plus the points. Over/Under–same thing. Loser pays a 10% vig. Winner collects the full bet amount.

Two years ago, I placed 7 $100 bets over the course of the season and won all 7. I was patient to look for favorable lines. I pocketed $700. I thought “This is easy!” and ramped up my betting last year. A dose of reality has set me straight on the “ease” of sports betting!

7

[QUOTE=divemaster]
Two years ago, I placed 7 $100 bets over the course of the season and won all 7. I was patient to look for favorable lines. I pocketed $700. I thought “This is easy!” and ramped up my betting last year. A dose of reality has set me straight on the “ease” of sports betting!
[/QUOTE]

I’ve heard it said that if you could devise a way that a casino could guarantee that new customers (only) always went home winners, casinos would certainly pay you millions for this system. They know that those who win on their first try will surely be back to bet more. The saying is “Every winner is a loser.”

8

I’m a regular user of Betfair, which is a betting exchange site. On this, rather than betting against a bookmaker, you’re betting against other users of the site, and you can either back or lay a bet. So if you think Arsenal are going to get thumped by Barcelona tomorrow night, you can offer odds to another punter abouot Arsenal winning. Someone backs it with you, say £50 at odds of 2.8. If Arsenal lose, you get to keep his £50 (less the site’s commission). If Arsenal win, you return his stake and pay him winnings of 50 x 1.8 = £90. (He gets a little less than this, as the site takes commission).

Because there are so many people backing and laying on most matches, the markets are extremely efficient and quickly find their own level. Typically on busy markets you can back at 101% and lay at 99%, and sometimes you can even take advantage of movements in the market and back at less than 100% for a guaranteed profit.

You can also back and lay on the same market, to guarantee a profit. So if you think a price will shorten, you can back it in order to lay off later. Say a horse is trading at 2/1 (3.0), you back it for £500, giving potential profits of £1000. Later the price drops to 2.75. You can now lay for (1500/2.75) = £545.45.

Now, if it loses, you lose your £500 back stake but win a £545.45 lay stake.

If it wins, you win your £1000 back stake but lose the lay stake (£545.45 x 1.75) = £954.54.

Either way, you’ve made a profit of over £45.

9

[QUOTE=Colophon]
A bookmaker is called a bookmaker because he makes a book. Simple, yes?
[/QUOTE]
I understand the math you are discussing, to a first approximation.

My question is more about language. Why is this person called a “bookmaker”, specifically? Why “book”? Is it because of keeping reconds in ledgers? I was always confused by the term “bookmaker” as a kid; I thought it should mean “bookbinder”, as in “someone who physically constructs a book”. :slight_smile:

10

[QUOTE=Colophon]
A bookie will always keep track of what his exposure is on each runner. If he is too exposed on one, then he will either cut the odds on it, and hope that punters will go elsewhere where they can get better odds, or even stop taking bets altogether.
[/QUOTE]

Here in the States, a bookie whose book has gotten out of balance will often lay off some of his action with another (and usually bigger) bookie. Bookmaking is remarkably similar to the life insurance business. I once explained how life insurance works by comparing it to bookmaking, because the kids understood that already.

[QUOTE=Sunspace]
I understand the math you are discussing, to a first approximation.

My question is more about language. Why is this person called a “bookmaker”, specifically? Why “book”? Is it because of keeping reconds in ledgers? I was always confused by the term “bookmaker” as a kid; I thought it should mean “bookbinder”, as in “someone who physically constructs a book”. :slight_smile:
[/QUOTE]

Yes, some bookies use an actual ledger-type book. I’ve only seen one, though, so I can’t say how many use some other method of keeping track. I’ve heard about flash paper but I’ve never seen it.

11

[QUOTE=divemaster]
Please elaborate. I’ve played casino games and poker for years and have a pretty good handle on odds and payouts, but I’ve only been betting football a couple of years.

I use a bookie through a friend. I give him the game and he gives me his spread. Ok. Let’s say I take the favorite to cover for $100. If I win, he gives me $100. If I lose, I owe him $110. All his bets are like this. It’s not like the spread changes based on whether I pick the favorite to cover or the dog plus the points. Over/Under–same thing. Loser pays a 10% vig. Winner collects the full bet amount.
[/QUOTE]

Here is what I think he is saying.

Let us imagine that over time you are going to be backing roughly as many favorites as you are dogs, and that further you will bet on half winners and half losers.

That means that in your life you will have, say, 1000 bets, 500 in which you bet on the favorite, 500 in which you bet on the dog, 500 in which you win, and 500 in which you lose.

Pretend you knew in advance which bets were going to win and which would lose (but you made them anyway). In half the bets, you’d need to put up $100 (those are the winning bets). In half the bets, you’d have to put up $110 (those are the doomed-to-lose bets). Thus, your average price per (any bet) is $105.

But when you win, you “only” win $100, for bets that (over time) cost you $105.

(The “good” news is that when you hand over $110 for a losing bet, it’s really not quite as big a vig as you think because over time, the “real” cost-per-bet for (aggregate of all bets, including losing bets) is actually, also, $105).

The other point that I think has been made pretty well but that’s essential to grasp is that the key here, as in all markets, is in the differential between what the house/book will pay you for X vs. what you pay them for contra-X (call it bid:ask, etc.). The OP was I think (sorry if I’m wrong) a bit baffled because he thought he had the option of betting $9 to win $2 or vice versa, which leads to a wash, when in reality a book offering 9:2 on Bender would offer, as others have pointed out, something not quite so favorable as 2:9 on his opponent.

Two factors (at least) lead to disproportionately big spreads between the odds offered for X and not-X:

(1) House greed. I’ve concluded that, for instance, whatever I know about horse-racing isn’t enough to allow me to make money over time if, say, the track is structuring the parimutuel odds so as to accomodate a house rake-off of 16% on every race.

(2) illiquidity (mentioned above). A bookmaker who knows he can get an infinite number of bets for either X or not-X, if he moves the price over time to stimulate/stunt respective demand, can be confident that on average, he can take on no probabalistic risk and guarantee his 5% per bet margin (putting aside inefficiencies, timing problems (a huge last minute influx of money on X), etc. However, if there aren’t enough players in the market, or if the market functions in a not-very-transparent or efficient way, the bookie will need to build into his spreads enough profit to account for the fact that he may not be able to perfectly balance or lay off X and not-X bets. A market neutral bookie doesn’t want probabalistic risk exposure. If he’s afraid he’ll get caught with three punters betting on X, and none on not-X, he will have to offer terms much worse (for either proposition) than if he could be sure that for every X punter he could match up a not-X punter, if he is to guarantee a desired profit margin for himself.

12

I’m not following this. If he asks Fry to take a dive, that means he wants Zoidberg to win, right? Why would he want Zoidberg to win if that means he loses money?

13

[QUOTE=Just1Lurk]
I’m not following this. If he asks Fry to take a dive, that means he wants Zoidberg to win, right? Why would he want Zoidberg to win if that means he loses money?
[/QUOTE]

From rereading, I can see that I tripped myself up on “win” and “lose”. What I meant was that Bender had obviously gotten more bets on Fry (presumably from people interested in the assumed 3-8 odds) and if Fry wins (as he arguably ends up doing, though by then no-one cares), Bender will lose money.

Obvioulsy I don’t have a head for bookmaking because I lost track of the optimal outcome.

14

[QUOTE=Huerta88]
(1) House greed. I’ve concluded that, for instance, whatever I know about horse-racing isn’t enough to allow me to make money over time if, say, the track is structuring the parimutuel odds so as to accomodate a house rake-off of 16% on every race.
[/QUOTE]
Parimutuel odds are set not by the track, but by the bettors themselves. If a horse is showing 10 to 1 odds, and Joe Richbucks dumps say, five times the pool’s total on that horse to win, the next time the board flashes, that horse is going to be 1 to 5.

Like you said, the track rakes off 15 to 22 percent (depending on the state it’s in and the bet-type --exotics being higher) and divvies the remainder among those holding the winning tickets. It got its share (less the state’s portion) and, with a rare exception, could not care less who actually wins the race.

That exception is if the favorite is such a heavy favorite, that after the rake-off the money left won’t give 1.05 back per per dollar bet (1 to 20 odds) when distributed, the track has to chip in the difference. When you see payouts of 2.10, the track lost money. Because of that, if such looks likely, the track will take steps to make betting on the long-shots more attractive, generally by lumping them together in a field bet. (Ooooh! Secretariat vs. ten other horses. I’ll bet on the ten!)

DD

15

Don’t forget all the fun quirky bets you can do with spreads, like parlays and teasers.

A parlay means you pick multiple bets, like say the Bears and Patriots. If either lose, you lose you your whole bet. But if both win, you win more than double your money. You can also parlay three teams, which pays aroun 5:1. Parlays are equivalent to the “light side” of the craps table, slots, and the lottery. Smaller buyin with a smaller chance to win a large payout. One interesting note is that if you do a two team parlay where one covers the spread while the other pushes, your parlay reverts into a straight bet.

A tease is picking multiple teams like a parlay, but instead of giving you a higher payout, you get points shaved off all the spreads, and your bet pays even money if you win. IIRC, a two team tease will shave 5 points off, while a three team tease will shave 8 points off. A tease is like a “darkside” craps bet, or a system bet on the roulette wheel. A slow grind that should hit a bunch of times but not pay very well. (Not really, but it’s the general idea.)

So if the Colts are favored by 14 over the Texans, the Giants are favored by 13 over the Eagles, (snerk), and the Chargers are favored by 12 over the Raiders, you might bet a tease on the three favorites, reducing each spread by 8. (Meaning Colts by 6, Giants by 5, and Chargers by 4.) All three teams must cover, and like the over/under, a push is a loss.

The other logic is to boost the underdogs to nosebleed spreads, by teasing the Texans getting 22, the Eagles getting 21 and the Raiders getting 20. (Of course you’d lose when the Eagles got blown out by 40, but that’s why it’s called gambling.)

One “high action” approach is to play a 3-team tease and a 3-team parlay on the same three teams. This means that if you hit them all, you get a ton of money, while if you come close, the teaser should pay for the parlay breaking you even. Of course, it is inevitable that if you do this, two of the teams will cover easily while the third will be a blowout in the wrong direction.

16

[QUOTE=DesertDog]
Parimutuel odds are set not by the track, but by the bettors themselves. If a horse is showing 10 to 1 odds, and Joe Richbucks dumps say, five times the pool’s total on that horse to win, the next time the board flashes, that horse is going to be 1 to 5.

Like you said, the track rakes off 15 to 22 percent (depending on the state it’s in and the bet-type --exotics being higher) and divvies the remainder among those holding the winning tickets. It got its share (less the state’s portion) and, with a rare exception, could not care less who actually wins the race.

[/QUOTE]

Correct, I was sloppy in implying that parimutuel betting involved the track doing anything with the odds – they rake off their take as the money comes in, and display the odds on an instantaneous basis in accordance with the pro rata ratio of the money bet on each horse.

You also draw attention to the important fact that when you bet on a horse at the track whose odds are shown as “10:1”, that does not mean you will get back $20 on a $2 bet. If a lot more money comes in on that horse, you could get less. If a lot more comes in on another of the contenders, but yours wins, you’d get more. This is what used to be (for all I know, still is) called “Starting Price” betting – you don’t know the odds until the race starts. You used to be able to alternatively bet “Ante Post,” which meant the book quoted you 10:1 odds and they never changed (but, you’d lose your bet entirely if the horse did not race, whereas in Starting Price I think a scratch equals a refund). You can’t, AFAIK, make an Ante Post bet at a U.S. track, but I suspect you could online or maybe in other countries.

17

In most UK bookies, you can either take SP or take the odds quoted, even right up to the race, and you’ll still get a refund if it’s a non-runner. Ante-post bets are a separate thing, and are struck before the line-up is confirmed, with the attendant risk.