Making a Fair Line

Two friends want to bet on the outcome of a playoff series using a fair line (no juice) so neither has an advantage. The sport books show the favorite at -900 and the underdog at +600. So the fair line is somewhere in between, but where?

They discuss a few different methods:

1) Average the American style odds to get -750 and +750.

2) Convert the odds to probabilities and squeeze out the juice proportionately: -900 = 90% and +600 = 14.29%. That adds to 104.29%. So divide both probabilities by that total so they add to 100%. That yields American fair odds of -630 and +630.

3) Convert the odds to probabilities and take 50% of the juice from each side. So of the 4.29% juice, we would reduce each sides probability of winning by 2.155%. This yields American odds of -723.5 and +723.5.

4) Acknowledge that there is implicitly more juice embedded in the underdog side of the line. One way to think about this is a fair parlay where you have to keep win multiple -110 odds bets to get to the underdog line. In this case +600 pays like a 3 team parlay so there would be triple the juice on the dog side vs the fav side. Using the overall juice of 4.29% we would then remove 3.21% from the dog and 1.07% from the fav. That yields American style odds of about -800 and +800.

Does anyone have a view as to which method is most fair, or whether there is a different method you would use?

Quote: unJon

Two friends want to bet on the outcome of a playoff series using a fist line so neither has an advantage. The sport books show the favorite at -900 and the underdog at +600. So the fair line is somewhere in between, but where?

They discuss a few different methods:

I think the best way is for one of the people to set any line they think is fair both ways, then the other player gets to pick which side they want.

Quote: DRich

Quote: unJon

Two friends want to bet on the outcome of a playoff series using a fist line so neither has an advantage. The sport books show the favorite at -900 and the underdog at +600. So the fair line is somewhere in between, but where?

They discuss a few different methods:

I think the best way is for one of the people to set any line they think is fair both ways, then the other player gets to pick which side they want.
link to original post

I like this in theory as the I cut, you choose method. But it doesn’t answer the question of where Vegas thinks the fair line is.

And also assume that the two friends are fans of the two sides so it is clear one friend only will bet the dog and one only the favorite.

Quote: unJon

I like this in theory as the I cut, you choose method. But it doesn’t answer the question of where Vegas thinks the fair line is.

And also assume that the two friends are fans of the two sides so it is clear one friend only will bet the dog and one only the favorite.

The fairest line you will find in Vegas is the closing line of an NFL game between two small market unpopular teams. For example, Browns vs Jaguars closing line on a typical Sunday afternoon non primetime game.

Quote: DRich

Quote: unJon

Two friends want to bet on the outcome of a playoff series using a fist line so neither has an advantage. The sport books show the favorite at -900 and the underdog at +600. So the fair line is somewhere in between, but where?

They discuss a few different methods:

I think the best way is for one of the people to set any line they think is fair both ways, then the other player gets to pick which side they want.
link to original post

Doesn’t answer OP’s question, but I love the answer. Whenever a friend says ‘there is no way the Bunkers beat the Jefferson’s’, I say, “Ok, give me 10-1 odds and I’ll take the Bunkers’. It leads to a discussion of what at least we think are the fair odds.

I’m not good at ‘finding old stuff here’, but I’m pretty sure the Wizard has answered the OP’s question in the past.

Quote: SOOPOO

Quote: DRich

Quote: unJon

Two friends want to bet on the outcome of a playoff series using a fist line so neither has an advantage. The sport books show the favorite at -900 and the underdog at +600. So the fair line is somewhere in between, but where?

They discuss a few different methods:

I think the best way is for one of the people to set any line they think is fair both ways, then the other player gets to pick which side they want.
link to original post

Doesn’t answer OP’s question, but I love the answer. Whenever a friend says ‘there is no way the Bunkers beat the Jefferson’s’, I say, “Ok, give me 10-1 odds and I’ll take the Bunkers’. It leads to a discussion of what at least we think are the fair odds.

I’m not good at ‘finding old stuff here’, but I’m pretty sure the Wizard has answered the OP’s question in the past.
link to original post

You are much nicer than I am. If someone tells me no way team XYZ will win I will be asking for at least 1000-1 minimum.

Here's my thinking:
With the given line, bet F on the favorite, and U on the underdog
If the favorite wins, you profit F / 9 - U
If the underdog wins, you profit 7U - F
These are equal when 10/9 F = 8 U, or F = 7.2 U
The fair line is +/- 720

However, unless that was the opening line, there's no way of using it to determine a "fair" line, as the line will change in order to balance the amount of money bet on each side, rather than be a fair reflection of the teams' abilities.

Quote: unJon

Two friends want to bet on the outcome of a playoff series using a fair line (no juice) so neither has an advantage.

since they both want the expected result to be zero, the easiest and most obvious solution is to just not bet and that way it's guaranteed no one has an advantage. But if they are the type of bettors driven by compulsion instead profit, then it's probably best to just go to one of the many places that take bets as their business. My friend is selling a car and I want to buy a car, I'm still going to go to a car store and likely be a lot better off in doing so.

Quote: unJon

The sport books show the favorite at -900 and the underdog at +600. So the fair line is somewhere in between, but where?

the sportsbook offering this price believes the probability the favorite wins is somewhere between 600/700 and 900/1000. But everyday we see endless examples that these beliefs are wrong. If this sportsbook attaches equal vig on both sides, then the no vig price would be +630. That's very rarely the case.

We can get a much better estimate by using a consensus line or best available. For one series tonight, I'm seeing OKC at -290 at DraftKings, while Stations and South Point have Denver at +290. None of those places really take bets, so that's more like an mspr on a BMW, not what any dealership is actually selling it for. FanDuel and Caesars are at -300 and Betcris +267. I would feel comfortable saying a fair number is right around 3.75 - 3.80 on the underdog

In the other series, Circa has the Knicks at +295 and I can see an exchange has Celtics at -302 with $30k posted. Pick any random number between the two and we can't be off by more than 0.4%.

Quote: ThatDonGuy

Here's my thinking:
With the given line, bet F on the favorite, and U on the underdog
If the favorite wins, you profit F / 9 - U
If the underdog wins, you profit 7U - F
These are equal when 10/9 F = 8 U, or F = 7.2 U
The fair line is +/- 720
link to original post

Er, that's if the underdog pays +700. If it is +600, you profit 6U - F if the underdog wins, so the fair line is +/- 630.

If the lines are -A for the favorite and +B for the underdog, the "fair line" number is A (B + 100) / (100 (A + 100)).

10:00 morning of playoff games and Circa is now at +300 on New York, with 4casters at -302

DraftKings is holding the line at -290 on the Thunder, with pinnacle at +297.

If someone can't figure out a way to bet these games with greater than zero edge, just don't bet.

Quote: unJon

Two friends want to bet on the outcome of a playoff series using a fair line (no juice) so neither has an advantage. The sport books show the favorite at -900 and the underdog at +600. So the fair line is somewhere in between, but where?

They discuss a few different methods:

1) Average the American style odds to get -750 and +750.

2) Convert the odds to probabilities and squeeze out the juice proportionately: -900 = 90% and +600 = 14.29%. That adds to 104.29%. So divide both probabilities by that total so they add to 100%. That yields American fair odds of -630 and +630.

3) Convert the odds to probabilities and take 50% of the juice from each side. So of the 4.29% juice, we would reduce each sides probability of winning by 2.155%. This yields American odds of -723.5 and +723.5.

4) Acknowledge that there is implicitly more juice embedded in the underdog side of the line. One way to think about this is a fair parlay where you have to keep win multiple -110 odds bets to get to the underdog line. In this case +600 pays like a 3 team parlay so there would be triple the juice on the dog side vs the fav side. Using the overall juice of 4.29% we would then remove 3.21% from the dog and 1.07% from the fav. That yields American style odds of about -800 and +800.

Does anyone have a view as to which method is most fair, or whether there is a different method you would use?
link to original post

The fairest way to do it would be 4. But the way you are adjusting for juice is arbitraty. I'd recommend:

Method 5: Empirically-based juice distribution
Research suggests that in heavily imbalanced lines (like -900/+600), bookmakers place approximately 65-75% of the juice on the underdog side and 25-35% on the favorite side.
Using a 70/30 split of the 4.29% juice:

Remove 1.287% (30% of juice) from favorite: 90% - 1.287% = 88.713% → approx. -785 American odds
Remove 3.003% (70% of juice) from underdog: 14.29% - 3.003% = 11.287% → approx. +785 American odds

This approach:

Accounts for the favorite-longshot bias
Uses empirical data on how bookmakers distribute juice
Still results in symmetrical American odds for your friendly bet
Produces probabilities that sum to exactly 100%

This method acknowledges the market inefficiency of the favorite-longshot bias while creating a fair betting line between friends.

Bookmakers generally want to maximize their expected Kelly bankroll growth and weight the vigorish on long-shots heavily. The house take on extremely short odds is by contrast almost non-existent. This is because long-shots attract more action proportionately.

There are endless academic papers written on this. Google or AI "favourite-longshot bias". It varies a little by sport and specific proposition but it is fairly constant generally. The only issue is working out the generic vig in actuality, you'd need to look through a lot of historical data.

I favor option 1 (+750,-750). Nice and simple. When I book Super Bowl props with DJTB that is how we do it.

Quote: Wizard

I favor option 1 (+750,-750). Nice and simple. When I book Super Bowl props with DJTB that is how we do it.
link to original post

It may be simple but it definitely isn't the most fair, which was the op's question.