How the house sets decimal odds

Subtitle: two ways to win at sports betting

In my previous post, I looked at decimal odds from the players perspective. In this post I will consider decimal odds, or the price in general, from the sportsbook perspective.

I'll use a running example for this post. Suppose for some upcoming football game the analysis desk at the sportsbook determines that the favorite for this game has an 80% chance to win the game. The underdog has a 20% chance to win.

How would the house post a line for players to bet against. From my previous post, from the players perspective

x = 1 / D

where x is the players break-even probability, and D is the decimal odds.

Now for the house it then is

D = 1 / x

The house is holding the probabilities x, and can use these to calculate its break-even odds D. So for this game the favorite is 4/5, and the underdog is 1/5. So the house is indifferent with the lines

favorite decimal odds line: 1 / (4/5) = 1.25

underdog decimal odds line: 1 / (1/5) = 5.0

If the analysis desk is right about the probability, then this line would be unexploitable to the house. The house would expect to break even.

Now the house wants to make a profit, not just break even. So the book could take the mathematical break even line above, and shave a bit off it to create some profit margin - a some margin of error in their analysis of the game.

So if the house takes a 10% discount off the mathematical line, then the players could see a posted line of

favorite line: 1.13

underdog line: 4.5

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Now I promised to show two ways to win at sports betting. The first way to win is when your analysis of the game is better than the sportsbook analysis. Suppose you've studied this football game and you feel the favorite is stronger, 90% to win the game. 

At 1.13, your break even point x is 88.4% if your analysis is better than the house analysis then you can make an expected profit betting on the favorite.

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When the house posts lines, one of their goals is to balance the action. When the action is properly balanced, the house will make a profit on the game no matter which side actually ends up winning.The house has none of its own money at risk. Winning wagers are paid out from losing wagers, and there is some left over for an operating margin for the sportsbook.

I imagine that when the profit is assured, the sportsbook can pour a cold beer, sit back and just enjoy watching the game along with all of the players.

Consider again the football game above. Suppose the betting action comes in at the same ratio as the mathematical line. 80% on the favorite, 20% on the underdog. Suppose 5 people each make a $10 bet on the game. So 4 bets on the favorite at 1.13 and 1 on the underdog at 4.5. The house takes in $50 from the five players.

If the favorite wins then the house pays out 4 $11.30 tickets, so it pays out $45.20

If the underdog wins then the house pays out 1 $45 ticket, so it pays out $45

So the action on this game is properly balanced. The house will make a profit no matter what happens in the game. All winning bets are paid out with the money from the losing bets. None of the sportsbook money is at risk in this game.

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Trying to balance the action leads to the second way to win at sports betting. Suppose the risk management desk looks at the discounted mathematical line from above of 1.13 / 4.5  risk management is concerned there will be too much action on the favorite, putting house money at risk if the favorite wins. Cutting the line on the favorite to 1.10 might help some. But to get more action on the underdog to balance the action, the house moves the line to 5.5 on the underdog.

Now the break even line on the underdog is 5.0  at 5.5 it is profitable to take the underdog - even though you will lose the bet 80% of the time. So sometimes the house may post lines to balance the action that are profitable opportunities.

Calculating the break even point of decimal odds

 On ALC at least, the odds on the lines are expressed using decimal odds. So you will see things like 1.05, 1.90, 4.35, etc. This post is just to do a quick primer on decimal odds, and to demonstrate the break even point for a given decimal odds wager.

I find an easy way to think about decimal odds is this. Suppose the decimal odds for some event is D. You give the house $1 when you make your bet. If you win the bet the house pays you D. If you lose the bet then the house just keeps your dollar.

From there it should be clear that the decimal odds D will always be greater than one. After all nobody is going to give a bookie $1 in order to "win back" 85 cents, and that's only if you win the bet.

Some examples

if the decimal odds are 1.1, then you wager $100 to try to win $110

if the decimal odds are 1.5, then you wager $10 to hope to win $15, for a $5 profit

if the decimal odds are 2.5, then you wager $1 to profit $1.50

so thinking about it a bit, decimal odds are what the player is laying on a wager. so at 1.5, you lay $10 to make $5 profit. so laying 2:1 you need to win this bet 2/3 of the time to break even.

at D=1.1 you are laying 10:1, so basically you are laying 1 : ( 1 - D ) with decimal odds.

Or to put it into a formula. let D be the decimal odds. let x be how often you win the wager

then your break even point is

( D - 1 )x - ( 1 - x ) = 0

given D, solving for x yields

x = 1 / D

here's table based on some common decimal odds posted at ALC Pro-Line

Decimal Odds	Break Even Point (Percent)
1	100
1.05	95.24
1.1	90.91
1.25	80
1.5	66.67
1.75	57.14
1.85	54.05
1.89	52.91
1.9	52.63
1.91	52.36
1.92	52.08
1.95	51.28
2	50
3	33.33
4	25
5	20
6	16.67
10	10
12	8.33
13	7.69

Accounting for the value of lotto free tickets

At this time the Lotto Max jackpot is at the max $70 million. It was at 70 for the Tuesday draw earlier this week but it didn't go.

I had a ticket in the Tuesday draw. I had some free play money on ALC from a $50 for $25 deposit reload bonus. I bought a $5 ticket.

In the Tuesday draw, as sometimes happens, I won a free ticket into tonight's draw. That's okay with me, a second shot at the big jackpot, or one of 29 $1 million secondary maxmillions prizes, off one ticket purchase.

It did get me thinking, what's the value of winning a free ticket? Either for the player, or the house. (of course mathematically they must be the same) The free lotto ticket could be worth something, or improbably quite a lot. it could also roll over again into another free ticket. mostly of course they turn out to be worthless since most lotto tickets just lose.

From the house perspective, how to calculate the profit or loss on each individual draw when free tickets into future draws are awarded. How would especially winnings off free tickets that the player was given be accounted for.

I realized if you set it up and think about it properly it's not that hard. The way to think about and calculate the value of winning a free lotto ticket is like this. 

In the first draw, your ticket actually won a $5 prize which was paid out. The $5 win was then "intercepted" by ALC, and the house used the $5 to purchase a $5 ticket into the next draw. ALC then gave the ticket it just bought to the player who becomes the legal owner of the lotto ticket.

To the house, everything is clean. On the first draw your ticket won $5, which is accounted as a $5 winning payout in the profit and loss on that draw. ALC can close the books on the first draw and know exactly how much came in from ticket sales and how much was paid out to winning tickets. The accountant for the first draw does not care or have any interest in how the free tickets fared in the later draws.

On the second draw the same $5 is accounted as income as a regular $5 ticket purchase, the same as buying a ticket at a corner store or on alc.ca  To the accountant on the second draw, they received a $5 payment and issued a ticket. Everything is in order and they don't care if the ticket was then gifted to some customer as a free ticket.

To the player, it's a ticket into the second draw which would have cost $5 to buy at a gas station or online. So basically you won $5 on the first draw, but the house on your behalf used your $5 win to buy you a ticket into the next draw.

ALC Pro-Line payouts have improved

In recent advertising, ALC Pro-Line has been emphasizing a more studious approach. The commercials talk about analyzing odds, studying matchups, etc. When you're ready to make your picks, then Pro-Line payouts are in line with anything out there.

This is a change in the tone of the marketing. Historically the Pro-Line advertising has featured this goofy, oafish guy and his friends. They go to corner stores and make their picks. The goofy guy is clumsy and always knocking over a display or something. He just makes silly picks and it's all good fun among friends.

In the new advertising it's a departure for Atlantic Lotto, normally a monopoly, to even acknowledge there are other options for sports betting. On the same mainstream channels and TV shows Pro-Line buys advertising, there are also commercials for William Hill, 888, Bodog, Party, Odds Shark, various online casinos. 

By appealing to the more serious player, ALC seems to realize they have lost online sports business to offshore books. In the past I calculated that Pro-Line was paying about 77 cents per dollar wagered, keeping a 23% vig for itself. This is excessive and unfair. Even recreational players who aren't good with math, who still like to play a few games every week, could instinctively tell something isn't right with the payouts.

I logged in recently due to an ALC promo. I have an ALC.ca account from promos in the past. Over on Pro-Line I noticed that payouts have indeed improved. On a two-game parley with even payouts - the house pays out the same on both sides of the bet on a totals or point spread wager. In these games, on a $10 wager the house pays out $36.10 to a winner.

So if you bought 4 $10 tickets to cover the four possible combinations. You spend $40. Three tickets lose, and one will win $36.10. So for $40 spent, $36.10 is paid out to winners, or a $90.25 payout for every $100 wagered. The house keeps $9.75 of every $100, a 9.75% vig.

This seems reasonable and is in line with standard 11/10 vig at sports books. So +1 to ALC for improving their payouts and truth in advertising.

is Pro-Line beatable

At 9.75% vig it may creates some opportunities for playing for fun and profit. The break even point can be calculated on a two-game parley at .9025. So on a $10 wager you can win $26.10 or lose $10. Let X be the fraction of the time you win your bet.

26.1x - 10(1 - x) = 0

x = 0.277

So the break even is about 28%. If you use a random number generator to make your picks you would win by pure luck 25%. Remember you need to win two bets to win the ticket.

So if from your analysis you have two good picks then the square root of 0.277 is .5263. So if you can run 53% and find two games priced at 1.9 (the .9025 payout) then you would be profitable.

If you only have one good pick there is still an opportunity. On a game where the house pays out the same on both sides you can use the random number generator to make the pick and you would win the bet half of the time. So you can run 50% on events you know nothing about such as Mexican soccer, Euroleague basketball, or whatever. As long as the payout is the same on both sides of the bet.

Or buy two tickets, with your good pick, and both sides of the even payout game. 

With one good pick, and one random pick at 50%, you need to be 55.4% on your good pick to be profitable.

There is also a limited form of single game betting now on ALC Pro-Line. For hockey it's win the game and score in regulation. These games are attractively priced. On evenly priced games Pro-Line pays out $19 for every $20 wagered. So only a 5% vig on these moneyline plays with single-game allowed.

Now there is a slight catch where the payout is not quite 95 cents on the dollar. If the game is scoreless 0-0 at the end of regulation, then the house pays out nothing and scoops all the wagers on the game. It's a bit like the 00 in roulette, but less common. So be aware of that small risk. Still 0-0 games are uncommon in the NHL, and scoring is up this year. I haven't done the research but I'm guessing it reduces the payout to maybe 94 cents on the dollar.

Still good to know moneyline NHL at low vig. It's a good format for the players and I hope it sticks. 

These games are handy for clearing play though bonuses as they pay 0.95 instead of 0.9025 on the two-game ticket. Also you only need to win one bet to win the ticket. 

 

If you're a more casual fan and not sharp action, then a trick with ALC Pro-Line is use bonuses to improve your odds. Pro-Line and ALC run bonus promotions fairly frequently so it's good to sign up for the emails so you know when something's running. 

I wonder if this will be looked back on as the good time on Pro-Line. Payouts are competitive, it is easy to get money on or off, and there are frequent promos and bonuses.