How it works

Here’s how it works (using my real world example):

Taking a look at the odds of matches for round 14, I can calculate the potential gaurenteed profit I will make under a few assumptions.

My aim is to match the profit I would get if I staked the free bet on my preferred team. For example if I put the $100 free bet on a team at 1.40 odds, my potential profit is $40. So I want to determine what amount of money I need to put on the opposing team to match this profit. Then I want to determine if my overall profit is positive. If it is then its a good match to hedge on.

So lets take a look at how this works on the actual match I staked on.

I chose to use my $100 free bet to stake on the Broncos playing at home to beat Canberra in round 14.

The Broncos were at odds of 1.33 while Canberra were at odds of 3.45

If I use the $100 free bet to stake on Broncos my potential profit is $33 ($100*1.33 - $100).

If I want to ‘match’ this profit by betting on Canberra I would need to put $13.75 on Canberra to win. ($13.47*3.45 - $13.47 = $33)

So now; given I have placed a $100 (free) bet on Broncos and 13.75 bet on Canberra then I am gaurenteed to profit $19.53. Yup that’s right, no matter who wins I get $19.53 profit. Now I don’t even have to watch the game and I can go off and buy that ‘special’ something I’ve always wanted….

But in all seriousness at least its a profit, and I only had to outlay $13.47 to gaurentee it.

You can double check the math if you like:

I put $13.47 on Canberra to win @ 3.40 (total actual outlay $13.47).

I put $100 (free bet) on Broncos to win @ 1.33 (total actual outlay = $0.00 because its a free bet)

If Broncos win I get (1.33*100-100)-$13.47 = $19.53

If Canberra wins I get (3.4*13.47)-$13.47 = $19.53

So there you go! As demonstrated you can use that free bet to guarantee yourself a profit (I actually did)

Math

Here’s the step by step guide (with formula) to determine how much to stake on the opposing team, and how much overall profit you will make using this strategy. You can use the amount of overall profit to determine which match is the best value to hedge on

1. Determine the:

• free bet amount (s1)

• odds of the team which free stake will be used (o1)

• odds of the opposing team (o2)

2. Calculate the expected profit (p) from the free bet stake

• p = s1*o1 - s1

3. Calculate the amount of money needed to bet on the opposing team in order to match the expected profit from the free bet stake (s2)

• s2 = p/(o2-1)

4. Calculate the total expected profit (tp) from the hedge betting

• tp = p-s2

5. Use the hedging strategy to stake on the game with the highest total profit (tp).

Using my real world example:

s1 = $100

o1 = 1.33 (Odds on Broncos)

o2 = 3.4 (odds on Canberra)

p= $100*1.33-100 = $33

s2 = 33/(3.45-1) = $13.47

tp = $33- $13.47 = $19.53

This was the highest tp of all matches in round 14 (at the time of betting) so was my preferred hedging stake.

If we wanted to quickly look at the best free bet hedging opportunities we can tabulate and graph to get a bit of an idea of how this works.

Assuming a $100 free bet and a completely fair market free of vig/overround; lets tabulate and plot the total potential profit of odds from 1.0 through to 2.0:

o1	o2	s1	p	s2	tp
1.00	Inf	100	0	0.00	0.00
1.05	21.00	100	5	0.25	4.75
1.10	11.00	100	10	1.00	9.00
1.15	7.67	100	15	2.25	12.75
1.20	6.00	100	20	4.00	16.00
1.25	5.00	100	25	6.25	18.75
1.30	4.33	100	30	9.00	21.00
1.35	3.86	100	35	12.25	22.75
1.40	3.50	100	40	16.00	24.00
1.45	3.22	100	45	20.25	24.75
1.50	3.00	100	50	25.00	25.00
1.55	2.82	100	55	30.25	24.75
1.60	2.67	100	60	36.00	24.00
1.65	2.54	100	65	42.25	22.75
1.70	2.43	100	70	49.00	21.00
1.75	2.33	100	75	56.25	18.75
1.80	2.25	100	80	64.00	16.00
1.85	2.18	100	85	72.25	12.75
1.90	2.11	100	90	81.00	9.00
1.95	2.05	100	95	90.25	4.75
2.00	2.00	100	100	100.00	0.00

We observe that in a fair market the maximum profit of $25 is achieved when you put a $100 free bet on odds of 1.5 and $25 on the opposing team at odds of 3.00. Profit declines from this maximum as you move lower towards 1.2 or higher towards 2.0. At odds of 2.00 no profit is achieved. While this is the theoretical maximum in a fair market, the reality is that the ‘best’ value hedging opportunity will vary based on the vig/overround offered for the match, and the vig/overround bias. To refresh your memory a bookmakers market is never fair as the probabilities they offer on each team will add up to over 1.00.

For example, in a fair market assuming even probability (50%) that each team will win, then the odds offered should be 2.00 on each team.

In the bookmakers market when the odds are ‘even’ instead of being set at 2.00 you will observe that they might be at 1.92.

For example, the opening odds for the round 14 match up between the Sharks and Cowboys were 1.92 each. This is equivalent to an implied chance of 52% chance that each team will win. This adds up to 104% so the bookmaker has a 4% overround.

So unfortunately you can’t use 1.50 exclusively, you will need to do the calculation to determine which match has the highest profit potential like I did.

Lets take the odds of the round 14 matches* and see how the profit is affected by the vig/overround. We will also order the odds lowest to highest.

NB these odds are slightly different to the odds determined at the time of my stake - these are just the latest odds I had in my database

favorite	favorite.odds	non.favorite	non.favorite.odds	vig	overround	s1	p	s2	tp
Brisbane Broncos	1.32	Canberra Raiders	3.50	0.041	0.043	100	32	12.800	19.200
New Zealand Warriors	1.32	Newcastle Knights	3.50	0.041	0.043	100	32	12.800	19.200
Canterbury Bulldogs	1.38	St George Illawarra Dragons	3.15	0.040	0.042	100	38	17.674	20.326
Melbourne Storm	1.42	Sydney Roosters	2.95	0.041	0.043	100	42	21.538	20.462
Penrith Panthers	1.47	Manly Sea Eagles	2.75	0.042	0.044	100	47	26.857	20.143
South Sydney Rabbitohs	1.58	Wests Tigers	2.45	0.039	0.041	100	58	40.000	18.000
Gold Coast Titans	1.73	Parramatta Eels	2.15	0.041	0.043	100	73	63.478	9.522
Cronulla Sharks	1.92	North Queensland Cowboys	1.92	0.040	0.042	100	92	100.000	-8.000

We can see that odds of 1.5 no longer represents the maximum profit but rather, maximum profit is achieved at odds of ~1.42. You can also see that the vig/overround does actually vary slightly between matches which does play into the potential profit. So the bottom line is that to maximize your profit you need to make sure that you do your math in the market you want to apply your hedging stake in.

Finally, although I said that this hedging strategy guarantees you a profit… there is a slight caveat. In the event of a draw I would have lost my free bet and also lost my $13.47…. however draws are a relatively rare beast..

Also as a final disclaimer in reality I had to put $14 on Canberra to win, as I wasnt able to put fractional bets on.. so my actual profit was very slightly lower