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