What betting odds mean and how they relate to probability

Decimal odds tell you what your stake is multiplied by if you win. $100 at 2.50 returns $250, of which $150 is profit. If you lose, you lose only the stake.

Odds are also a probability

Divide 100 by the odds to get the implied chance: 1.50 is about 67%, 2.00 is 50%, 4.00 is 25%, 10.00 is 10%. A big number does not mean good value. It means you will rarely win.

Where the margin comes from

Add up the chances of every outcome in a match and you get more than 100%, say 106%. The extra is the margin, the bookmaker's cut. Because of it, random bets lose over the long run even if they occasionally pay well.

When a bet makes sense

Mathematically a bet is justified only when the true chance is higher than the odds imply. At 2.50 the price implies 40%. If you have reasons to think it is closer to 50%, that is value. If you have no reasons, it is guesswork.

The favourite trap

At 1.20 with a $100 stake, five straight wins earn $100, and a single loss takes that same $100 away. Looking safe is not the same as being profitable.

Accumulators

In an accumulator the odds multiply, but so do the chances. Three events at 60% each all land only about 22% of the time, and you pay the margin on every leg.