sourceLet’s say you’re a bookmaker and you want to publish the odds on the matches played today. How do you do it so that you don’t lose the money to those pesky punters? For our simplified version on what goes on into the making the odds I’ll be using decimal (European) odds.
Your main target, as a bookie, is to make the odds in such a way that the percentage of the stakes placed on a bet is in the proportion to the probability of that bet winning. If the probability of a home win is 55%, you want 55% of the money you take in as the stakes to be placed on that bet.
Let’s say you employ a team of statisticians that will do their magic and arrive at the true probabilities for the three outcomes (home win, draw, away win) you want to offer. You sent the word and they’ve came with the following probabilities:
| Outcome | Probability | Probability (%) |
|---|---|---|
| Home Team Win | 0.55 | 55% |
| Draw | 0.30 | 33% |
| Away Team Win | 0.15 | 15% |
As you know, the probability of an event goes from 0 to 1, or from 0% to 100%. So how do you convert the probabilities to the odds you want to offer? It’s simple, really, just divide 1 by the probability of an event:
| Outcome | Formula | Odds |
|---|---|---|
| Home Team Win | 1/0.55 | 1.8181* |
| Draw | 1/0.3 | 3.3333* |
| Away Team Win | 1/0.15 | 6.6666* |
There you have it – the true odds. But you are not offering them to the public yet. Why not?
Imagine that you take the bets at these odds and you’ve managed to get an ideal situation for the bookie, the stakes are proportional to the odds you offered. Out of 100$ wagered:
| Bet | Stake |
|---|---|
| Home Team Win | 55$ |
| Draw | 30$ |
| Away Team Win | 15$ |
Now, let’s say, the home team wins and you have to pay out 55$ x 1.8181* or 100$. All your effort has been in vain! What you took in as stakes you returned back to the winners. How do you go around this? How do you guarantee your profits?
Simply you shorten the odds. Instead of the true odds you offer the following:
| Bet | True Odds | Odds You Offer |
|---|---|---|
| Home Team Win | 1.8181* | 1.74 |
| Draw | 3.3333* | 3.20 |
| Away Team Win | 6.6666* | 6.40 |
Assuming again the ideal situation, you took 55$ on the home team victory and they had won, now you have to pay out 1.74x55 = 95.70$. You’ve just made 4.30$ on that bet. That 4.30$ you've made is called the bookie’s vig (short for vigorish) or the juice.
That's the profit you'll always make as long as you take the stakes in the right proportions.