Odds and Probability

From AusRace

This article will introduce you to some important concepts but without dwelling too much on the mathematical rigour.

What has statistical probability got to do with gambling? In a word, everything. If gamblers had even a modest understanding of probability then the casino's of the world would all be empty. In this article I will explore the basic statistical probability you will need to know before you start betting either on the horses or other forms of gambling.

Converting Odds to Probability

Now let's solve one of the great mysteries for many a punter, converting odds to probability. But before we do a word about odds. Odds are simply the ratio of the losing outcomes (or chances) to the winning outcomes.

Bookmakers express odds as odds against winning. So a 10/1 bet indicates ten chances of losing and one chance of winning, as a ratio this is 10:1. A 6/4 bet would have six chances of losing and four of winning and of course an even money bet has one chance of winning and one chance of losing.

Since you will generally only see the bookmakers style notation I will use this in expressing odds but never forget that odds are really a ratio and should be expressed as 10:1, 6:4, 1:1 on so on.

I can only assume that bookmakers replaced the ':' (colon) with a forward slash (/) because this made it easier to write out tickets in the days when they did this quickly by hand.

The forward slash, '/', is not the division operator so mentally replace it with a colen, ':', and you will find life much easier when doing math involving probability and odds.

A special case is when a horse has more chance of winning than losing, for example odds of 4/6 represents 4 chances of losing and six chances of winning. These horses are called 'odds on� and usually appear in red on the bookmakers board. Just to confuse you further most people just say 6/4 ON. If you see this just convert it in your head back to 4/6, or more correctly 4:6.

As we have discussed a horse showing odds of 10/1 has 10 chances to lose and only one chance to win (remember bookies odds are odds against an event happening). Now this is where knowing that the odds are really a ratio is important. 10/1 is really 10:1 and so you have 10 chances of losing and 1 chance of winning. The total number of chances (possible outcomes) is 11.

Therefor the probability of winning is 1 chance in 11 or 1/11 = .09 or 9%. Many people get this wrong because for some reason when they see 10/1 they immediatley divide 1 by 10 rather than 11. If you treat odds as a ratio you will never make this mistake again.

So the rule is mentally convert the "/" to a ":" and hopefully this will remind you to ADD the numbers each side of the ":" to determine the total number of possible outcomes, N.

Then Probability = 1/N or as a percentage = (1/N)*100

One last example, odds of 4/1. Express this as a ratio, 4:1, therefor N = 4 + 1 = 5 and probability becomes: Probability of Success = 1/N = 1/5 = .2 or 20%

It is a simple formula but always remember odds are a ratio when calculating the number of possible outcomes, N. Understanding this will make it easy to work out the probablilty of success for any bet you may be offered.