Can you really defy the odds?

This post is dedicated to people who love to play the game of chance, in other words, gambling. One of the more interesting and favorite gambling game is that of sports betting where you can wager on the results of a game.

Betting shops thrive on ill informed betters and uneven odds or payout to tilt the edge in their favor. Therefore I attempt to create a short analysis on our friendly neighborhood betting outlet to see how much of an edge they have over us.

The screenshot below shows a typical given set of odds for a match up.


1 meaning you take the home team and for each $1 you bet, you will get back $3, X for draw and 2 for away win. You then use 1 divided by the odds to get the probability an outcome is expected. Example the probability for a home win is 1/3 = 0.333. You then repeat this for X and 2 to find their probability.

But wait, as we learnt in school about probability and statistics that the probability has to be = 1 if you can list out all the outcomes, how could the probability be 1.129 instead? As we know, a betting shop is not a charity organisation, it needs to ensure there is a profit generated(we call this water money), thus the excess amount generated after 1 which in this scenario is 0.129 means that if a better were to play this game 100 times,each time wagering $1, and have an even winning rate, which in this scenario is 33.3%, he will be statistically be down $12.90 after 100 matches.

This 12.9% excess of the pool of money meant that the organizer earned $12.90 regardless of what outcome happened. This is their profits just for organizing this market for punters and their main aim will be to balance the books to make sure there is an even number backing each outcome. This also meant that if this is a game of tossing coins for heads and tails, you will need to win (0.5 * 112.9% = 64.5%) just to break even.


So, with all the odds not in your favor, should you really gamble? Hmm, unless you can win 75% of the time.