Odds on Favourites
This lesson we take a look at the exact science of gambling and probability. Over the years people have obsessed over systems and surefire ways of beating the odds; from Rain Man counting cards in the Vegas casinos to Derren Brown beating the lottery on live tv. Obviously some methods are more effective than others; find yourself a genius human-computer like Rain Man and counting cards at the Black Jack table is a pretty safe bet. Follow the advice of Darren Brown however and you’re more likely to end up trading hand-jobs for a crack fix in Skegness; probably.
If, like most of us, you’re not blessed with a massive calculator for a brain then counting cards is probably out of the question. There are other ways to guarantee a win however. Lets take a walk to the roulette table where a bet on red or black pays out at one to one (a successful bet of £10 will win £10 plus original stake). A spin of the roulette wheel is just like the toss of a coin. Each spin is independent, with a pretty much 50:50 chance of the ball landing on black or red. Contrary to intuition, a black number is just as likely to appear after a run of 20 consecutive black numbers as the seemingly more likely red. This randomness means there is a way of using probability to ensure a profit: always bet on the same colour, and if you lose, double your bet on the next spin. Because your colour will come up eventually, this method will always produce a profit. The downside is that you’ll need a big pot of cash to stay in the game: a losing streak can escalate your bets very quickly. Seven unlucky spins on a £10 starting bet will have you parting with a hefty £1280 on the next. Unfortunately your winnings don’t escalate in the same way: when you do win, you’ll only make a profit equal to your original stake. So while the theory itself is sound, be careful. The roulette wheel is likely to keep on taking your money longer than you can remain solvent. There are more calculated ways of gambling, leaving the casino let’s head of to the bookies.
Although each bookie will stack their own odds in their favour, thus ensuring that no punter can place bets on all the runners in a race and guarantee a profit, that doesn’t mean their odds will necessarily agree with those of a different bookie. And this is where gamblers can seize their chance. Let’s take, for example, the Oxford – Cambridge boat race. One bookie may offer 3 to 1 on Cambridge to win and 1 to 4 on Oxford. But a second bookie disagrees and has Cambridge evens (1 to 1) and Oxford at 1 to 2. Each bookie has looked after his own back, ensuring that it is impossible for you to bet on both Cambridge and Oxford with him and make a profit regardless of the result. However, if you spread your bets between the two bookies, it is possible to guarantee success. Having done the calculations, you place £37.50 on Cambridge with bookie 1 and £100 on Oxford with bookie 2. Whatever the result you make a profit of £12.50. Guaranteeing a win this way is known as “arbitrage”, but opportunities to do it are rare and fleeting. The maths is easiest to do when there are only two possible outcomes, i.e. win or loose. Good places to spot possible arbs are with big football matches where bookies may favour their home team; finals are good as draws are out of the question. The next step is betting at the dogs which will tend to have up to 6 runners meaning the maths is still manageable as apposed to the horses which can have anything up to 15 riders. Online gambling has given a hole new scope to betting with people making a good living from arbitrage.
Before you sack in your day job and start your new career as a mathematician there are a few things you must first consider. Situations where arbitrage is viable are hard to find and once found the maths of calculating what bets to make is quite tricky. In order to see variable returns your stakes are going to have to be quite high, meaning if you make a mistake with your maths your losses can be high too. One massive downfall in the system comes in the bookies’ right to cancel bets. Although not a problem for your average gambler this can result in massive losses for arbers and will undoubtedly lead back to hand jobs in Skegness.
