# Want to win at gambling? Use your head

GAMBLING IN AUSTRALIA – Some say “punting is a mug’s game”. But is this always true, or can an astute gambler make long-term profits?

Certainly not from casino games. Casinos make profits by paying less than they should on winning bets. A roulette wheel has 37 numbers, so a gambler who bets a dollar has a 1/37 chance of winning and should receive back \$37 on a winning number.

But the casino pays only \$36.

On average, a gambler loses \$1 for every \$37 they bet: a loss of 2.7%.

This is the cost of playing the game and it’s the profit the casino makes often called the “house percentage”.

## Houses of all sizes

For casino games such as roulette, Keno and poker machines, the house percentage can be calculated mathematically, and in spite of many proposed betting systems, is an immutable and unchangeable number. No strategy can be used by the punter to make the game profitable.

While gamblers may experience short-term lucky streaks, in the long run they will lose this predetermined percentage of their wagers. But a sensible casino gambler should at least be familiar with the house percentages:

Betting the win line at craps at 1.4%, or red or black at roulette at 2.7%, might be a better option than Keno or Lotto with a house percentage of over 40%.

Let’s be clear here: for every \$100 bet through Tattslotto or Powerball, the “house” only pays out \$60, keeping \$40 for itself.

But sports betting is different.

In a horse race, the chance of winning (and hence the price for a winning bet) is determined subjectively, either by the bookmaker or by the weight of money invested by the public.

If 20% of the amount a bookmaker takes on a race is for the favourite, the public is effectively estimating that particular horse’s chance of winning at one in five. But the bookmaker might set the horse’s winning price at \$4.50 (for every \$1 bet, the punter gets \$4.50 back), giving the bookie a house percentage of 10%.

But a trainer, or jockey with inside knowledge (or statistician with a mathematical model based on past data), may estimate this same horse’s chances at one in three. If the savvy punter is correct, then for every \$3 bet they average \$4.50 return.

A logical punter looks for value – bets that pay more than a fair price as determined by their true probability of winning. There are several reasons why sports betting lends itself to punters seeking value bets.

## A sporting chance

In general, more outcomes in a game allow for a higher house percentage. With two even outcomes (betting on a head or tail with a single coin toss, say), a fair price would be \$2.

The operator might be able to pay out as little \$1.90, giving a house percentage of 5%, but anything less than this would probably see little interest from gamblers.

But a Keno game with 20 million outcomes might only pay \$1 million for a winning \$1 bet, rather than a fair \$20,000,000. A payout of \$1 million gives a staggering house percentage of 95%.

Traditionally, sports betting was restricted to horse, harness and dog racing – events with several outcomes that allowed house percentages of around 15%-20%.

With the extension into many other team and individual sports, betting on which of the two participants would win reduced a bookmaker’s take to as little as 3%-4%.

Competition reduces this further. Only the state-run totalisator (an automated system which like Tattslotto, determined the winning prices after the event, thus always ensuring the legislated house percentage), and a handful of on-course bookmakers were originally allowed to offer bets on horse racing, whereas countless internet operators now compete.

Betfair even allows punters to bet against each other, effectively creating millions of “bookmakers”.

Many sports punters bet with their hearts, not their heads. This reduces the prices of popular players or teams, thereby increasing the price of their opponents. The low margins and extensive competition even allow punters to sometimes find arbitrage opportunities (where betting on both sides with different bookmakers allows a profit whoever wins).

To overcome their heart, and lack of inside knowledge, many mathematicians create mathematical and statistical models based on past data and results to predict the chances of sports outcomes. They prove the veracity of their models by testing (either on past data or in real time) whether they would profit if the predictions were used for betting.

Academics call the ability to show a profit the “inefficiency of betting markets”, and there are many papers to suggest sports markets are inefficient. Of course the more successful have a vested interest in keeping their methods to themselves and may not publicise their results.

Astute punters can make sports betting profitable in the long term. But the profits made by the plethora of sports bookmakers indicate that most sports punters are not that astute.

This is part four of The Conversation’s Gambling in Australia series. Read part one: Gambling in Australian culture: more than just a day at the races; part two: Promotion of gambling short-changes Australian sport … and its fans; and part three: Get rich or die trying: when gambling becomes a problem.

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