## Scientific Gambling – how do betting shops make money….?

Betting shops are commercial businesses, that is, they want to and must make money in order to survive. Like any other business. So take a casino as an example: they make money – in the long run – by having set the odds just a tiny bit in their favor, the typical “house advantage” in games like Roulette is 5.26% (American Roulette) and 2.70% (European Roulette). What the house advantage tells us, is the relative amount a player is expected to lose for each play.  In the long run. Thus, making a bet of 1\$, you should expect to lose about 5 or 3 cents, each time. Over time, these tiny wins for the casino accumulate to quite a lot of money. I have no idea what turnover per day the typical Las Vegas casino has, but let’s say 10.000.000 USD. 5% of that is 500.000 USD, not bad for spinning a few wheels…

The cool thing about games like Roulette is that they are based on “known unknowns”, where the risk is fully understood mathematically, i.e. all the probabilities involved are fully known.

In sports betting, on the other hand, the probabilies are not known, since we are dealing not with risk, but uncertainty, i.e. we are dealing with Unknown Unknowns. So how do betting shops like Unibet, Svenska Spel and others make money on sports betting…?

Easy: just apply a markup to the probabilies/odds: Below an illustration, from a simulation run on my computer:

The blue line shows the cumulative returns given “fair odds”, i.e. odds that are a direct reflexion of the probability of the game outcome: for instance, if the probabilities for a given game are believed to be 1/3 each for WIN, DRAW, LOSS, then each of these outcomes would have odds set to 3 (decimal), or 1:2 (fractional) , that is, you’d get 3\$ back for your 1\$ stake, if you happened to win.  As can be seen from the graph, after a million games the blue line ends up a little bit above 0, meaning that the player, i.e. you, in this case would leave the casino – or betting shop – with a small gain.

The red line shows what happens to expected returns when I have applied a tiny markup to the probabilities/odds, as all betting shops or casinos do: the line grows almost monotonically towards the negative side, i.e. constantly accumulating wins for the casino/betting shop. That’s the “house advantage” at play.  In this simulation run, I’ve set the house advantage, or markup, to a rediculously low value, regardless, the result is clear, the house is making money.

Anyone wanting to take a guess on the house advantage set in this example…? 🙂

But remember that in sports betting, we are dealing with Unknown Unknowns. That means that to safeguard against potentially huge losses due to all the uncertainties involved in sports game outcomes, the betting shops need to apply a fairly hefty markup to their odds, otherwise the would run a clear risk of going bankrupt in the case when they have set way too high odds.

“Prediction is difficult, particularily about the future”.