Regular readers know that I don’t care much about football. Still, thanks to the beautiful game, these days when I tell people that I studied at the University of Leicester, they don’t ask me, “ati where?”. This is because, against all predictions, the Leicester City Football Club — the Foxes — are at the top of the English Premier League (EPL).
So unexpected was the team’s performance that bookmakers (betting companies) in Britain were offering odds of 5,000-to-one on bets of a Leicester win. That was before the season started. That is, for every pound wagered, they’d pay 5,000!
That’s the thing about sports: it is very difficult to predict the outcome. In fact, it boils down to almost random guesswork! So all those people participating in sports betting are deluding themselves if they think there is a way of picking winners. There is none — just close your eyes and select at random!
In such cases, bettors are at the mercy of the laws of probability. So the question is, what is the probability of winning the jackpot?
For those readers who, like me, don’t participate in this new craze, here is how it works. The betting card has 13 matches. For each match, bettors predict which team will win or whether it will be a draw.
Thus for each match, there are three possible choices: team-1 wins or team-2 wins or a draw — signified by an “X”. There are different prizes for different numbers of correct predictions but the jackpot is for predicting all matches correctly.
Suppose there were just two matches featuring A v/s B and C v/s D: how many outcomes are possible? Well, they are: A-C (meaning A & C win); A-D; A-X; B-C; B-D; B-X; X-C; X-D; X-X. These are a total of nine possibilities. Thus, with two matches, the probability of winning the jackpot is one-out-of-nine, that is, 0.111.
A closer look at the possible outcomes from two matches reveals a simple pattern. There are three outcomes in which A wins the first match, three others where B wins the first match and yet another three where the first match is a draw. Therefore, the total number of outcomes is, 3x3 = 9.
Clearly, if there were three matches, then the number of possible outcomes is simply 3x3x3 = 27. So, following this same pattern, it turns out that the total number of possible outcomes with 13 matches is three raised to the power of 13; that is 3x3x3x3x3x3x3x3x3x3x3x3x3x = 1,594,323.
In other words, the probability of winning the jackpot is almost one-out-of-1.6 million. Do you feel that lucky?
We can turn this result on its head: it means that for every jackpot winner, there are about 1.6 million losers! You see; betting is a zero-sum game. For you to win, there must be losers — very many losers. Perhaps the licence rules should be changed to require the betting companies to declare how much money people are losing in each bet.