The concept of “Expected Value” is a key concept for market traders and more particularly to this article and our expertise, Sports Investment – the exploitation of sports investment markets for profit opportunities.
Expected value is what keeps professional black jack players playing when they are down “in the hole” $200,000. Expected value is what keeps a professional sports bettor wagering when they are 2-8 in their last 10 positions. Expected value is how hedge funds create algorithms to capitalise on price movements in the stock and futures markets.
So, in layman’s terms, what is Expected Value?
EV is the money you expect to win (or lose) statistically by participating in any “event” – whether a hand of poker, a spin of a roulette wheel, or a wager on a sporting event. It is your mathematical advantage (or disadvantage) in games of chance and skill. This is the advantage that a casino exploits to gradually take money away from you when playing games such as roulette, craps, slot machines and continuous multi-shuffle blackjack.
Let’s take a simple example using a dice – something everyone is familiar with.
Obviously a dice has 6 numbers printed on it, in a statistical event these are called “outcomes”. 1, 2, 3, 4, 5, & 6. So we have six possible outcomes. Each roll of the dice gives us a result with a “one in six” chance of occurring as all are equally likely.
To calculate the expected value, we need probabilities, so let’s calculate the probability of any one number occurring. 1 / 6 = 0.166
We can multiply each of the outcomes on the dice (1 through 6) by their probabilities to get the expected value.
1 x 0.1667 + 2 x 0.1667 + 3 x 0.1667 + 4 x 0.1667 + 5 x 0.1667 + 6 x 0.1667 = 3.5
This figure can then be used in games of chance to calculate who has an advantage in a dice gambling game.
Suppose a casino is willing to pay us a dollar amount corresponding to the number on the dice (such as you roll a 2 you win $2 and so on) – with two caveats:
1) our wager must be $3 and 2) if we roll a 6 we lose our stake. Is this an attractive game for us to wager on?
In this game we have 5 profitable outcomes of equal probability, but with unequal payoff.
To get the expected value we calculate the games return by calculating the expected value – which is essentially an average of the return. We use the probabilities multiplied by the return.
So we have 5 options that give us a financial result:
0.1667 x 1 + 0.1667 x 2 + 0.1667 x 3 + 0.1667 x 4 + 0.1667 x 5 = 2.5
and one losing payoff for rolling 6 (a return of zero): 0.1667 x 0 = 0
All together we have:
0.1667 x 1 + 0.1667 x 2 + 0.1667 x 3 + 0.1667 x 4 + 0.1667 x 5 + 0 = 2.5
Since the cost of playing the game is $3, we have 100% probability (probability of 1) of paying $3 to play, represented by -3 x 1 = -3
adding this to the equation gives us: -3 + 2.5 = – 0.5.
So for every game played with an outlay of $3 we can expect to lose 50c as an Expected Value. Obviously when playing we willl win some games by rolling a 4 or 5, and some games we lose a dollar or two, but with a profit expectation that is negative, this is a typical casino game – a game of “negative expectation”.
In your investing, and sports betting, look to select positive expectation situations, these are the only situations where you will create wealth for yourself long term.
Dr. Sport. – aka – Sam J. Perry.
