Probability and Statistics (Part 3)

Probability and Statistics (Part3)

By Madison Nef

Expected Value: You Can Bet On It

 Expected value is calculated by multiplying probability and profitable outcome. An expected value is the weighing of odds you do before making a big decision; for example insurance. If considering insurance for a house you are buying, you need to take into consideration some of the things that could happen and their likelihoods. A good example is the chance of a house burning down. There is a good chance your house will NOT burn down, but then again, there is also a smaller chance that it will and if it does, it would be beneficial to have insurance because it could save a lot of money.

Another PERFECT example of expected value is the odds of playing the lottery. Everyone uses the same phrase “you can’t win if you don’t play” and then throws away roughly $10 a week on a stupid obsession that has horrible odds. Have you ever LOOKED at the statistics for the lottery?! It’s craziness! “Well I’ve looked, but someone always wins so why not me?” Let me put it this way: would you bet $10 a week that you would get hit by lightning? “No no, that’s ridiculous!” NO! Throwing away money to a corporation who won’t even give you the full jackpot if you DO somehow win is ridiculous… because you have a higher chance of being struck by lightning than winning the Powerball. Here are the statistics:

Powerball: 1 in 175,000,000 people win the jackpot
Lightning: 1 in 700,000 people per year die in the US alone from lightning strike and IN YOUR LIFETIME you have a 1 in 3,000 chance of getting struck by lightning.

Hell, if those statistics aren’t good enough for you… you have a higher chance of getting killed by a VENDING MACHINE than winning the lottery. That’s right- people die because of vending machines, in fact, 1 in 112,000,000 people are killed by a vending machine per year. If that doesn’t show you the error in your gambling, money-wasting ways… I don’t know what will. There is no help for you.

A roulette table has 38 possible spaces. An expected value is an expectation (winning or losing).

We have outcomes, and we weigh the probability of each outcome. Each outcome has a value- in roulette, for example:

If you bet 13, you have a 1/38 chance of winning. It is $10 to play. If you win, however, you get $350. This is all well and good, but you have a 37/38 chance of losing.

Therefore:

 vO (Value Outcome)for pO1 (winning) is +$350

vO (Value Outcome) for pO2 (losing) is -$10

A bet on red in roulette has a 18/38 chance of winning (net gain is +$10) and a 20/38 chance of losing. However, if you win, you gain $20. At $10 per bet, you are only earning $10, and upon calculating the expected value (18/38($10) + 20/38(-$10)) you are expecting a loss of 53 cents per bet you make on red.

This is the same expected value as if you bet on a singular number in roulette- the long term results are the same.
 Expected probability: Payoff x Probability + Payoff x Probability + Payoff x Probability… = expected probability