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The Sociology of Risk

The Sociology of Risk. Objective Probabilities Goals: To understand how to calculate objective probabilities To recognize that our understanding of objective probabilities is shaped by our perceptions. Risk and Uncertainty. Arnoldi defines ‘risk’ as potential dangers

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The Sociology of Risk

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  1. The Sociology of Risk Objective Probabilities Goals: To understand how to calculate objective probabilities To recognize that our understanding of objective probabilities is shaped by our perceptions

  2. Risk and Uncertainty • Arnoldi defines ‘risk’ as potential dangers • Risk usually refers to negative events, but ‘risk’ is sometimes used in a generic ways for positive and negative events • Probability is implied in the definition (i.e., ‘potential’) • ‘Risk’ refers to a situation where the probability of the event can be calculated • ‘Uncertainty’ refers to a situation where the probability of the event cannot be calculated • There is a difference between objective and subjective probabilities

  3. Subjective probability • Subjective probabilities depend on the person making the assessment • Compare a coin flip to a horse race – what is the difference? • Some events/games are not repeatable

  4. Objective Probability • “An objective probability is a probability that everyone agrees on” (Amir D. Aczel. 2004. Chance: A Guide to Gambling, Love, the Stock Market, & Just About Everything Else.) • Probability is the ratio of the number of times the desired outcome can occur relative to the total number of all outcomes that can occur over the long run. • Probabilities are often expressed as ratios and/or proportions.

  5. Coin example • The probability of a ‘heads’ on one flip of an honest coin=1/2=0.5 • The flip of a coin is a purely random event – we cannot predict the outcome of one flip with certainty • We can predict that the proportion of heads over many flips is 0.5 • As the number of flips increases, the proportion will center on the value of 0.5

  6. Coin example • Elementary outcomes: heads, tails • This is an equal probability process

  7. Dice example • The probability of a ‘6’ on one roll of an honest die=1/6=0.1667 • The roll of a die is a purely random event – we can’t predict the outcome of any one roll • We can, however, predict that the proportion of 6s over many rolls is about 0.1667 • As the number of rolls increases, the proportion will center on 0.1667

  8. Dice example • Elementary outcomes: 1, 2, 3, 4, 5, 6 • This is an equal probability process

  9. Basic rules for more complex events… • The ‘or’ rule (when to add) • The probability of a 1 or a 6 on one roll of an honest die=1/6+1/6=2/6=0.333 • The ‘and’ rule (when to multiply) • The probability of a 6 and a 6 on the roll of two honest dice=1/6*1/6=1/36=0.0278

  10. Coin example • Four flips of an ‘honest’ coin and the number of heads • This is a binomial process • Both outcomes (heads and tails) are equally likely so there is a uniform distribution for one flip • There is NOT a uniform distribution for multiple flips – with 4 flips there are 5 possible outcomes but 16 ways to get them

  11. Other Games – the Lottery • It is possible to calculate the objective probability of many games… • Lottery (6 balls numbered 1-54) • You need the 1 correct set of six numbers out of the 25,827,165 possible unique combinations of six numbers • …So don’t play the lottery

  12. Roulette • A roulette wheel has 38 buckets: • 36 numbers (1-36) • 0 (green) • 00 (green) • 2 colors for the 36 numbers: red and black • The house has a built-in advantage (because of how it sets the bets – for example, 35 to 1 for a single number); it wins over the long run

  13. Blackjack • What makes Blackjack so interesting is that it is based on continuous probability; the probabilities actually change during play with each passing card…it is a game with a memory; this is what makes it possible to beat the casino (assuming an auto shuffler is not used after every hand with replacement) • Basic rules • Closest to 21 wins; tie=‘push’ • Ace=1 or 11 • 2-9=face value • 10, J, Q, K=10 • Dealer must hit until sum totals 17, 18, 19, 20, or 21 • Blackjack=21 on two cards; beats all but dealer blackjack, pays 3 to 2 • Plays: hit, stay, split, double down (double bet for 1 card), surrender (you get 50% of your bet back), insurance (costs half of current wager, pays 2 to 1 if Blackjack 21)

  14. Blackjack • The longer you play, the greater the likelihood that you will lose everything, but you can improve your chances by following basic strategy…

  15. Blackjack • Counting cards – the Hi-low System • Developed by MIT Professor Edward Thorp • Simulations show that when low cards (7 and under) are left in the deck, the odds favor the dealer; high cards (9 and up) favor the player • The Hi-lo system is based on a running tally, not memorizing every card • +1: 2-6 • -1: 10, J, Q, K, Aces • 7, 8, 9 are not counted • You increase your bet when the count is high • An equation determines how much to raise the bet (count/number of decks not seen); also incorporate house advantage

  16. Probabilities are confusing • Calculating objective probabilities is not always easy, but it can be done • Despite this, many problems/games confound people because they are non-intuitive • Monty Hall Problem / Let’s Make a Deal • http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html • Contestant selects one of three doors • From the remaining two doors, the host selects one non-winning door • The contestant is asked: stay with their original selection or change doors? • What should they do? • Probability of picking the winning door is 1/3 • Probability of not picking the winning door is 2/3 • When one of the non-selected doors is revealed, the probability for the two non-selected is still 2/3 • So the probability of switching and winning is 2/3 • The probability of not switching and winning is still 1/3

  17. Monte Hall vos Savant, Marilyn (1990). "Ask Marilyn" column, Parade Magazine p. 16 (9 September 1990).

  18. Paul the Octopus • Paul the octopus picked the winner of 8 straight soccer matches in 2010 FIFA World Cup • Is Paul some sort of soccer genius?

  19. Paul the Octopus You didn’t hear about the other 255 animals that didn’t predict as well as Paul…

  20. Perceptions of Objective Probabilities • Things casinos do: • Pictures of recent big winners with checks • Slots that flash, have sirens, and falling coins – these draw our attention • Use of chips instead of US Dollars • Biases: • We have selective memory • We suffer from hopeful thinking • We use faulty logic • Gambling versus counting • Good ‘cheats’ don’t always win; they utilize information to increase their chances • They must be subtle or it won’t work

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