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# Jason Arhart: Why Gambling Theory Matters

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I’ll talk about the core concept in gambling theory and why, far from being limited to games of chance, it is a universal principle that applies to every decision you make.

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### Jason Arhart: Why Gambling Theory Matters

1. 1. Why Gambling Theory Matters
2. 2. Expected Value (EV) Weighted average of all possible outcomes Quantifies what you can expect to gain, on average A fundamental concept in gambling theory... And in life
3. 3. Example 1: A Coin Flip Game Two-player game We each put \$1 on a table You flip a coin Heads: you win the money on the table Tails: I win the money on the table
4. 4. Example 1: A Coin Flip Game Probability is 50/50 Heads: you win \$1 Tails: you lose \$1 You can expect to break even on average. The expected Value is \$0.
5. 5. Calculating Expected Value Consider all possible outcomes Multiply the value of each outcome by the probability of that outcome Add up all of those products The result is the expected value
6. 6. Example 1: A Coin Flip GameCalculating Expected Value Outcome Value Probability Heads \$1 0.5 \$1 x 0.5 = Tails -\$1 0.5 \$0.50 -\$1 x 0.5 = -\$0.50 EV = \$0
7. 7. Using EV to Make Decisions Consider all of your options Calculate the expected value of each option Choose the option with the highest EV In many cases your decision is simply whether or not to gamble.
8. 8. Example 2: Six-Sided Die You put \$1 on the table I put \$6 on the table You roll a 6-sided die Roll a 6, you win the money on the table Roll anything else, I win the money on the table
9. 9. Example 2: Six-Sided Die You only win if you roll a six You are five times as likely to lose as to win You can expect to lose most of the time. Should you play this game?
10. 10. Example 2: Six-Sided DieCalculating Expected Value Outcome Value Probability 6 \$6 1/6 \$6 x 1/6 = \$1 Other -\$1 5/6 -\$1 x 5/6 ≈ -\$0.83 EV ≈ \$0.17
11. 11. Life Is Gambling In the last example, even though you are five times as likely to lose, the expected value is a win. If you played the game repeatedly, over time you could reasonably expect to win an average of (almost) \$0.17 per game. Many decisions in life resemble this game
12. 12. Life Is Gambling Most sales contacts dont result in a sale. Most start-ups fail. Most movies lose money at the box office. There are many more examples. These games are winnable if you keep playing.
13. 13. Insurance For when the worst case is unacceptable You accept a lower EV in exchange for a better worst case scenario It is almost always a mistake to insure what you can reasonably cover yourself
14. 14. Insurance For when the worst case is unacceptable You accept a lower EV in exchange for a better worst case scenario It is almost always a mistake to insure what you can reasonably cover yourself Not all insurance is called insurance!
15. 15. When Insurance Isnt Called Insurance
16. 16. Extended Warranties Extended warranties are a type of insurance Usually 10% of the cost of the item In most cases you could replace it yourself Unless you are more than 10% likely to need the item replaced within the warranty period, purchasing the warranty is -EV.
17. 17. Extended Warranties Extended warranties are a type of insurance Usually 10% of the cost of the item In most cases you could replace it yourself Unless you are more than 10% likely to need the item replaced within the warranty period, purchasing the warranty is -EV. Selling extended warranties is +EV for the stores, otherwise they wouldnt sell them.
18. 18. Gambling Theory Matters