Gain Expected Gain means who much on average

Gain Expected Gain means who much – on average – you would expect to win if you played a game. Example: Mark plays a game (for free). He throws a coin. If it’s a Head he wins $1. If he throws a Tail he loses $1. What is his expected gain?

In a new game: Mark pays $1 to enter. If he gets a head he wins $3. If he gets a tail he loses $2. What is his expected gain?

1 In an attempt to create a really complicated game, and make some money, Mark makes a 2 4 3 spinner. 3 4 • He charges $5 to play the game. 2 1 • If a player spins a 1, the player loses the money they paid. • If they spin a 2, they get $2 back. • If they spin a 3, they get their money back. • If they spin a 4, they get their money back and $5.

• If a player spins a 1, the player loses the money they paid. • If they spin a 2, they get $2 back. • If they spin a 3, they get their money back. • If they spin a 4, they get their money back and $5. We make a distribution table for the Gains: g -5 P(G=g) 0. 25 -3 0. 25 0 0. 25 5 0. 25

g -5 P(G=g) 0. 25 -3 0. 25 0 0. 25 5 0. 25 The work out the Expected Value of this distribution: = -0. 75

This means that on average a player will lose $0. 75 for every game they play. Now try the Learning Workbook p. 6 Exercise B, Question 1

Two new words: Winnings: Similar to “gain”, but ignores the cost of playing the game. Fair: A game is ‘fair” if the expected gain is 0.

Now do the Learning Workbook p. 6 – 8 Exercise B.