Choose a gambling game. Describe it, and find the expected value of playing the game. Is it fair? Why or why not?
Ans : I have chosen betting on black/red on roulette wheel
There are 18 black slots, 18 red slots and two green slots (0 and 00) on a US roulette wheel*.
Your chances of hitting a black or red are equal,
I.e. Expected value of getting a black or red slot = 18/38= 47.4%. This translates to a 52.6% probability that the house will be scooping up all your chips on a black/red bet. The 5.26% 'spread' is known as the house edge.
Let's say if you bet a $1 on black. If the dice ends up on black, I will get my $1 back and an additional $1 but if it doesn't end up on black, I will lose my one dollar
Expected value of winning = (18/38)*1 - (20/38)* -1
= -0.0526
Since the expected value is negative, the game is not fair. I am expected to lose approximately $0.05 per game in the long run if I keep betting on black
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