Another way to define a fair game is that a player’s probability of winning must be equal to the player’s share of the pot of money awarded to the winner. All money is put into a pot at the start of the game, and the winner claims the entire amount that is in the pot. (Compare this definition to that in Exercise 31.)
(a) The player and the host each put $20 into the pot. The player rolls a die and wins the pot if the die produces an even number. Is this game fair to the player?
(b) A player at a casino puts $1 into the pot and names a card from a standard deck (e.g., ace of diamonds). The casino puts $99 into the pot. If a randomly selected card matches the choice of the player, the player wins the pot. Is this game fair to the player?