Mr. Gamble and Mr. Prude went to the Brain Den Casino, which offered the following game:
A customer bets on a number on a die (1 through 6). The dealer rolls a single die. If the customer’s number comes up, he is paid 4 times his bet, if not - customer loses his bet.
Without delay, Mr. G makes his mind to play 5 rounds betting $1 on number “1” each time. Mr. P, believing the game is in favor of the house offers a side bet, whereby if after 5 rolls Mr. G ends up behind he must pay $5 to Mr. P, otherwise Mr. P pays $5 to Mr. G.
After 5 rounds, what is the average payoff to:
1) BrainDen Casino?
2) Mr. Gamble?
3) Mr. Prude?
Results may be rounded to the nearest cent. Calculators are allowed.
Answers obtained by way of computer simulations may not claim the “best answer” spot.