A Bet On The Side
Mr. Gamble and Mr. Prude went to the CycleChat 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) CycleChat Casino?
2) Mr. Gamble?
3) Mr. Prude?
Results may be rounded to the nearest penny.