Back in the Grymindor common room, Ron was showing Harry the latest magic from the Weasley shop and these are the dice we should use when gambling." "Hold on, Ron,"replied Harry. "They look normal to me." "Wot when you roll them. The way they work, if either dice come up a '6' then both dice will magically be 6: Remember that dice game we played the other day -- betting on the sum of the two dice? As you recall, in a fair game, here's the price to play, probabilities, and payoffs:" Sum to Two 6-sided Dice 2 3 4 5 6 7 8 9 10 11 12 Pribe to Play / $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 Probability / 1/36 2/36/3/364/36/5/366/365/364/36 3/36 1/36 Winning Payoff $36.00 $18.00 $12.00 $9.00 $720 $6.00 $7.20 $9.00 $12.00 $18.00 $36.00 "We can use these dice to our advantage." "Let me see if I understand this," said Harry, scribbling on an used part of the Daily Prophet. "If my calculations are right, for example, the sum can never be 11." "You got it. Since an 11 is a '5' and '6; the one '6' will magically change the '5' to a '6, giving you a sum of 12. You can still get numbers like 7. '3' and '4 '2' and '5. But not '6' and '1: The '1' will change to a 6 6' and '1' will become '6' and '6, with a sum of 12. What's the plan, Ron?" "What's the plan, Ron?" "Well, just to avoid being too obvious, we'll go long on '12' and short '9. "Great By the way, where did your brothers get the idea for these?" "Professor Banko's class." "The muggle?" "Yeah. Turns out you need some magic to get through that class!" What is your expected payoff to Ron's strategy? Enter your answer in dollars and cents, rounded to the nearest cent, with no punctuation. For example, if your answer is $5.286, enter "5.29