Dween
Joined: Jan 24, 2010
• Posts: 339
September 14th, 2010 at 5:05:14 AM permalink
Intro
On the 70's-80's game show High Rollers, the bonus round was simply a game of Shut the Box. The consolation and grand prizes varied during the years, but the rules stayed the same.

Even if you are not able to mathematically determine an answer, I'd like to hear some guesses and estimates thrown out for any and all questions.

Rules
The numbers 1-9 were lit up. Player rolled a pair of dice, and would knock out numbers that matched the total of the dice. For example, dice totaling 9 could knock out 9, 1+8, 2+3+4, etc. The number 1 could never be knocked out by itself. If the player could knock out every number, they win the grand prize. If they rolled a number that could knock out no other numbers (a "bad roll"), they would win \$100 per number previously removed. Partial knockouts are not allowed, so a roll of 7 could not knock out a 3 by itself.

Questions
1. Assume the grand prize is \$5,000. What is the most money you would pay to play this game?

2. Assume the grand prize is \$10,000. Now what's the most you would pay?

3. On early versions, players could choose to stop at any time and take \$100 per removed number. A bad roll would end the game, and the player would win nothing. How does that change your previous answers?

Extra Credit
To really complicate your calculations, there is an extra rule that gives the players an advantage on the show. If a player rolled Doubles of any kind, they would receive an Insurance Marker. If they made a bad roll and had a Marker, they could turn in the Marker and roll again. There was no limit to the number of Markers a player could have. If a player makes a bad roll that itself is Doubles, the Marker they would receive is used instantly, in effect letting them roll again for free.

4. Given the possibility of receiving Insurance Markers, what would you pay to play for a possible \$5,000 or \$10,000 pay out?

5. Is it possible to determine the odds of winning this game mathematically, with or without Insurance Markers? Or is it best left up to brute force?
-Dween!
Dween
Joined: Jan 24, 2010
• Posts: 339
September 22nd, 2010 at 5:22:36 AM permalink
I want to bump this back to the top. Does anyone have a wild guess they want to throw out there for any of this?

Sidenote: I found a webpage showing some details of how Shut the Box could be played as a casino game. Do you find it feasible?
-Dween!
Ibeatyouraces
Joined: Jan 12, 2010