Casino Game Puzzle #2

You own casino #2. A bright young employee suggests a new game. Players will pay a fee to enter. Then they engage in a series of 50/50 coin tosses. If their first tail occurs on turn 1, they get $1. If their first tail is on turn 2, they get $2. If their first tail is on turn 3, they get $3. If it's on turn 4, they get $4. Their potential winnings at each turn are equal to the turn number. They can flip until they flip a tail, or they can declare a tail at a turn they have successfully arrived at, and take the winnings for that turn. After they flip a tail or declare a tail, they take their winnings and the game is over.

You know what your target profit margin is, but to establish a profitable fee for this game, you need to know the break-even point; the point at which the income from the fee covers, at least, the payouts to winners over time. How much would you need to charge as an entry fee, to at least, break even in this game, over time?

Same as previous post except the sum(E(payout)) is a function that approaches $2 which is the break even price. Pick a margin, say $0.50 and you have your entry price of $2.50.

Link to other post: http://www.redhotpawn.com/board/showthread.php?subject=Casino_Game_Puzzle&threadid=138453

Originally posted by andrew93
Same as previous post except the sum(E(payout)) is a function that approaches $2 which is the break even price. Pick a margin, say $0.50 and you have your entry price of $2.50.

Link to other post: http://www.redhotpawn.com/board/showthread.php?subject=Casino_Game_Puzzle&threadid=138453

Yes. It would be interesting to see what profit margin would make the most money from a population and how it could be maximized by jazzing up the game to enhance the psychological rewards for playing. The Vegas statisticians and the Vegas psychologists both have a role in these games of chance.

That would be a function that would measure demand versus supply. Given enough data and research I'm sure the sweet spot could be found. And as you say, you can attempt to manipulate the demand side of the equation to up that price.

Furthermore, you restrict the supply of such games to also try to keep the price up, while minimising the opportunity cost of customers who don't want to wait their turn.

There is one other key measure and that would be the throughput rate - how many punters can you push through one 'game' in an hour. You could partially remove / exploit this constraint by inviting others to also place bets on the outcome......but that's another subject.