Shake a Day 'edge' calculation...

A lot of the bars in the small town I'm in have a shake-a-day where a person can shake 5 dice in hopes of getting a 5-of-a-kind for the progressive jackpot of all the $$ that has been put in the pot by previous shakers. Often a full house, four of a kind and/or a straight get a free drink token (worth up to $6 if you get a microbrew or cheap glass of wine).

So the odds of getting 5-of-a-kind with 5 six-sided dice is 1/1296. A shake costs $.50, once per day, and 10% of the jackpot is withheld for the next pot. So I figure ($1296 * 1.1)/2 = $712.8 is the break-even point for a zero 'house' edge on the shake. This is disregarding the value of a free drink from full houses, straights and 4oaKs.

My question is how would one calculate the edge the player has when the jackpot gets to $x. Right now the biggest jackpot in town is $1560, what is the edge on that?

Last three shakes I've gotten a full house every time, each 'worth' $3.50, so I've essentially already won. :)

Quote: drussell0208

So the odds of getting 5-of-a-kind with 5 six-sided dice is 1/1296. A shake costs $.50, once per day, and 10% of the jackpot is withheld for the next pot. So I figure ($1296 * 1.1)/2 = $712.8 is the break-even point for a zero 'house' edge on the shake. This is disregarding the value of a free drink from full houses, straights and 4oaKs.

My question is how would one calculate the edge the player has when the jackpot gets to $x. Right now the biggest jackpot in town is $1560, what is the edge on that?

Last three shakes I've gotten a full house every time, each 'worth' $3.50, so I've essentially already won. :)

We will refer to fifty cents as one unit, and thus, you have a 1/1296 probability of winning 90% of 3,120 units, which is 2,808 units:

(2808 * 1/1296) - (1295/1296) = 1.1674382716

In other words, you expect to win 1.1674382716 units, which is an expected win of 0.5837191358.

1/1296 of the time, you win 0.9 times the jackpot, and the other 1295/1296 of the time, you lose 0.5 dollars.
This does not take into account the value of the free drinks.

Your edge is (0.9 J - 1295 x 0.5) / 1296 = (9J - 6475) / 12960, where J is the jackpot in dollars.
The break even point is J = 6475 / 9 = 719.444.

For J = 1560, the player edge is 58.37%.

Thank you both for the calculations!