new casino game, whats the odds?

In the casino where I work, I recently got a preview of a new casino game in the uk, and have my doubts on the mathmatics of it, I believe it gives a negative house edge.
The factors are 3 dice and you can bet on the outcome of these. the bet I have inquestion is what is the chance of rolling no six with all 3 dice being thrown together.

5/6 x 5/6 x 5/6 = 125 - number of throws with no six included
6/6 x 6/6 x 6/6 = 216 - total possible outcomes
This displayed as a percentage is 57.87%

However the house pays out at odds of 3/5 on this outcome. £5 bet wins £3, stake returned.
so if a player places £100 bet on this outcome they will win £60 and there stake returned.
this as a percentage is 60%

In my opinion the table is paying out 60% when the actual probability is only 57.87% creating a negative house edge.

Am I correct in what I say or is there something Ive overlooked in my equation.
Your thoughts and help are greatly appreciated.
Cheers for the great site!!!!!!

It looks to me like you got the math right.

Are you sure about the rules and the payout?

Don't say anything to the bosses and let them put it out there. Then start betting the max and get richish. Also, notify us when and where it comes out so we can get our plane tickets to England lined up ... :)

Edit: Me bad at maths

Quote: spacecat2000

In the casino where I work, I recently got a preview of a new casino game in the uk, and have my doubts on the mathmatics of it, I believe it gives a negative house edge.
The factors are 3 dice and you can bet on the outcome of these. the bet I have inquestion is what is the chance of rolling no six with all 3 dice being thrown together.

5/6 x 5/6 x 5/6 = 125 - number of throws with no six included
6/6 x 6/6 x 6/6 = 216 - total possible outcomes
This displayed as a percentage is 57.87%

However the house pays out at odds of 3/5 on this outcome. £5 bet wins £3, stake returned.
so if a player places £100 bet on this outcome they will win £60 and there stake returned.
this as a percentage is 60%

The player loses if a six is rolled. So the player loses 1 unit on 91 of the outcomes. The player wins 3/5 = 0.6 units on 125 of the outcomes. Hence the EV is:

EV = (91/216)*(-1) + (125/216)*(0.6) = -0.07407,

so the house has an edge of 7.407%.

I agree with the 7.407% house advantage.

Over 216 rolls, assuming a $100 bet, the player will lose 9,100 dollars (91 x $100) and win $7,500 (125 x $60). These will lose then $1,600 over 216 rolls or an average of $7.41/roll.

The mistake in the "math" here is that although the odds of indeed throwing no sixes is indeed 125/216 = 57.87% and the payout is 0.6 units doesn't mean that this is a good game. The comparison here is saying that the odds of throwing a twelve in craps is 1/36 = 2.778% but the payout is 30 units... must be awesome!!! It is not awesome. The house advantage is (1 / 36) x 30 - (35 / 36) = 13.89%

Nope, you have to take all of the outcomes into consideration, which is that on 42.13% of the rolls you will lose 1 unit and therefore across all combinations: (125 / 216 ) x .6 + (91 / 216) x -1 = -.07407 = 7.407%

In fact, the break even point for this bet would be if they paid you .728 unit on a winning bet. (125 / 216) * .728 - 91/216 = 0

So hold off on purchasing those plane tickets.

Thank you all for your thoughts and time in answering this for me, I really appreciate it.
Cheers