place 5 or 9 pays 3 to 2... positive expectation?

I have a charitable casino nearby that has low minimums and maximums and pays 3 to 2 on a winning 5 or 9 place bet. That win is usually 7 to 5, right? 3 to 2 is the same as 7 1/2 to 5. The tradeoff is the 6 & 8 pay only even money on a winning place bet, but one can of course simply choose not to place those numbers. I feel silly for having not looked to see what the 4 and 10 payoff was.

Supposing 5 & 9 do have a positive expectation, could someone better at math than me calculate two things for me: If I bet $4 on the pass line and place the 5 & 9, what is the overall house edge? Second, if 5 & 9 do have a positive expectation, what is the optimal strategy for betting them? Keep the bets up till the table 7ms out or take them down after getting paid once?

Thanks for any help.

There is no bet on the table that has a positive expectation. I will let the math gurus on this site do the numbers for you.

Hint: what's the payout on the free odds bet on the 5?

Quote: snowngr

I have a charitable casino nearby that has low minimums and maximums and pays 3 to 2 on a winning 5 or 9 place bet. That win is usually 7 to 5, right? 3 to 2 is the same as 7 1/2 to 5. The tradeoff is the 6 & 8 pay only even money on a winning place bet, but one can of course simply choose not to place those numbers. I feel silly for having not looked to see what the 4 and 10 payoff was.

Supposing 5 & 9 do have a positive expectation, could someone better at math than me calculate two things for me: If I bet $4 on the pass line and place the 5 & 9, what is the overall house edge? Second, if 5 & 9 do have a positive expectation, what is the optimal strategy for betting them? Keep the bets up till the table 7ms out or take them down after getting paid once?

Thanks for any help.

5 and 9 have a zero expectation of gain at 3:2. That being said, it is also a zero expectation of loss, too.

Math math math.

There are 4 ways to throw a 5 or 9. There are 6 ways to throw a 7.

House advantage, place 5 and 9, 7-5 payout: 1.4 x (4 / (4+6)) - 1 x (6 / (4+6) = (5.6 - 6) / 10 = -.4 / 10 = 4%.

Go ahead and do the math on 3-2 payout.

On the pass line, it's always 1.414 percent with no odds.

Putting them together depends on whether you leave the 5 and 9 "on" during the comeout roll.

-Tim

You could skip the pass line and just play the 0 edge 5 and 9 all night long. But that wouldn't be very charitable... :)