More House Edge questions...

For the custom Chuck-A-Luck table we are making there are several additional bets that are simply a lift from Sic Bo. However, the payouts that I want to use are greatly reduced from typical Sic Bo payouts. Wonder if somebody could calculate the house edge on these various bets for me based on my payout schedule. I might be too aggressive and keep players away. But then again, it's a charity game.

"Specific triple": (i.e. 333, 444, 555) 40:1

"Any Triple" 10:1

"Odd/Even" 1:1 (loses on any triple)

"High/Low" 1:1 (loses on any triple)

"Total of Numbers"
4 = 20:1
5 = 10:1
6 = 8:1
7 = 5:1
8 = 4:1
9 = 3:1
10 = 2:1
11 = 2:1
12 = 3:1
13 = 4:1
14 = 5:1
15 = 8:1
16 =10:1
17 =20:1

" pick-a number 1-6"
One dice match = 1x wager
Two dice match = 2x wager
Three dice match = 3x wager

Thanks, as always, for your help.

Quote: Riva

For the custom Chuck-A-Luck table we are making there are several additional bets that are simply a lift from Sic Bo. However, the payouts that I want to use are greatly reduced from typical Sic Bo payouts. Wonder if somebody could calculate the house edge on these various bets for me based on my payout schedule. I might be too aggressive and keep players away. But then again, it's a charity game.

Let's look at the problems one at a time.

Quote:

"Specific triple": (i.e. 333, 444, 555) 40:1

There's one way to roll each specific triple, and 215 ways not to.
1/216 of the time, the house loses 40; 215/216 of the time, the house wins 1.
HA = 215 / 216 x 1 + 1 / 216 x (-40) = 175 / 216 = 81.02%

Quote:

"Any Triple" 10:1

6 rolls lose for the house, and 210 rolls win
HA = 210 / 216 x 1 + 6 / 216 x (-10) = 150 / 216 = 69.44%

Quote:

"Odd/Even" 1:1 (loses on any triple)
"High/Low" 1:1 (loses on any triple)

These are both the same: 105 rolls lose for the house, and 111 win.
HA = 111 / 216 x 1 + 105 / 216 x (-1) = 6 /216 = 2.78%

Quote:

"Total of Numbers"
4 = 20:1
5 = 10:1
6 = 8:1
7 = 5:1
8 = 4:1
9 = 3:1
10 = 2:1
11 = 2:1
12 = 3:1
13 = 4:1
14 = 5:1
15 = 8:1
16 =10:1
17 =20:1

Let's see if you can figure these out - out of the 216 possible rolls, the number of times each one comes up is:
4: 3
5: 6
6: 10
7: 15
8: 21
9: 25
10: 27
11: 27
12: 25
13: 21
14: 15
15: 10
16: 6
17: 3

Quote:

" pick-a number 1-6"
One dice match = 1x wager
Two dice match = 2x wager
Three dice match = 3x wager

For any particular number - let's say 6:
1 of the 216 rolls has 3 6s; the house loses 3
15 rolls have 2 6s; the house loses 2
75 rolls have 1 6; the house loses 1
125 rolls have no 6s; the house wins 1
HA = 125 / 216 x 1 + 75 / 216 x (-1) + 15 / 216 x (-2) + 1 / 216 x (-3) = 17 / 216 = 7.87%

Note that the 1-2-3 payout you use is the actual payout traditionally used in Chuck-A-Luck.

Thank you, ThatDonGuy, for this information.

Obviously, some of these numbers are horrific bets. I know that 90% of the time, the players will stay on the "pic-a number 1-6",
"high/low & odd even" and, to a lesser degree, the field bet. 10% of the time the player will say "oh what the heck" a toss a shekel on the goofy bets. That becomes almost a free gift in by books. Plus, we have a $5 per-spot max bet limit so, the worst I can hurt on any one bet is $200 (however, I might limit the "specif triple" and "total of numbers" to a $1 max bet, just to be safe).

Frankly, we get a ton of mileage when we have to make a big payout. On our big six money wheel, we pay 40:1 on the joker or the flag. When somebody hits on one of those, all hell breaks loose, particularly when it's a $5 wager (pays $200). It brings in more players like flies. Probably pay on the joker or flag 4 times per night.