How do you figure house edge on "wheel games?"

Sorry if this is on WoO already.

Has a monte carlo night was pretty much all "wheels" tonight for reasons I will not get into publicly. I knew these wheels had a house edge that makes 6:5 and center-bets look good, but wow they are killers. With table games I limit bets so my bank doesn't break. This game I didn't go thru one working stack. Which made me wonder if I was calculating house edge right.

Two wheel games. First was a "horse race" where you bet on 1 of 10 horses. Within that horse are five different odds payouts. lets say 2-3-4-5-8. Am I right in figuring the house edge is 1-(.10 * average of odds) or 1- (.10 * (22.5)) or 1- (.10 * 4.4) = 5h% if it had these payouts? (actual odds were higher, this was for example.)


Second wheel was a "dice wheel" or "little 6" as some churches called it when I was a kid. 6 numbers to bet, dice per slot. Number of dice is your payoff, if any. E.G.: if you bet a 2 and the dice show 2-2-3 you get 2:1 and the person who bet 3 gets 1-1. Anyone else loses. Given the dice are even and equal in the wheel you at bets have a 50:50 shot of 1-1 payout. (six numbers to bet, three different ones at most can come up.) If it weren't so late I'd take a guess how to calculate edge here but I will probably get it wrong and Wiz or MathExtremist will wonder if I can even count. (just kidding guys.)

BTW: now I know how they bought the candleholders in gold.

Quote: AZDuffman

I didn't go thru one working stack. Which made me wonder if I was calculating house edge right.

I think you're experiencing the difference between 'edge' and 'hold'.

Dice Wheel:
The wheel is large, but it does not have every one of the 216 combinations on it.
It may have each unique combination... or it may have a spread that makes the odds of each number equal.
A Google Image search shows a number of different dice wheels, so it's hard to say which one was being used at your charity night.

Horse Race Wheel:
The ones I have seen usually have payouts of 3, 4, 5, 6, 7 and 3 again. Average of 4.666 per win. With 10 horses, it should be easy to determine the HE.

Quote: Dween

Horse Race Wheel:
The ones I have seen usually have payouts of 3, 4, 5, 6, 7 and 3 again. Average of 4.666 per win. With 10 horses, it should be easy to determine the HE.

So am I correct, take the average win, multiply by the % of winning that horse, and subtract it all from one?


Another thing on the dice wheel came to me later. Part of the advantage is in the combinations. Lets say 6 people flat bet one unit on each of the numbers. You can have the following results.

1 person wins 3:1 and the rest lose. House rakes 5 losse and pays out three winners. 5-3 = hold of 2 units.

1 person wins 2:1, one 1:1 and 4 lose. House rakes 4 losses and pays out 3 winners. 4-3 = hold of 1 unit.

3 people win 1:1 and 3 lose. House rakes 3 losses and pays out 3 winners. 3-3 = hold of 0 units.

So now I know why the carneys are so happen when "3 of a kind" comes up.

The dice game is chuck-a-luck and I think it's on the Wizard of Odds site. This one is crafty because it tricks people into thinking it's a 100% payout, when it is not.

On the horse game, you calculated thsi correctly if you are paying "x for 1" and not "x to 1.". If you are also returning the original bet, then the house iedge is 0.1 less.

Quote: CrystalMath

The dice game is chuck-a-luck and I think it's on the Wizard of Odds site. This one is crafty because it tricks people into thinking it's a 100% payout,when it is not.

I thought chuck-a-luck involved drawing balls like keno? I know that what I heard it called may be wrong as the church didn't have many gambling people running it. (I fought with them every year saying the flag and joker paid more than 20:1 and it was costing them as there were 2 $20s and one each flag/joker and who would play them?

Quote:

On the horse game, you calculated thsi correctly if you are paying "x for 1" and not "x to 1.". If you are also returning the original bet, then the house iedge is 0.1 less.

I pay "to one" when I work that one. To pay "for one" on that game is to tell the guy who's car you stole he didn't leave a full tank of gas.

https://wizardofodds.com/chuckaluck

The marks thinking is "Gee, I bet on 6. There's 3 dice, so 3 chances to hit my number. 6 sides on the dice. 3 is half of six. If I hit my number I win half the time. Plus they pay a bonus if I hit twice or three times! Woohoo!"

Of course, the chance of hitting your number is 1 - the chance of all missing, which is 5/6*5/6*5/6 => 125/216. Only 43% of the rolls have your number. And the pay off on doubles and trebles doesn't make up for this.

7.8% house edge... and I guess a relatively low variance, so you'll be doing okay as the house.

Thats for the dice game, if your small 6 wheel has less than 216 slots, then who knows... you could probably engineer that to have even better edge for the house.

Quote: thecesspit

https://wizardofodds.com/chuckaluck

Nope, similar but not identical. I suppose the wheel is imitating the dice on the real thing, but here you only had one choice, the number. This may explain some people who thought betting a six paid off if three 2s came up.

Quote:

The marks thinking is "Gee, I bet on 6. There's 3 dice, so 3 chances to hit my number. 6 sides on the dice. 3 is half of six. If I hit my number I win half the time. Plus they pay a bonus if I hit twice or three times! Woohoo!"

When I came to this site I would not have believed that. After reading here and doing the dealing at the parties (which started a year before WoV) I can believe a mark is thinking anything. Less than 1 in 4 ask about if "sixteen ways to win in the field" is good.

Quote:

Of course, the chance of hitting your number is 1 - the chance of all missing, which is 5/6*5/6*5/6 => 125/216. Only 43% of the rolls have your number. And the pay off on doubles and trebles doesn't make up for this.

7.8% house edge... and I guess a relatively low variance, so you'll be doing okay as the house.

The house did even better than I thought it would and I assure you I assumed I'd be sucking up their chips like a vacuum cleaner. I ran out of room in my rack. I was stacking them in plastic cups and I was running out of space there. They got a cupfull of chips and even if you discount some almost tried to lose I kept scooping them. I considered teaching martingale but even on a fun game that was too much. It is no wonder casinos can pay two people to deal this game but are looking to eliminate boxmen to save money on a craps crew.

I was only thinking of the single number bet on chuck a luck. It soulds like yours would be the same if you had 3 wheels with 6 numbers each or if you had one wheel with all 216 outcomes.

Quote: AZDuffman

Nope, similar but not identical. I suppose the wheel is imitating the dice on the real thing, but here you only had one choice, the number. This may explain some people who thought betting a six paid off if three 2s came up.

Yeah, I was just thinking about the single number bet in Chuck-a-luck...

Quote:

When I came to this site I would not have believed that. After reading here and doing the dealing at the parties (which started a year before WoV) I can believe a mark is thinking anything. Less than 1 in 4 ask about if "sixteen ways to win in the field" is good.

I am amazed sometimes by the logic applied by some of my very intelligent friends when it comes to gambling and betting. Even in boardgames they play a lot, they underestimate streaks, odds and weird events.

Must be nice being on the side with the scales tipped well in their favour....

Quote: AZDuffman

Quote: Dween

Horse Race Wheel:
The ones I have seen usually have payouts of 3, 4, 5, 6, 7 and 3 again. Average of 4.666 per win. With 10 horses, it should be easy to determine the HE.

So am I correct, take the average win, multiply by the % of winning that horse, and subtract it all from one?

Only if every horse has the same combinations.

To determine the HE on a particular bet on any wheel, look at each possible position on the wheel, multiply the probability of landing on that position by what you win or lose if it happens, then add up all of the results, divide by the number of positions on the wheel, and multiply by 100% (actually, for the HE, you multiply by -100%).

For example, on the "1-12" bet on a double-zero roulette wheel:
There are 38 positions
On 12 of them (1 through 12), if you bet 1, you are +2.
On the other 26 (0, 00, and 13 through 36), if you bet 1, you are -1.
The total is (12 x +2) + (26 x -1) = 24 - 26 = -2; dividing by 38, you get -1/19, or -5.263%. (The HE is -1 x this, or 5.263%.)

I can't remember the details but once saw a similar idea [in UK] using symbols (such as diamonds and squares). Essentially each symbol appeared a sensible number and the odds were calculated using 36/n -1 on a 37 slot wheel (e.g. 6 symbols paid 5-1). I would guess it was 12 (2/1), 9 (3/1), 6 (5/1), 4 (8/1), 3 (11/1), 2 (17/1), 1 (35/1).