Another thing to point out at my local Casino… where it appears that I hold the advantage…
They have this thing called the ‘money wheel’. It is like one of those prize wheels where you give it a spin and win what it lands on.
Anyways… in front of the wheel are options on what you can bet on… 2 of them being ‘1-1’ and ‘3-1’.
If you bet 2 dollars on ‘1-1’, and it comes up on the wheel, you will double your money (eg 4 dollars).
If you bet 2 dollars on ‘3-1’ ,and it comes up on the wheel, you will quadrouple your money (eg 8 dollars).
A closer inspection of the wheel reveals that just over 60% of the wheel is covered in either ‘1-1’ or ‘3-1’. A friend and I decided to put to test a strategy of putting 2 dollars on ‘1-1’ and 2 dollars on ‘3-1’ for every spin. After about an hour… we were 30 dollars up.
My question is… if over 60% of the wheel is covered in
‘1-1’ or ‘3-1’ (which it is), and we use the strategy mentioned above… are the odds in our favor of winning?
The big money wheel is the second worst game in the casino, behind Keno. Bad for the player, that is. It’s a great game for the casino.
I could run down the odds for you, but I would need exact information on how many spaces/chances are present, and exactly what the total spread of payoffs are. How many spaces are “blanks” where you win nothing? Are you telling me that the ‘1-1’ space is a win of your bet and not a push?
I ask because some casinos have gone from ‘3-to-1’ to ‘3-for-1’ in describing their payoffs. There’s a big difference. In the former, you would win $6 and drag your original $2 back. Note that this is a $6 win, not an $8 win.
3-for-1 means you win $6, but they keep your original bet of $2. Net $4 for you. Note that 3-for-1 is the same as saying 2-to-1, but casinos try to trick you into thinking it is a larger payoff.
In short, more info please.
In shorter, the only thing you can take to the bank when playing the money wheel is that the Casino, not you, has the overwhelming advantage.
You don’t say how many (1-1) and (3-1) spaces there are individually, but let’s say there’s the same number of each. So out of 53 spaces, 30 % are (1-1), 30% (3-1) and 40% (others). You are putting $2 on (1-1) and (3-1) each time. To play 100 rounds will cost you $400 ($4 spent per hand times 100 hands); you should end up with approximately these results:
win $8 30 times = $240
win $4 30 times = $120
Total $360 back for $400 spent = 10% to the house. Even more will go to the house if there are more (1-1) than (3-1) spaces.
Ok, here goes. I’ll have to make some assumptions, but hopefully it will illustrate the point.
1-1: 22 spots
3-1: 10 spots
This adds up to 32 spots out of 53, or ~60.4% of the spaces. This corresponds to your observation of “just over 60%.”
To calculate the house advantage for each spot, we’ll assume a complete cycle of 53 spins and a constant bet.
On the 1-1 wager, the house will win 31 bets and pay off 22. House advantage = 17% (31/53 = 58.5%; 24/53 = 41.5%, for a difference of 17%).
On the 3-1 wager, the house wins 43 bets and pays off 30 (10 spots x 3-1 payoff). House advantage = 24.5%
For the other spots on the wheel, such as 5-1, 10-1, 20-1, etc., you can be assured that the odds are similarly bad. Actually, the house advantage on a typical money wheel ranges from about 9% to about 25%. Like I said, worse than any other game besides Keno.
Remember, if each bet encompasses a built-in house advantage (which they do as I have shown), you can’t oversome this by making more bets. Just the opposite. The more bets you make, the worse off you are. Sometimes people don’t ungerstand this. They think that by covering more spots in roulette or on the money wheel, they are somehow overcoming the house edge. No way!
As divemaster said, if somebody is to compute the expected return on the thing, we will need an exact count of how many slots have various payoffs. Most of these wheels also have a couple high payoff slots as well - 40-1 or something like that.
However, we can tell you something:
I’ll bet that 1-1 slots are < 50% of the wheel, and 3-1 slots are < 25% of the wheel. Note that this can still be a total > 60% of the wheel, and you have < 1/4 probability of hitting a 3-1 and < 1/2 probability of hitting a 1-1.
The way you are betting, you break even if you hit a 1-1, and wind up doubling if you hit a 3-1, because you lose the other bet. Not winning over the long run, I guarantee it.
Once upon a time I was a grad assistant teaching an elementary probability course. I let them calculate the odds on the local bar’s Keno games for extra credit (a nice exercise in using hypergeometrics). I was shocked at how bad they were.
Thing is, a gambling operation doesn’t need that much of an edge. You can do just fine with a game that returns 90% or so.
Yes, the house doesn’t need that much of an edge to make the big bucks. The games aren’t horribly unfair. But look around at how many bets are being placed every minute. The casino, on average, takes its cut of ~5% of every bet placed.
So, why don’t I open a casino of my own? The problem is that you have to have a large number of bets and a large bankroll. If you have a small number of bets then you are gambling that you number will come up, but with a large number of bets the “noise” will smooth out. And if you have a small bankroll it is possible that one lucky winner will bankrupt you, whereas if the casino has a large bankroll they can keep playing and the lucky winner is very likely to lose his winnings back.
MadHatter, the bottom line is that there are NO money-making games at the casino. If you like the casinos, fine, but you are not going to make money there, you are most definately NOT going to find a game where you can win. The casinos have trained mathemetians who can calculate the payoff of every bet it is possible to make in that casino, and if there are any that are in the players favor they carefully change the rules. This is how casinos work!
Think for a minute. How likely do you think it is that you could find a casino so stupid that they won’t notice that the money wheel, or whatever, is a net loser for them? No, they know the probabilities backward and forward, and they always keep an edge for themselves. If you ever do a back-of-the-envelope calculation of the odds and they seem to be in your favor somehow, rest assured that you haven’t calculated carefully enough.