Euro Wheel

In the casino's in Holland there's a new game since the beginning of this year. It is called Euro Wheel and it is played as a sort of Wheel of Fortune. On this wheel there are 52 possible outcomes.
One of these outcomes gives you a pay-out of 45 times your bet if you had bet on this outcome. So far, the advantage is still for the house.
However, you can choose to not take the 45 times your bet winnings, but instead push a button which stops a light on one of five numbers: 20, 35, 50, 100 or 200. On whichever number it stops, that's how much you will be payed, i.e. if it stops on 200 you will be payed 200 times your initial bet.

Your expected value if you bet on this outcome and won't take the 45 times your bet winnings but push the button is in my opinion the following:

-51/52+1/52*1/5*(20+35+50+100+200)=30/52

In other words, this bet will give you about a 60% advantage over the house.

My question to you is: Is my calculation wrong or shouldn't I have assumed that the change on the five different numbers is equal for all five numbers? Or better yet, does this game really give the advantage to the player?

Peter

You are assuming that each of the 20, 35, 50, 100 and 200 have an equal chance of coming up.

Dare I say that 20 and 35 would be much more common than the others?

My question to you is: Is my calculation wrong or shouldn't I have assumed that the change on the five different numbers is equal for all five numbers? Or better yet, does this game really give the advantage to the player?

Are you sure the entire wheel (base game) as well as the button stage are random? If not, on what basis are you assigning a 51/52 vs 1/52 weight on the base game and 1/5th weight for each payout on the button stage. If the 60% player advantage is suspect (thus indicating the game is not random), then exam the entire game as a system, then just one part. If you record enough observations, then you would have a pretty good idea how the game really works.

Good luck.

There is a blackjack game in the US where you can make a sidebet that you get a blackjack. If you do then you push a button and an electronic wheel selects a payout. It is very similiar in that if all payouts on the wheel had an equal chance of hitting the player would have a large edge. This is definitely not the case. The wheel is rigged so the lower payouts come up much more often. I'm told the house edge on the bet is over 10%. If it looks too good to be true it probably is.

As I had thought before I posted my question all responses told me that the chances for the different outcomes would probably not be the same. My assumption was purely based on how the game looks like. All the outcomes look like they have the same size, indicating that the chances are the same. Furtermore, in the booklet about the rules of this game there is no indication that they aren't.

My real question is: shouldn't the casino in one way or another make it possible for the public to know that the outcomes don't have the same chance of occuring. I feel that if they don't then they are misleading the player and the gaming control board should take measures against the casino.

I'm curious how you think of this.

Peter

Each symbol on a slot machine's wheel takes up the same amount of space, and yet they occur with different frequencies.