I had a go and to be able to aim is nigh on impossible, so I figured the chances are purely random. The prize was either a massive cuddly toy, or £20. I was obviously going for the £20 ;-)

I spent £5 before giving up.

I have now attempted to figure the odds, assuming random placement.

I believe there are three distinct patterns.

1) The first ball lands in the middle, the second ball can land anywhere, the third has one slot to hit. So i figure 1/9 * 8/8 * 1/7 = 1/63

2) The first ball lands on a corner, the second ball has 4 possible pockets, the third again has one. So 1/9 * 4/8 * 1/7 = 1/126

3) The ball lands on the outer middle, but has exactly the same odds as above.

I think I now combine these odds, and get a probability of 1 in 31.5

Is this right?

How many different ways cause a win? You have to count them by hand:

3 of this style

x.x.x

o.o.o

o.o.o

3 of this style

x.o.o

x.o.o

x.o.o

and 2 of this style

x.o.o

o.x.o

o.o.x

So 8 ways, and the ball can form one of these 8 patterns in 6 ways (123,132,213,231,312,321) 8*6 = 48

Answer 48/504 = 1 in 10.5

Of course, this assumes there isn't some sticky tape in a hole, or some other dishonest trick!

If the first ball lands in a corner, there are SIX good pockets for the second ball.Quote:WizardofEngland2) The first ball lands on a corner, the second ball has 4 possible pockets, the third again has one. So 1/9 * 4/8 * 1/7 = 1/126

But I agree with CardShark: The overall odds really depend on there being equal odds for any available pocket on any throw. Carnival games, almost by definition, can be counted on to NOT be played fairly.

Quote:DJTeddyBearIf the first ball lands in a corner, there are SIX good pockets for the second ball.

But I agree with CardShark: The overall odds really depend on there being equal odds for any available pocket on any throw. Carnival games, almost by definition, can be counted on to NOT be played fairly.

Your very right, don't know how I missed that

If they use larger balls then its often that from the angle you can see all containers are the same but in actuality the valuable container will have a bottom that encourages a bounce.

Quote:SOOPOOSo since wiz and card shark figured out if it is fair then the carnie will be losing money hand over fist. Most likely is the center hole is then least likely to accept a ball and the 4 non corners the most likely. This will skew the odds in the carnies favor significantly. Good for you that you only spent 5 pounds for the lesson.

I wonder how skewed they differant holes have to be? Excel here I come.

Quote:SOOPOOSo since wiz and card shark figured out if it is fair then the carnie will be losing money hand over fist. Most likely is the center hole is then least likely to accept a ball and the 4 non corners the most likely. This will skew the odds in the carnies favor significantly. Good for you that you only spent 5 pounds for the lesson.

You have to be in the spirit for a carnival though, and then there is the macho factor, trying to look good by winning, but ending up a loser.