HeyMrDJ Joined: May 29, 2015
• Posts: 101
March 27th, 2018 at 2:03:33 AM permalink
There is a new online wheel game called Dreamcatcher

Its a bit like Big6, but possibly better.

You can see it in action here Probably not safe for work

It has the following

23 1 slots
15 2 slots
7 5 slots
4 10 slots
2 20 slots
1 40 slot

And

1 2x Multiplier slot
1 7x Multiplier slot

The good thing is, the multipliers can stack, so in the video you see it land on 7x and then the 2x multiplier for a 14x total multiplier, it then lands on the 5 slot for a total payout of 70x the bet.

My question is, how do you calculate the edge on this? It could keep hitting the multipliers and pay huge. Once it hits one multiplier, all bets are frozen by the way.
Guess who peed in my Cheerios? Romes did...
JB Joined: Oct 14, 2009
• Posts: 2088
Thanks for this post from:  March 27th, 2018 at 5:30:19 AM permalink
( incorrect math stricken from the record )

If you bet on the 'X' spot, whose weight is 'W', the return is the following recursive equation:

(X * W/54) + (return * 2 * 1/54) + (return * 7 * 1/54)

If you call the return R, the above boils down to:

R = (XW + 9R) / 54

Let's get rid of the recursion. Multiply both sides by 54:

54R = XW + 9R

Subtract 9R from each side:

45R = XW

Divide both sides by 45:

R = XW / 45

So the return for each spot is its prize multiplied by its weight, divided by 45:

the 1 spot returns 23/45 = 51.1111%
the 2 spot returns 30/45 = 66.6666%
the 5 spot returns 35/45 = 77.7777%
the 10 spot returns 40/45 = 88.8888%
the 20 spot returns 40/45 = 88.8888%
the 40 spot returns 40/45 = 88.8888%

These numbers assume a fair wheel, which it looked like it was.
Last edited by: JB on Mar 27, 2018
HeyMrDJ Joined: May 29, 2015
• Posts: 101
March 27th, 2018 at 5:54:24 AM permalink
but does this allow for landing on 7x three times, then a winning number?
Guess who peed in my Cheerios? Romes did...
JB Joined: Oct 14, 2009
• Posts: 2088
March 27th, 2018 at 5:57:13 AM permalink
Yes, hence the recursion.
rsactuary Joined: Sep 6, 2014
• Posts: 1587
March 27th, 2018 at 6:45:10 AM permalink
Why does it seem like the film is edited in between each spin?
HeyMrDJ Joined: May 29, 2015
• Posts: 101
March 27th, 2018 at 9:31:49 AM permalink
Quote: rsactuary

Why does it seem like the film is edited in between each spin?

So the 1 spot has a 49% house edge? That cant be right surely
Guess who peed in my Cheerios? Romes did...
JB Joined: Oct 14, 2009
• Posts: 2088
Thanks for this post from: March 27th, 2018 at 10:21:30 AM permalink
( incorrect math stricken from the record )

There are 23 spots out of 54 total that land a 1. Before considering the multipliers, the return from this is 1 * 23 / 54 = 0.4259259

If you hit 2x and then the 1: this pays 2 * 1 with probability (1/54) * (23/54) for another 0.015775
If you hit 7x and then the 1: this pays 7 * 1 with probability (1/54) * (23/54) for another 0.05521262
If you hit 2x, 2x, 1: this pays 2 * 2 * 1 with probability (1/54) * (1/54) * (23/54) = another 0.000584261
If you hit 2x, 7x, 1: this pays 2 * 7 * 1 with probability (1/54) * (1/54) * (23/54) = another 0.002044912
If you hit 7x, 2x, 1: this pays 7 * 2 * 1 with probability (1/54) * (1/54) * (23/54) = another 0.002044912
If you hit 7x, 7x, 1: this pays 7 * 7 * 1 with probability (1/54) * (1/54) * (23/54) = another 0.007157191

As you can see, longer multiplier sequences can only increase the return by increasingly tiny amounts.

The total return, with every possible multiplier sequence factored in, is 23/45 = 0.511111
Last edited by: JB on Mar 27, 2018
CrystalMath Joined: May 10, 2011
• Posts: 1812
Thanks for this post from: March 27th, 2018 at 11:57:53 AM permalink
Quote: JB

There are 23 spots out of 54 total that land a 1. Before considering the multipliers, the return from this is 1 * 23 / 54 = 0.4259259

If you hit 2x and then the 1: this pays 2 * 1 with probability (1/54) * (23/54) for another 0.015775
If you hit 7x and then the 1: this pays 7 * 1 with probability (1/54) * (23/54) for another 0.05521262
If you hit 2x, 2x, 1: this pays 2 * 2 * 1 with probability (1/54) * (1/54) * (23/54) = another 0.000584261
If you hit 2x, 7x, 1: this pays 2 * 7 * 1 with probability (1/54) * (1/54) * (23/54) = another 0.002044912
If you hit 7x, 2x, 1: this pays 7 * 2 * 1 with probability (1/54) * (1/54) * (23/54) = another 0.002044912
If you hit 7x, 7x, 1: this pays 7 * 7 * 1 with probability (1/54) * (1/54) * (23/54) = another 0.007157191

As you can see, longer multiplier sequences can only increase the return by increasingly tiny amounts.

The total return, with every possible multiplier sequence factored in, is 23/45 = 0.511111

This game actually pays on a "to one" basis, so the rtp is much higher than this.
I heart Crystal Math.
JB Joined: Oct 14, 2009
• Posts: 2088
March 27th, 2018 at 12:51:41 PM permalink
Quote: CrystalMath

This game actually pays on a "to one" basis, so the rtp is much higher than this.

Ah, of course. I really need to stick to programming, it's so much easier than math.
FleaStiff Joined: Oct 19, 2009