Calculating Return for "Lock & Roll" 5X Pay Quarter Machine

Okay, I finally got around to this.

For only the original spin I get:

Hit Frequency = 0.032937
Expected return = 0.226268

Here is a frequency of each win.

Win	Hits
5000	1
1500	7
1000	12
500	26
300	15
250	54
200	41
150	80
125	35
100	221
60	9
50	497
40	30
30	294
25	4890
20	616
10	4311
5	13461
2	44474
0	2028078

For the respin my results don't seem reasonable, but here they are:

Hit Frequency = 0.102392
Expected return = 0.57471

Craig, your probability of "One 5x + Two Red7" reflects that it happened 21 times. I would argue it can happen 15 ways only as follows:

R7 R7 5X = 1*3*1 = 3
R7 5X R7 = 1*1*3 = 3
5X R7 R7 = 1*3*3 = 9

3+3+9=15

Here is my table for the draw. This is probably wrong somewhere.

Win	Hits
5000	2097152
1500	29192576
1000	40442624
500	95449472
300	109463040
250	181163648
200	232694272
150	339635968
125	143913344
100	1236706944
60	86299776
50	2315254144
40	218760960
30	1493475072
25	22682131328
20	4491891712
10	25257941760
5	67061415552
2	324305831168
0	3947722750592

Hey everyone,

THANK YOU for all the time put into this. It doesn't get any better than learning by example. I have really enjoyed following the process and seeing what it takes to get to the correct answer.

Again, thanks for the work. I find it extremely interesting to see the math behind slot machines because it is something that doesn't find the light of day very often.

-Craig

You're welcome. I hope this thread doesn't die out. I'd like to write this up on my Odds site. If anybody disagrees with my results, please challenge me.

Quote: Wizard

You're welcome. I hope this thread doesn't die out. I'd like to write this up on my Odds site. If anybody disagrees with my results, please challenge me.

I hereby challenge you... :)

I disagree with your counts on the initial spin for prizes of 0, 2, 5, 25, 30, and 150.

I didn't do all of them, but here's what I come up with for a prize of 30, which can only occur from three mixed sevens:

reel 1	reel 2	reel 3	weight	total
red seven	red seven	seven bar	1*3*6	18
red seven	seven bar	seven bar	1*5*6	30
red seven	seven bar	red seven	1*5*3	15
seven bar	red seven	red seven	1*3*3	9
seven bar	red seven	seven bar	1*3*6	18
seven bar	seven bar	red seven	1*5*3	15
Total				105

Your count for a prize of 30 is 294, which is 189 combinations too many.

I come up with a return of 22.2887% for the initial spin, and after the second spin I agree with miplet's result of 90.0619%, who I give credit to for being the first one to post what I believe is the correct result.

Quote: JB

I come up with a return of 22.2887% for the initial spin, and after the second spin I agree with miplet's result of 90.0619%, who I give credit to for being the first one to post what I believe is the correct result.

:+) All in 200 lines of php (including comments, blank lines, lots of echoing to see results ect. ). Of course I'm not much of a programmer, but it sure was fun.

My total wins of 30 were wrong. Here are my new figures for the initial spin.

Win	Hits
5000	1
1500	7
1000	12
500	26
300	15
250	54
200	41
150	50
125	35
100	221
60	9
50	497
40	30
30	105
25	4970
20	616
10	4311
5	13677
2	44474
0	2028001

Hit Frequency = 0.03295
Expected return = 0.224079

Where am I wrong now?

Quote: Wizard

My total wins of 30 were wrong. Here are my new figures for the initial spin.


Hit Frequency = 0.03295
Expected return = 0.224079

Where am I wrong now?

Your chart is right , but your Expected return is wrong. 467428/(128^3)=.222887039185

Thanks, you're right. Following is my table for the draw. Any thoughts where this may be wrong?

Win	Hits
5000	2097152
1500	28530048
1000	39848192
500	95449472
300	106993152
250	181163648
200	228144640
150	309765376
125	143913344
100	1236706944
60	85147776
50	2315254144
40	214068480
30	854620800
25	23009999488
20	4491891712
10	25224490752
5	67988566656
2	323654613248
0	3947835246080

Hit Frequency = 0.10236619
Expected return = 0.57108399

It seems that you aren't determining the best hold strategy correctly.

Looking at your draw combinations for 3 wilds, it looks like you have only one way to end up with 3 wilds, which is probably when all 3 were dealt, weighted to equal 128^3.

But that isn't the only way to end up with 3 wilds. For example, with wild-wild-blank, you should "discard" the blank and go for the third wild. With one or more wilds, the strategy should be:

With 3 dealt wilds, hold all 3.
With 2 dealt wilds, hold only the 2 wilds when the third symbol is a blank or single bar.
With 1 dealt wild, hold only the wild when the other symbols are blank-blank or blank-single bar.

Assuming a 5000x payout for 3 wilds, you should come up with 10,632,633 combinations for 3 wilds on the draw.