Deconstructing Blazing Sevens Numbers

So I've been coming to the forums for the past few months as a non-user and have been enjoying learning about the numbers behind the machines. I've been on the Wizard's site and have worked through a bunch of his deconstructions. I thought I was gaining an understanding on how the numbers worked ... until I hit Blazing Sevens.

The numbers I've come up with are different and I'm trying to understand where I've gone astray.

Here are my numbers. I've surrounded the number with '<' and '> to indicate where my numbers are different.

Symbol	5 in a row	4 in a row	3 in a row
F	1,250	3,750	35,000
7	4,375	21,875	210,000
Mixed 7s	111,875	<171,875>	<720,000>
D	17,010	119,070	641,520
B	36,288	145,152	855,360
3	1,260	11,340	88,200
2	3,000	21,000	<194,400>
1	1,680	20,720	<96,960>
Mixed Bars	<483,168>	<1,056,832>	<2,264,640>

The resulting RTP is still close, but varies for the 2 coin bet

Coin Bet	BAR,$, BELL	7's	Gross Return	Net Return
3	0.832637	1.840210	2.672847	0.890949
2	0.832637	0.854187	1.686824	0.843412
1	0.832637	0	0.832637	0.832637

I've derived my numbers 3 ways: brute force (as suggested by the Wizard), by building an excel spreadsheet, and by enhancing the spreadsheet by double checking by building out a table for all the variations for the given varitions.

To better explain the 3rd approach, let's take the example of a 3 in a row "mixed 7s". I built a table for all possible combinations of 3 in a row F/7s. This would be a table like below. I include the "formula" (just in case my thinking is flawed there), where a symbol F1 represents the blazing 7 (F) for reel 1. Unfortunately the 7 will read funny since 71 means 7 for reel 1.

FFF : F1 * F2 * F3 * (40 - (F4 + 74)) * 40 = 30000
FF7 : F1 * F2 * 73 * (40 - (F4 + 74)) * 40 = 30000
F7F : F1 * 72 * F3 * (40 - (F4 + 74)) * 40 = 30000
F77 : F1 * 72 * 73 * (40 - (F4 + 74)) * 40 = 30000
7FF : 71 * F2 * F3 * (40 - (F4 + 74)) * 40 = 210000
7F7 : 71 * F2 * 73 * (40 - (F4 + 74)) * 40 = 210000
77F : 71 * 72 * F3 * (40 - (F4 + 74)) * 40 = 210000
777 : 71 * 72 * 73 * (40 - (F4 + 74)) * 40 = 210000

The sum of all F/7 combos is 960,000. However, we now need to look at the paytable. First of all, FFF and 777 would match to 3 in a row FFF and 777. That would then give us 720,000. There are no other combos that would be eliminated. This would appear to mean that 3 in a Row Mixed 7s should be 720,000. But in the Wizard's deconstruction, it's listed as 960,000.

I've gone through a similar approach for all Mixed 7/Bar versions, with the exception of 5 in a Row mainly because of how long the table with be and I wanted to save a little bit of time.

But for example, my formula for 5 in a row mixed sevens would be:

((F1 + 71) * (F2 + 72) * (F3 + 73) * (F4 + 73) * (F5 + 75)) - (F1 * F2 * F3 * F4 * (40 - F5)) - (71 * 72 * 73 * 74 * 75) = 111,875

Which should represent "All combinations of F and 7 MINUS all 4 in a row F MINUS all 5 in a row 7"

This is because 4 in a row and 5 in a row F pays more than 5 in a row mixed sevens but only 5 in a row 7s pay more than 5 in a row mixed sevens.

It seems to me that the numbers listed in the Deconstruction page used for 3 in a row for 2-bar and 1-bar are the theoretical max combinations, but paytale rules should actually reduce the amount to lower values. For example 11122 (5 in a row mixed bars) should beat out 111 (3 in a row 1s) and would be hence subtracted from that theoretical max hit amount for 3 in a row 1-bar.

Or is there some rule which allows multiple awards for overlaps? I would tend to think not based on this statement from the Wizard's page "In cases where two equal wins are possible, for example three 3-bars or five mixed bars, the game counts it as the one composed of fewer symbols."

Sorry this was long and hopefully this has made sense. I've gone over this for the last couple of nights and can't quite seem to see why my numbers are different.

Thanks!

I have never done a slot machine by brute force - I always solve it with a spread sheet then double check everything with simulations. The problem with a brute force cycle is that the final results are hard coded copy/paste. Brute force doesn't allow the client to easily update the game on his end (e.g. change the symbol frequencies in the reel strips).

If you can figure out how to contact me directly and your credentials check out, I'll help you here.

Best.

@teliot, thanks for the reply, I've sent you a message.

I certainly can see what you mean about the efficacy of using a spreadsheet. Processing via brute force can take a bit of processing time. I ended up splitting up the problem into chunks to take advantage of multiple cores to reduce that time. Obviously it doesn't address flexibility issues.