Cracking Hexbreaker Reel Strip Order

On Monday I posted my analysis of the slot machine Hexbreaker. However, I failed to piece together the reel strips in order. Instead, I made an estimate of the symbol frequency and randomized the order myself. However, I can't shake the unsatisfying feeling that job is only half finished. Below is what I believe to be the 69 sequences of three symbols (from top to bottom) for reel 1. You'll notice some appear twice.

If anyone is up to the challenge, I'm looking to put these in sequence, forming a closed loop. Some connections are obvious. For example, consider what follows JX-UM-PN. There is only one possibility, UM-PN-HX. However, there is often at least two possibilities. For example, JX-CR-SH could be followed by CR-SH-13 or CR-SH-MR.

I did this before with Jackpot Party, but those reels strips were much shorter, and it still look me a while. There are still four other reels to the game besides this one. If anyone can piece this together they would be making a permanent contribution to my Odds site, as well as the study of slot mathematics in general. Plus, I'll throw in a free lunch/coffee with yours truly who whoever can crack this. Please, if anybody has access to the par sheet, don't use it. I don't want to cheat, but show that the game can be deconstructed using only information freely available to the player.

Any takers?

13-HX-DL
13-HX-SH
13-MR-SH
13-MR-SH
13-SL-CR
13-SL-HX
13-SL-MR
CR-CT-UM
CR-DL-13
CR-DL-MR
CR-DL-MR
CR-JX-UM
CR-SH-13
CR-SH-MR
CT-13-SL
CT-JX-SL
CT-PN-CR
CT-SL-13
CT-SL-MR
CT-UM-MR
DL-13-HX
DL-CR-CT
DL-CT-PN
DL-CT-SL
DL-JX-CR
DL-MR-SH
DL-MR-SL
DL-SL-MR
HX-DL-CT
HX-DL-SL
HX-SH-DL
HX-SH-PN
JX-CR-SH
JX-SL-13
JX-UM-PN
MR-CR-DL
MR-CR-SH
MR-DL-CR
MR-DL-JX
MR-SH-13
MR-SH-CR
MR-SH-CT
MR-SH-UM
MR-SL-13
MR-SL-SH
PN-CR-DL
PN-CT-SL
PN-HX-DL
SH-13-SL
SH-13-SL
SH-CR-JX
SH-CT-13
SH-CT-JX
SH-DL-CT
SH-MR-DL
SH-PN-CT
SH-UM-MR
SL-13-HX
SL-13-MR
SL-13-MR
SL-CR-DL
SL-HX-SH
SL-MR-CR
SL-MR-DL
SL-MR-SH
SL-SH-CT
UM-MR-CR
UM-MR-SL
UM-PN-HX

So there are 69 stops on each wheel, not 64 mentioned on your page???
PS. I've been at this for a while based on 64 strips, and trying to find an error in recording the data.

Sorry to lead you astray with my page. Perhaps we should PM, but after I added some repeating patterns to make the symbols balance between top, middle, and bottom position, I get 69 total stops. But yes, I stand behind 69. Please ignore the 64 currently on my site. I'll update that later this morning after I figure out the other reels.

Here is a possible solution:

13-HX-SH-PN-CT-SL-13-MR-SH-13-SL-CR-DL-MR-SL-13-MR-SH-UM-MR-SL-SH-CT-JX-SL-13-HX-DL-CT-SL-MR-DL-JX-CR-SH-MR-DL-CR-CT-UM-MR-CR-SH-13-SL-HX-SH-DL-CT-PN-CR-DL-MR-SH-CR-JX-UM-PN-HX-DL-SL-MR-SH-CT-13-SL-MR-CR-DL

Quote: JB

Here is a possible solution:

How did you get that so fast?

Regardless of that answer, here are all five reels.

Reel 1	Reel 2	Reel 3	Reel 4	Reel 5
13-HX-DL	13-DL-SL	13-PN-HX	UM-PN-MR	13-CT-UM
13-HX-SH	13-PN-MR	13-PN-MR	UM-MR-SH	13-MR-PN
13-MR-SH	CR-PN-SH	13-PN-UM	UM-MR-SH	13-PN-CT
13-MR-SH	CR-SH-DL	13-UM-PN	UM-MR-PN	13-PN-JX
13-SL-CR	CR-SH-SL	CR-PN-HX	UM-LD-PN	13-SH-MR
13-SL-HX	CR-UM-JX	CR-SL-DL	UM-JX-SH	13-SL-JX
13-SL-MR	CT-PN-UM	CR-SL-MR	UM-CR-SH	13-SL-MR
CR-CT-UM	CT-SH-JX	CT-DL-MR	UM-CR-DL	13-UM-PN
CR-DL-13	CT-SH-UM	CT-PN-DL	SL-UM-CR	CR-13-SH
CR-DL-MR	DL-13-PN	CT-UM-SL	SL-HX-SH	CR-CT-SL
CR-DL-MR	DL-CR-PN	DL-13-PN	SL-CT-DL	CR-DL-MR
CR-JX-UM	DL-MR-SL	DL-13-PN	SL-13-SH	CR-SH-CT
CR-SH-13	DL-MR-SL	DL-JX-UM	SH-SL-CT	CR-SH-MR
CR-SH-MR	DL-SL-MR	DL-MR-SH	SH-SL-13	CR-SH-MR
CT-13-SL	HX-PN-DL	DL-MR-SH	SH-PN-MR	CR-SL-DL
CT-JX-SL	HX-SL-CR	DL-PN-CR	SH-PN-DL	CR-SL-MR
CT-PN-CR	JX-PN-CT	DL-PN-MR	SH-PN-13	CR-SL-MR
CT-SL-13	JX-UM-PN	DL-SL-MR	SH-HX-UM	CT-CR-SL
CT-SL-MR	LD-SH-PN	DL-SL-MR	SH-DL-MR	CT-DL-MR
CT-UM-MR	LD-SL-DL	DL-SL-PN	SH-DL-CT	CT-SL-PN
DL-13-HX	LD-SL-PN	HX-DL-SL	SH-DL-CR	CT-SL-SH
DL-CR-CT	MR-PN-SL	HX-SL-SH	SH-CR-PN	CT-UM-MR
DL-CT-PN	MR-PN-SL	JX-DL-PN	SH-13-UM	DL-CR-SH
DL-CT-SL	MR-SH-CR	JX-SL-UM	PN-UM-MR	DL-JX-CT
DL-JX-CR	MR-SL-CR	JX-UM-CR	PN-UM-LD	DL-MR-13
DL-MR-SH	MR-SL-SH	MR-CT-UM	PN-SH-HX	DL-MR-UM
DL-MR-SL	MR-SL-SH	MR-DL-13	PN-MR-SL	HX-CR-DL
DL-SL-MR	MR-UM-13	MR-DL-PN	PN-MR-SH	HX-CR-SL
HX-DL-CT	MR-UM-DL	MR-DL-SL	PN-MR-DL	HX-SL-CR
HX-DL-SL	MR-UM-PN	MR-PN-DL	PN-DL-UM	JX-CT-DL
HX-SH-DL	PN-CT-SH	MR-SH-13	PN-DL-13	JX-SH-13
HX-SH-PN	PN-DL-13	MR-SH-DL	PN-CR-DL	JX-SH-13
JX-CR-SH	PN-HX-SL	MR-SH-SL	PN-13-UM	MR-13-SL
JX-SL-13	PN-LD-SL	MR-SL-UM	MR-SL-UM	MR-CR-SH
JX-UM-PN	PN-MR-SL	MR-UM-SL	MR-SH-SL	MR-CR-SH
MR-CR-DL	PN-MR-UM	PN-CR-SL	MR-SH-SL	MR-CR-SL
MR-CR-SH	PN-MR-UM	PN-CT-DL	MR-SH-PN	MR-DL-CR
MR-DL-CR	PN-SH-MR	PN-DL-13	MR-SH-DL	MR-PN-SH
MR-DL-JX	PN-SL-CT	PN-DL-JX	MR-SH-DL	MR-SH-13
MR-SH-13	PN-SL-MR	PN-HX-DL	MR-PN-SH	MR-SL-13
MR-SH-CR	PN-UM-LD	PN-HX-SL	MR-PN-DL	MR-UM-13
MR-SH-CT	SH-CR-UM	PN-JX-SL	MR-DL-PN	MR-UM-CR
MR-SH-UM	SH-CT-PN	PN-MR-SL	LD-PN-CR	PN-CT-CR
MR-SL-13	SH-DL-MR	PN-MR-UM	JX-SH-PN	PN-HX-CR
MR-SL-SH	SH-HX-PN	PN-UM-JX	JX-SH-13	PN-HX-SL
PN-CR-DL	SH-JX-UM	SH-13-PN	HX-UM-PN	PN-JX-SH
PN-CT-SL	SH-MR-PN	SH-DL-SL	HX-SH-CR	PN-SH-13
PN-HX-DL	SH-PN-HX	SH-MR-CT	DL-UM-CR	SH-13-CT
SH-13-SL	SH-SL-LD	SH-SL-13	DL-PN-MR	SH-13-PN
SH-13-SL	SH-UM-MR	SL-13-UM	DL-MR-SH	SH-13-SL
SH-CR-JX	SL-CR-SH	SL-CT-PN	DL-MR-SH	SH-13-UM
SH-CT-13	SL-CR-SH	SL-DL-MR	DL-MR-PN	SH-CT-SL
SH-CT-JX	SL-CT-SH	SL-MR-DL	DL-JX-SH	SH-HX-CR
SH-DL-CT	SL-DL-MR	SL-MR-DL	DL-CT-PN	SH-MR-CR
SH-MR-DL	SL-LD-SH	SL-MR-PN	DL-CR-UM	SH-MR-SL
SH-PN-CT	SL-MR-SH	SL-MR-SH	DL-13-SL	SH-MR-UM
SH-UM-MR	SL-MR-UM	SL-PN-CT	CT-PN-UM	SL-13-MR
SL-13-HX	SL-PN-MR	SL-SH-MR	CT-DL-JX	SL-CR-13
SL-13-MR	SL-SH-CT	SL-UM-CR	CR-UM-JX	SL-DL-JX
SL-13-MR	SL-SH-HX	SL-UM-MR	CR-SH-PN	SL-JX-SH
SL-CR-DL	UM-13-DL	UM-CR-PN	CR-PN-UM	SL-MR-CR
SL-HX-SH	UM-DL-CR	UM-CR-SL	CR-DL-MR	SL-MR-DL
SL-MR-CR	UM-JX-PN	UM-JX-DL	CR-DL-MR	SL-MR-SH
SL-MR-DL	UM-LD-SL	UM-MR-DL	13-UM-MR	SL-PN-HX
SL-MR-SH	UM-MR-PN	UM-PN-JX	13-UM-MR	SL-SH-HX
SL-SH-CT	UM-PN-LD	UM-SL-CT	13-SL-HX	UM-13-PN
UM-MR-CR	UM-PN-MR	UM-SL-MR	13-SH-DL	UM-CR-CT
UM-MR-SL				UM-MR-CR
UM-PN-HX				UM-PN-HX

CR-DL-MR and 13-MR-SH appear twice on the reel #1 list. Is it confirmed that each is idependent?

Quote: Ayecarumba

CR-DL-MR and 13-MR-SH appear twice on the reel #1 list. Is it confirmed that each is idependent?

Lots of combinations appear twice in separate locations on the same strip. I'm not saying these are the exact sequences. I had to make educated guesses at the duplicates, based on what balanced the reels, and what occurred frequently in my sampling.

" Please, if anybody has access to the par sheet, don't use it. "

I assume that afterwards a par sheet can can be used to verify the results ??

For us mathematically challenged.

It is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail.

A solution for reel 2:

UM-MR-PN-SL-MR-UM-13-DL-SL-MR-SH-CR-UM-JX-PN-CT-SH-JX-UM-PN-MR-SL-SH-CT-PN-UM-LD-SL-PN-MR-UM-PN-LD-SL-DL-MR-SL-CR-SH-SL-LD-SH-PN-HX-SL-CR-SH-DL-MR-SL-SH-HX-PN-DL-13-PN-MR-UM-DL-CR-PN-SH-MR-PN-SL-CT-SH

A solution for reel 3:

UM-CR-SL-MR-PN-DL-13-PN-MR-UM-SL-MR-SH-13-PN-HX-DL-SL-MR-DL-PN-MR-SL-UM-MR-DL-13-PN-UM-JX-DL-PN-CR-SL-DL-MR-SH-DL-SL-MR-DL-SL-PN-CT-DL-MR-SH-SL-13-UM-PN-JX-SL-UM-CR-PN-HX-SL-SH-MR-CT-UM-SL-CT-PN-DL-JX

A solution for reel 4:

13-UM-MR-SH-SL-CT-DL-JX-SH-PN-MR-DL-PN-MR-SH-DL-CT-PN-UM-MR-PN-DL-13-SL-HX-SH-CR-PN-UM-LD-PN-CR-DL-MR-SH-PN-DL-UM-CR-DL-MR-SH-DL-CR-UM-JX-SH-13-UM-MR-SH-SL-13-SH-DL-MR-PN-SH-HX-UM-PN-MR-SL-UM-CR-SH-PN

A solution for reel 5:

CT-SL-SH-HX-CR-SL-DL-JX-CT-DL-MR-UM-13-PN-CT-CR-SL-MR-SH-13-PN-JX-SH-13-SL-JX-SH-13-UM-PN-HX-CR-DL-MR-13-SL-MR-DL-CR-SH-MR-SL-13-MR-PN-SH-13-CT-UM-MR-CR-SL-MR-CR-SH-CT-SL-PN-HX-SL-CR-13-SH-MR-CR-SH-MR-UM-CR

-------

To answer your question, I wrote a program to figure it out. It uses trial and error to find a solution. The first reel has multiple solutions; the other reels likely do too.

Quote: buzzpaff

I assume that afterwards a par sheet can can be used to verify the results ??.

I would accept that.

Quote: JB

To answer your question, I wrote a program to figure it out. It uses trial and error to find a solution. The first reel has multiple solutions; the other reels likely do too.

Thank you. Very quick work; I'm impressed.

Here is a reel 1 possibility:

SH-13-SL-CR-DL-13-HX-SH-DL-CT-SL-13-MR-SH-CR-JX-UM-PN-HX-DL-SL-MR-CR-DL-MR-SL-SH-CT-13-SL-HX-SH-PN-CT-SL-MR-DL-CR-CT-UM-MR-CR-SH-MR-DL-JX-CR-SH-13-SL-MR-SH-CT-JX-SL-13-MR-SH-UM-MR-SL-13-HX-DL-CT-PN-CR-DL-MR

Thanks, Aye, but JB beat you to the punch.

Thanks to all who helped with this project. My new and imporved Hexbreaker page is now ready for your review.

Quote: Wizard

Thanks, Aye, but JB beat you to the punch.

Thanks to all who helped with this project. My new and imporved Hexbreaker page is now ready for your review.

Not a problem. It was fun.

Does the possibility of several different combinations affect the odds of hitting a prize? For example, if the symbols were sequenced so that the strip placed the higher paying symbols as close together as possible, would that make it more or less likely to payout a large prize, compared to the sequencing of the same symbols where the higher paying symbols are distributed as uniformly as possible?

Also, could the fact that several combinations exist at 69 symbols indicate that the reel is actually 138, or 207 or more symbols long, with the various combinations of symbols interlaced within the ones that must follow each other?

Quote: Ayecarumba

Does the possibility of several different combinations affect the odds of hitting a prize?

Yes. Not the RTP, but the hit frequency. For a given weighting, there is a direct tradeoff between hit frequency and avg award size.

Quote: Ayecarumba

Does the possibility of several different combinations affect the odds of hitting a prize?

If the player plays one line only then the symbol order won't make any difference. However, if the player plays multiple lines then the variance will be less if the high and low paying symbols are more mixed together. Also, you can never have two scatters appear on the same reel at the same time, except perhaps games like Davinci Diamonds, with collapsing reels.

Quote: Ayecarumba

Also, could the fact that several combinations exist at 69 symbols indicate that the reel is actually 138, or 207 or more symbols long, with the various combinations of symbols interlaced within the ones that must follow each other?

Yes, in theory that is possible. It would not affect the odds to splice together two identical reel strips.