Non-Random: how to synchronize parallel streams?

[falkor2k15]

Let's say we have Dozen Cycles and Line Cycles (or VdW with 2 colours, 3 integers paired with 3 dozens, 3 integers); these 2 examples of parallel streams are already in perfect synchronization and suitable to play together. When a repeat happens in one stream it will often occur simultaneously in the other stream, hence both streams in both examples are relative to each other at all points along them.

But how do we create a valid "view" to ensure other types of paired streams are synchronized correctly so that results of one stream doesn't slowly skew the results of the other stream in terms of them working together effectively?

From what I can gather there are 2 ways of referencing parallel streams, including combinations of the two:

Live Lookup

In this type of lookup we already began tracking the lookup stream since the beginning of the session, i.e. how many 0s, 1s, 2s, 3s (or just 0s vs. 1s > = "uniques") and so are keeping a tally of certain stats.
We can check these "live" stats at any time to help us with the other stream - providing they are in sync.
For example, we could be playing dozen cycles and then note the live result on the line cycles stream - that it was previously defined by line 6 on the previous cycle - this could then help us with our current/next dozen cycle and decisions relating to that.

Custom Lookup

Here we may or may not begin tracking a stream, such as positions (see "outside the box" topic), but regardless we do not keep a tally of any live stats.
When we require a lookup we make a custom "view" of the previous results that were manually tracked or are on the marquee. The stats are then formed there and then as and when needed. For example, let's say the current dozen cycle ended on dozen 3 (line 6): we can look back to the last time line 6 hit, i.e. how many positions back, and then make stats for any other lines that hit in-between. This could then quickly help us make a decision on either of the streams.

Next I will discuss how we might go about synchronizing 2 streams for live lookup and custom lookup, and I hope to get feedback on which are correct/incorrect. Other suggestions are also welcome, including any possible additions to the above.

[falkor2k15]

A cycle begins and ends on a repeat.

(121) 1232

Here we ended the current cycle (1232) on a repeat. It began with a 1 (the repeat that defined the previous cycle) and ended with a 2 (the repeat that defined the current cycle). If we were using this stream to create live stats across all dozens/cycles that had appeared thus far then it could tell us information like the following:
0s: nothing
1s: Dz 1, Order 1, Order 2, Defined by 1, Defined by 2, CL1, CL2
2s: Dz 1
3s: Dz 2
Spins: 6

With live stats it's easy to refer to the above info when referencing this stream, but if we had nothing recorded and instead performed a custom lookup then our "view" of that stream - looking backwards - would be different and there would be less information.

1) Counting back: spins

If we create our custom stats by looking back at a set number of spins consistently each time can we keep both streams in sync? For example, if we look back 3 spins then I will arrive back at the start of the dozen cycle above:
1232
That seems like a pretty good key-frame because it happened to be the start of the cycle - 3 spins brought us there precisely. However, if the cycle was CL2 or CL1 then 3 spins could have taken us to the middle of a different cycle instead. However, in 3 spins we are limited to how many events could have happened in that time, i.e. the repeat level would never be above the 3s - mostly constrained to 1s and 2s.

So is counting backwards to spins correct or incorrect? Are we likely to retain proper synchronization using this lookup method?

[falkor2k15]

Or if we retracked the live stats every 3 spins and did a live lookup would the streams be in sync thereafter?

2) Counting back: uniques

Let's say we count back to the last 18 unique numbers instead of 18 spins as our lookup without tracking these numbers as cycles:

...23 1 13 1 22 13

Here there are already 2 repeats within 6 spins, so the number of uniques (numbers >0) is only 4 and the number of non-hits is 33 (on a European table).

For live lookups would retracking after 18 unique numbers retain synchronization from the perspective of a separate Line Cycles stream?

So will looking back on uniques keep our streams working effectively together?

[falkor2k15]

3) Counting back: repeats

(121) 1232

If we counted back to the previous repeat it would only take us back to:
...232

Certainly it won't take us back to the start of the cycle that was created in the first place from tracking repeats, so we have a rather different view. And here we would have very limited stats:
*position 2
*Uniques = 2
*0s = nothing, 1s = 3, 2s = 2

If it were a standard stream of dozens without any framework coming from cycles then would it remain in sync from the viewpoint of a separate stream that did use cycles?

How about looking back to the last 2 repeats:
(..21) 1232

Here we would have more information - but would it be out of sync?

When it comes to retracking a live stats stream after a repeat, here was can say for sure that it works and is valid in keeping - at least a cycles based stream - in sync.

Conclusion

Besides the three methods I've covered above, could there exist any other practical methods for custom lookups on a parallel stream that may or may not retain synchronization? And how else might we retrack a live lookup stream that would keep it in sync with a separate cycles stream?

Lastly, let's say we retracked a live stats stream, say, of straight up numbers then whenever a repeat occurred on the primary cycles stream, could we keep the numbers stream in sync??

[falkor2k15]

The last question worded better:
Lastly, let's say we retracked a live stats stream of straight up numbers whenever a repeat occurred on the primary cycles stream, could we then keep the numbers stream in sync??

[praline]

I'm quite sure that, if you will make a simplified version of all your posts in this topic, you will find the answer to your questions.

Can you. Explain me this
0s: nothing
1s: Dz 1, Order 1, Order 2, Defined by 1, Defined by 2, CL1, CL2
2s: Dz 1
3s: Dz 2

[falkor2k15]

I'm quite sure that, if you will make a simplified version of all your posts in this topic, you will find the answer to your questions.

Can you. Explain me this
0s: nothing
1s: Dz 1, Order 1, Order 2, Defined by 1, Defined by 2, CL1, CL2
2s: Dz 1
3s: Dz 2

Just stats: 0s appeared 0 times = non-hit
1s: appeared once
2s: appeared twice = 1 repeat
3s: appeared three times = 2 repeats