Random Thoughts

[3Nine]

What if you looked within those cycles, Falkor?

[falkor2k15]

What if you looked within those cycles, Falkor?

I'm unable to find her quote but that might be sacrilege? I'm sure it was Priyanka who said that we must look at the events, which are not equally likely, instead of individual spins?

[3Nine]

I'm unable to find her quote but that might be sacrilege? I'm sure it was Priyanka who said that we must look at the events, which are not equally likely, instead of individual spins?

Why not take a closer look?

[falkor2k15]

Some interesting stats come through:

If Cycle Length is 1 or 2 or 3 or 4 then what cycle length will we expect next time providing the defining dozen is the same?

CL1 to CLX (same): 1228   (44.%) 942   (34.%) 490   (18.%) 134   (5.%)
CL2 to CLX (same): 1931   (46.%) 1401   (33.%) 704   (17.%) 174   (4.%)
CL3 to CLX (same): 1438   (44.%) 1132   (35.%) 557   (17.%) 32   (3.%)
CL4 to CLX (same): 449   (45.%) 363   (36.%) 124   (4.%) 160   (16.%)

If Cycle Length is 2 or 3 or 4 (CL1 ignored) then what cycle length will we expect next time providing the defining dozen is different?

CL2/234 to CLX (same): 1932   (46.%) 1402   (33.%) 705   (17.%) 175   (4.%)
CL3/234 to CLX (same): 1439   (44.%) 1133   (35.%) 558   (17.%) 125   (4.%)
CL4/234 to CLX (same): 450   (45.%) 364   (36.%) 161   (16.%) 33   (3.%)

CLX to defining quad on spin 2 (same): 5046   (100.%) 0   (0.%) 0   (0.%) 0   (0.%)


If Cycle Length is 1 or 2 or 3 or 4 then what cycle length will we expect next time providing the defining dozen is different?

CL1 to CLX (diff): 0   (0.%) 980   (44.%) 944   (42.%) 328   (15.%)
CL2 to CLX (diff): 0   (0.%) 1468   (42.%) 1543   (44.%) 506   (14.%)
CL3 to CLX (diff): 0   (0.%) 1107   (42.%) 1112   (42.%) 121   (15.%)
CL4 to CLX (diff): 0   (0.%) 334   (40.%) 414   (16.%) 374   (45.%)

If Cycle Length is 2 or 3 or 4 (CL1 ignored) then what cycle length will we expect next time providing the defining dozen is different?

CL2/234 to CLX (diff): 0   (0.%) 1469   (42.%) 1544   (44.%) 507   (14.%)
CL3/234 to CLX (diff): 0   (0.%) 1108   (42.%) 1113   (42.%) 415   (16.%)
CL4/234 to CLX (diff): 0   (0.%) 335   (40.%) 375   (45.%) 122   (15.%)

CLX to defining quad on spin 2 (diff): 3917   (25.%) 5943   (38.%) 4572   (29.%) 1416   (9.%)
CL234 to defining quad on spin 2 (diff): 5944   (50.%) 4573   (38.%) 1417   (12.%)

[falkor2k15]

Above = defining quad NOT dozen!

The last test is our first look inside the cycle: can the cycle length help us to guess whether the first betting result (spin 2; spin 1 is the final result of the last cycle that is brought forward to the next cycle) will be the same as the defining quad or different?

[falkor2k15]

Those CL234 tests used the wrong variable... running all stats again. 

[falkor2k15]

Let's try again... hopefully this will make more sense too:


Defined by Total (same): 24278 (55.%) (different): 19485 (45.%)


Cycle Lengths - same or different to previous cycle length

CL1234 Totals (same): 12616 (29.%) (different): 31146 (71.%)

Cycle Lengths (CL1 ignored) - same or different to previous cycle length

CL234 Total (same): 13292 (40.%) (different): 19551 (60.%)

Cycle Lengths (CL1 ignored then 1st bet ignored) - same or different to previous cycle length

CL234 Total (same): 13292 (30.%) (different): 30471 (70.%)


Cycle Lengths - overall general stats

CL1234 Totals 1: 10920 (25.%) 2: 16296 (37.%) 3: 12374 (28.%) 4: 4173 (10.%)

Cycle Lengths (CL1 ignored) - overall general stats

CL234 Totals 2: 16296 (50.%) 3: 12374 (38.%) 4: 4173 (13.%)

Cycle Lengths (CL1 ignored then 1st bet ignored) - overall general stats

CL234 Totals 1: 10920 (25.%) 2: 16296 (37.%) 3: 12374 (28.%) 4: 4173 (10.%)


Cycle Lengths - depending on whether the defining quad is same/different to previous cycle

CL1234 Totals (same) 1: 10920 (45.%) 2: 8111 (33.%) 3: 4173 (17.%) 4: 1074 (4.%)
CL1234 Totals (different) 1: 0 (0.%) 2: 8185 (42.%) 3: 8201 (42.%) 4: 3099 (16.%)

Cycle Lengths (CL1 ignored) - depending on whether the defining quad is same/different to previous cycle

CL234 Totals (same) 2: 8096 (61.%) 3: 4666 (35.%) 4: 530 (4.%)
CL234 (different) 2: 8200 (42.%) 3: 7708 (39.%) 4: 3643 (19.%)

Cycle Lengths (CL1 ignored then 1st bet ignored) - depending on whether the defining quad is same/different to previous cycle

CL234 Totals (same) 2: 8096 (61.%) 3: 4666 (35.%) 4: 530 (4.%)
CL234 (different) 1: 10920 (36.%) 2: 8200 (27.%) 3: 7708 (25.%) 4: 3643 (12.%)


Cycle Lengths - which cycle length will most likely be the same or different to the previous cycle length

CL1/1234 1: 2693 (25.%) 2: 6055 (37.%) 3: 3481 (28.%) 4: 387 (9.%) to same
CL1/1234 1: 8226 (75.%) 2: 10241 (63.%) 3: 8893 (72.%) 4: 3786 (91.%) to different

Cycle Lengths (CL1 ignored) - which cycle length will most likely be the same or different to the previous cycle length

CL2/234 2: 8096 (50.%) 3: 4666 (38.%) 4: 530 (13.%) to same
CL2/234 2: 8199 (50.%) 3: 7708 (62.%) 4: 3643 (87.%) to different

Cycle Lengths (CL1 ignored then 1st bet ignored) - which cycle length will most likely be the same or different to the previous cycle length

CL2/234 2: 8096 (37.%) 3: 4666 (29.%) 4: 530 (9.%) to same
CL2/234 2: 13700 (63.%) 3: 11694 (71.%) 4: 5076 (91.%) to different


If Cycle Length is 1 or 2 or 3 or 4 then what cycle length will we expect next time providing the defining quad is the same

CL1 to CLX (same): 2693   (45.%) 2000   (33.%) 1046   (17.%) 256   (4.%)
CL2 to CLX (same): 4151   (46.%) 2988   (33.%) 1564   (17.%) 392   (4.%)
CL3 to CLX (same): 3001   (44.%) 2320   (34.%) 1171   (17.%) 103   (4.%)
CL4 to CLX (same): 1075   (45.%) 803   (34.%) 323   (5.%) 392   (17.%)

If Cycle Length is 1 or 2 or 3 or 4 then what cycle length will we expect next time providing the defining quad is different

CL1 to CLX (diff): 0   (0.%) 2010   (41.%) 2163   (44.%) 751   (15.%)
CL2 to CLX (diff): 0   (0.%) 3067   (43.%) 2964   (41.%) 1170   (16.%)
CL3 to CLX (diff): 0   (0.%) 2356   (42.%) 2310   (42.%) 284   (16.%)
CL4 to CLX (diff): 0   (0.%) 752   (42.%) 893   (16.%) 764   (42.%)

If Cycle Length is 2 or 3 or 4 (CL1 ignored) then what cycle length will we expect next time providing the defining quad is the same

CL2/234 to CLX (same): 4152   (46.%) 2989   (33.%) 1565   (17.%) 393   (4.%)
CL3/234 to CLX (same): 3002   (44.%) 2321   (34.%) 1172   (17.%) 324   (5.%)
CL4/234 to CLX (same): 1076   (45.%) 804   (34.%) 393   (17.%) 104   (4.%)

If Cycle Length is 2 or 3 or 4 (CL1 ignored) then what cycle length will we expect next time providing the defining quad is different

CL2/234 to CLX (diff): 0   (0.%) 3068   (43.%) 2965   (41.%) 1171   (16.%)
CL3/234 to CLX (diff): 0   (0.%) 2357   (42.%) 2311   (42.%) 894   (16.%)
CL4/234 to CLX (diff): 0   (0.%) 753   (42.%) 765   (42.%) 285   (16.%)


Can the cycle length help us to guess whether spin 2 (spin 1 is the final result of the last cycle that is brought forward to the next cycle) will be the same as the defining quad

CLX to defining quad on spin 2 (same): 2693   (25.%) 4151   (38.%) 3001   (27.%) 1075   (10.%)
CL234 to defining quad on spin 2 (same): 4152   (50.%) 3002   (36.%) 1076   (13.%)

Can the cycle length help us to guess whether spin 2 (spin 1 is the final result of the last cycle that is brought forward to the next cycle) will be different to the defining quad

CLX to defining quad on spin 2 (diff): 8430   (25.%) 12481   (37.%) 9628   (29.%) 3193   (9.%)
CL234 to defining quad on spin 2 (diff): 12482   (49.%) 9629   (38.%) 3194   (13.%)

[RMore]

Falkor, can I ask a dumb question please? I'm just trying to get my head around the concept of Cycle and Cycle Length in terms of quads because I want to make sure I properly understand your stats and what they mean.

Are we talking about repeaters here? That is, a cycle length of 1 means that, from the point where we start the process we have a repeat immediately. So quad 1 appears and then straight-away quad 1 appears again - this is a cycle of length 1. If we skip 1 spin and get a repeat then that is a cycle of length 2. And so on. So that the maximum is 4 because a repeater absolutely must appear at least by the 5th spin and in this case it is a cycle of length 4.

Also, are you calculating your stats on the basis that the quad that terminated the cycle is also used as the first spin in the new cycle?

thanks
Rog

[3Nine]

Are we talking about repeaters here? That is, a cycle length of 1 means that, from the point where we start the process we have a repeat immediately. So quad 1 appears and then straight-away quad 1 appears again - this is a cycle of length 1. If we skip 1 spin and get a repeat then that is a cycle of length 2. And so on. So that the maximum is 4 because a repeater absolutely must appear at least by the 5th spin and in this case it is a cycle of length 4.

That's correct.

[falkor2k15]

Falkor, can I ask a dumb question please? I'm just trying to get my head around the concept of Cycle and Cycle Length in terms of quads because I want to make sure I properly understand your stats and what they mean.

Are we talking about repeaters here? That is, a cycle length of 1 means that, from the point where we start the process we have a repeat immediately. So quad 1 appears and then straight-away quad 1 appears again - this is a cycle of length 1. If we skip 1 spin and get a repeat then that is a cycle of length 2. And so on. So that the maximum is 4 because a repeater absolutely must appear at least by the 5th spin and in this case it is a cycle of length 4.

Also, are you calculating your stats on the basis that the quad that terminated the cycle is also used as the first spin in the new cycle?

thanks
Rog

Yep - what you are describing is exactly the framework used for the above stats. I need to check exactly how Priyanka is missing out cycle length 1 - but it seems to have no affect on the stats hardly - certainly I'm not seeing any potential exploit with it (yet).

[RMore]

Thanks 3Nine. And regarding the starting point? Do I have that correct also?

Now, trying to figure out the numbers in Falkor's analysis.

Defined by Total (same): 24278 (55.%) (different): 19485 (45.%)

Do I understand that this means: out of 43,763 cycles total there were 24,278 that completed with the same quad as the one that completed the last cycle, and 19,485 where the completing quad was different?

I really have to question my understanding of this because I would have expected the figure to be somewhere around the 25% for same and 75% for different. A little variation I can cope with but this? That is huge! There are 4 possibilities to complete a cycle right? Any one of the 4 could do it and in a random game the chances of any one of the 4 coming up is 25% (not including the zero). The same quad as the last cycle completion is just one of the quads - the other 3 did NOT complete the cycle - right? So the chances for that particular quad to come up is still just 25% in my book. So how can it possibly be 55%. Plainly I have misunderstood what these stats mean.

[3Nine]

Rog,
A recent post of Priyanka's may be helpful:

"There was once a discussion around sequences and the probability of sequences. There was always a twist to it.

It went like this, consider the sequences RB, RR, BR, BB. ¼ is the likelihood of each of these sequences to occur. So you are playing for the sequence RB. Place a bet on red. Red comes through. Now what is the probability that you will get a sequence RB after a red has come through? It is 50% and not 25%. Simple as it may sound, but a complex subject to get your head around it.  Why complex? It seems a very simple thing. The odds of next spin is always the odds of the position you are playing. Hmm! Let me think again.

Transfer that thought to dozen cycles. We established that probabilities of cycles of length 1, 2 and 3 are 1/3, 4/9 and 2/9. Yes, definitely the first thing we discussed. No doubts. Lets play for cycle 1. Very straightforward. The odds of cycle 1 occuring are as good as the dozen to repeat. Fair.

Now lets play for cycle 3. After two unique dozens appear, what is the odds that the next dozen will occur. Is it 1/3 which is the odds of next dozen or is it 2/9 the odds of cycle length 3? Getting the answer for this right is significant for us to progress. As I said, no hints, no puzzles. So the answer is 1/3. Why is it not 2/9. It is not 2/9 because at the point when two dozens have rolled, <EM>the probability of the cycle length being 1 has to be ruled out</EM>. It is a question of whether it is going to be cycle of length 2(4/9) or cycle of length 3 (2/9). If those are the only available probabilities, it is very clear that one is 2/3 and other is 1/3 and hence cycle length 3 forming after 2 dozens appear is at a probability of 1/3. Which again is equal to the probability of a single dozen."

Hope that helps.

[falkor2k15]

Do I understand that this means: out of 43,763 cycles total there were 24,278 that completed with the same quad as the one that completed the last cycle, and 19,485 where the completing quad was different?

I really have to question my understanding of this because I would have expected the figure to be somewhere around the 25% for same and 75% for different. A little variation I can cope with but this? That is huge! There are 4 possibilities to complete a cycle right? Any one of the 4 could do it and in a random game the chances of any one of the 4 coming up is 25% (not including the zero). The same quad as the last cycle completion is just one of the quads - the other 3 did NOT complete the cycle - right? So the chances for that particular quad to come up is still just 25% in my book. So how can it possibly be 55%. Plainly I have misunderstood what these stats mean.

It's the same stat as the one in Priyanka's spreadsheet:


It's been covered before for dozens:
rrbbyou can calculate the probability that a repeat on dozens occurs on the previous "defining" dozen: 17/27 (which is of course Priyanka's 63%)
link:://s32.postimg.org/gml4xyxl1/defining.jpg
link:://:.rouletteforum.cc/index.php?topic=15938.450 (page 31)


rrbb I think that what Priyanka shared is extremely important: 

The probability on any dozen is of course 1/3. But Under the condition of a repeat, the probability is "suddenly" 17/27
Btw: there are many other imbalances. Priyanka showed you some...
link:://:.rouletteforum.cc/index.php?topic=15938.450 (page 31)


Nothing strange or new. Going to bayes site it is link:://:.roulettician.com/probability1.html#mozTocId598749
winkel: link:://:.vlsroulette.com/index.php?topic=13004.0
link:://:.rouletteforum.cc/index.php?topic=15938.795 (page 54)


This stat has a 75% chance:

Cycle Lengths - which cycle length will most likely be the same or different to the previous cycle length

CL1/1234 1: 2693 (25.%) 2: 6055 (37.%) 3: 3481 (28.%) 4: 387 (9.%) to same
CL1/1234 1: 8226 (75.%) 2: 10241 (63.%) 3: 8893 (72.%) 4: 3786 (91.%) to different

Also "probability asserting itself" based on the outcome of 3/4 quads besides the defining quad:

Can the cycle length help us to guess whether spin 2 (spin 1 is the final result of the last cycle that is brought forward to the next cycle) will be the same as the defining quad or different?

CLX to defining quad on spin 2 (same): 2693   (25.%) 4151   (38.%) 3001   (27.%) 1075   (10.%)
CLX to defining quad on spin 2 (diff): 8430   (25.%) 12481   (37.%) 9628   (29.%) 3193   (9.%)

(8430 / (2693 + 8430)) * 100 = 75%

[falkor2k15]

3Nine, yeah, the defining dozen (or quad) result is based on stitching bets and predicting that the next cycle (as an event) will be the same as the previous defining element:

Defined by Total (same): 24278 (55.%) (different): 19485 (45.%)

I'll just grab a Krispy Kreme... one sec.

OK, so perhaps this is where missing out cycle length 1 can change the above stats? I don't think I've covered or considered that test before? 

The next opportunity seems to be at spin 3 where Priyanka either bets the last 2 quads or the opposite of the last 2 quads. Spin 2 doesn't seem to offer any bias, so perhaps something happens at spin 3 (to also be tested next).

[RMore]

Thanks guys. This is getting real interesting. OK, so the 55% is the COMBINED probability of the possibility that the previous defining quad will hit on one of the next four spins - determined by simulation rather than theoretical calculation? Does this include the zero?

The theoretical number for this (taking into account the zero) is 67% (I think, if I have it right). So the simulation is worse than the theoretical. This would indicate that we should NOT play for the same I would have thought.

This seems to contradict where this is all going so where am I going wrong in my thinking here?