Random Thoughts

[3Nine]

27 Quad Cycles:

411
133
313
34211
1433
311
141
1244
424
44
44
44
41233
3311
133
3122
22
22
22
2132
22
2343
3123
33
3211
1431
1322

[3Nine]

20 Line Cycles:

5125
55
515
563125
55
54125
51365
535
566
66
61244
44
41254
4232
232
22
21533
346522
245311
1541

[3Nine]

30 Dozen Cycles:

311
133
313
33
3211
133
3211
131
1233
323
33
33
33
311
122
22
211
1321
121
121
11
11
1322
22
233
311
1232
211
1321
122

[rrbb]

27 Quad Cycles:

411
...
1322

Hi 3Nine, not to nitpick: technically a cycle either starts on, and ends before a repeat, or it starts after a repeat and ends on a repeat. That kind of depends on the view.

The essence of these kind of cycles is that they only contain unique numbers!. In your case it starts with a repeat, so the last number can be left out!

Other than that: the cycles seem to be correct!

grts rr

[Tomla021]

when you get down to it and with my limited understanding Priyanka is banking on repeaters

[rrbb]

when you get down to it and with my limited understanding Priyanka is banking on repeaters

Hi Tomla021,
I think that you are both right and wrong (hmm reminds me of Schroedingers cat  ). What I mean with this is that if for example VdW is used on a two-coloring of numbers (like high low, odd even) you are right.

However, in case VdW is for example used for wins and losses (W, L ==> also a two coloring!) then not...

grts rrbb

Please note: I do not claim to know exactly what Priyanka is doing, but the principles she is talking about are extremely versatile.

[3Nine]

Thank you for this thread, Priyanka.

I now look at all games with fresh eyes!

[Scarface]

30 Dozen Cycles:

311
133
313
33
3211
133
3211
131
1233
323
33
33
33
311
122
22
211
1321
121
121
11
11
1322
22
233
311
1232
211
1321
122

Trying to figure out something on the dozen cycles.  What percentage of dozens will complete a cycle in 1 spin vs 2 spin vs 3 spins?  I'm assuming about 1 in 3 will complete in the first spin of a new cycle.  What about the others?  Can someone help out on the math here? 

Out of 99 cycles, I'm thinking 33 will complete on the first spin....44 on the second...and 22 on the third.  Is this right?

[rrbb]

Trying to figure out something on the dozen cycles.  What percentage of dozens will complete a cycle in 1 spin vs 2 spin vs 3 spins?  ... spin....44 on the second...and 22 on the third.  Is this right?

Hi scarface,

This can best be visualized by a "tree"

You start at the top with the first spin.

You have two possibilities for the next spin:
1.  A repeat. Out of 3 possible dozens you can only pick one (the first spin)-> 1/3 this ends our spincycle of length one!

2. No repeat. Out of 3 possibilities you can choose from 2 (no repeat of the first spin)-> 2/3.

For the next spin we again have 2 possibilities
A. A repeat. Now we have 2 possibilities to choose from (2/3).  But remember: to reach this point, we first had to choose the second spin to be no repeat!

The total probability of a repeat on the second spin equals 2/3 x 2/3, which equals 4/9.

So yes, your calculation is correct!

[rrbb]

In the same fashion you can calculate the probability that a repeat on dozens occurs on the previous "defining" dozen: 17/27 (which is of course Priyanka's 63%)

Sorry the very bad drawing (sorry, i'm not an artist)

Grts rrbb

[rrbb]

The idea is, to "travel" from the top (first spin) to the end of a branch, you have to multiply the probabilities.

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.

This "phenomena" has a certain name an applications. Bayes could tell you more about this!

The relevance for roulette remains to be seen, but admit: it is fascinating!

Btw: there are many other imbalances. Priyanka showed you some...

Hope this helps a little bit.

Grts rrbb

[Priyanka]

Some interesting thoughts from rrbb there. 

Can someone help out on the math here?

rrbb gave you the mathematical explanation in a very simple manner. For some however data speaks. Attached is what will give you a data view for cycles in dozens, quads and lines.

[Priyanka]

Btw: there are many other imbalances. Priyanka showed you some..

Completely true.

[Turner]

Attached is what will give you a data view for cycles in dozens, quads and lines.

Thats a generous give-away

[Priyanka]

Thats a generous give-away

Hope thats not a tongue-in-cheek      
If not there is many more to come.. Already rrbb is giving away a lot....