Quote from: Scarface on Apr 28, 02:58 PM 2017This is very confusing

Hi Scarface - it is a bit consuming to get ones head around it.  I agree. That's the reason I asked that question to you.

There are two ways to look at it.
1. The probability that you got 1/3x1/3x1/3 is correct. What it means is "once in 27 sets of three spins". It does not mean 27 spins. Because what you calculated is the probability of a dozen to appear the same in three spins. 

2. Think a bit about how many fours and fives of dozens you got. If you are doing one after the other, rather than starting a fresh set of three spins, then a four will count as two sets of three Ina row. A fiver will count as three sets of three in a row and so on. 

Quote from: DoctorSudoku on Apr 28, 04:00 PM 2017
Scarface,
The 1/27 ratio does NOT refer to 1 in 27 spins.

What the 1/27 ratio refers to is that in 27 sets of 3 consecutive spins, you will have -- on average -- ONE instance of dozen no. 3 repeating in 3 consecutive spins.

Scarface,
This is an expansion of my above post.

When you consider 3 consecutive spins, there are 27 separate sets of 3 consecutive spins that are possible for the three dozens. They are as follows (1, 2, and 3 refer to the three dozens):

111
112
113
121
122
123
131
132
133

222
221
223
212
211
213
232
231
233

333
332
331
323
322
321
313
312
311

Of these 27 separate sets of 3 consecutive spins, only one is 333 -- and that is what the 1/27 is referring to.

Thank you DoctorSoduku and Priyanka for clearing this up for me!  So, 1 in 27 spins was definitely wrong!  So statistically,  cycle 333 will appear once in 27 cycles of 3...which is 81 spins.  Unless, of course there are two cycles that join to cause it like 123 and 332.  Anyways, it's still far off from 1 in 27.  Thanks for your help!