Pineapple has well summarized the behaviour of the Cultris 2 randomizer:

QUOTE(Pineapple @ Mar 15 2013, 10:15 AM)

My initial observations are that the randomizer is unbiased, strongly excludes interval 1 (the same piece twice in a row), weakly excludes interval 2 (the same piece appearing with just one other piece in between), and makes no attempt to prevent droughts.

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I have prepared some pics. And I will also describe randomisers which create similar piece sequences.

First of all, Cultris randomizer is unbiased. The sequence consisted of 10,000,000 pieces and the number of I,L,J,O,T,S,Z pieces just differed by a few 1000 - that's roughly as much as you would expect to get with memoryless randomizer ( there the standard deviation lies at sqrt( 10,000,000 * (6/7)*(1/7) ) = 1106 pieces ).

This image shows the chances of getting the current kind again within the next 7 pieces (

here in comparison to memoryless randomizer). There's just roughly a 2.7 % chance for repetions - this isn't even a fifth of memoryless randomizer! Chances that the 2nd and 3rd next piece is from the same kind is also a bit reduced.

But then chances stay the same! And that's a very interesting point. I am quite sure some theoretical result was used to assure this. This is harder to achieve than you might think. Let's take for example a randomizer, that keeps a history of the 2 most recently generated pieces and lowers the chance to generate one of those as the next piece. Let's say you currently got an I. Then chances are reduced that you get an I as next or 2nd next piece, which results in a bigger chance for an I as the 3rd next piece - although the 3rd next piece doesn't depend directly on your current piece. I hope you understand what I mean. In the case, Cultris 2 randomizer is some kind of history randomizer, it uses at least a history of the 5 last pieces, e.g. I counted 539652 sequences of the kind ITOLJI 1079304 (5th next piece the same as first, the rest is different) and 2*546973 sequences of the kind ITOLJS (now 6th piece is different!). Those numbers differ by more than 1 %.

This image shows how long you have to wait until you get the same kind again (

here in comarison to memoryless randomizer). Droughts of 29 or more pieces are possible, but not as common as for memoryless randomizer (as there are less repetitions). This statistic has a standard deviation of 5.258 (i.e. most often you have to wait 7 +/- 5.258 pieces) in comparison to sqrt( 8 ) = 2.828 pieces for bag randomizer and sqrt(42) = 6.481 pieces for memoryless randomizer.

This image shows how often you get a certain piece sequences of length 3 (

here in comparison to memoryless randomizer).

I used those percentages to create a history randomizer which keeps track of your last 2 pieces:

CODE

If the last 2 pieces are of the same kind, repeat it with a chance of 2.8105 % or hand out one of the other 6 kinds with a chance of 16.1982 %. Otherwise (last 2 pieces different), repeat the last with a chance of 2.7055 %, repeat the 2nd with a chance of 11.7361 % or hand out one of the other 5 kinds with a chance of 17.1117 %.

I created a 10,000,000 piece sequence with this randomizer. Here the first 2 pics in comparison to the Cutris 2 sequence.

The 2-history randomizer overshoots the chance of getting the same kind after 3 pieces (as I tried to explain a bit above). Beside that it's very similar.

As you can see, droughts of length 15 or more is very similar, which also shows that Cultris 2 randomizer doesn't use mechanics to reduce droughts.

And I also created a 3-history randomizer by evaluating the numbers of length 4 sequences:

CODE

last 3 pieces of the same kind: (e.g. III)

give last = 2.7719 %

give other = 16.2047 %

3rd last = 2nd last, but last different (e.g. IIT)

give last = 2.9313 %

give 2nd last = 11.8981 %

give other = 17.0341 %

3rd last = last, but 2nd last different (e.g. ITI)

give last = 2.6498 %

give 2nd last = 11.6954 %

give other = 17.1310 %

2nd last = last, but 3rd last different (e.g. ITT)

give last = 2.8116 %

give 3rd last = 15.1683 %

give other = 16.4040 %

all 3 last pieces different (e.g. ITO)

give last = 2.7061 %

give 2nd last = 11.7366 %

give 3rd last = 15.5810 %

give other = 17.4941 %

Here the results: