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[http://uraharaben1hime.blogspot.com cheap phentermine table] [http://114418523.blogspot.com casino guide online] [http://huapatossu.blogspot.com casino online review] [http://7982257596.blogspot.com california casino] [http://nostawnevets53.blogspot.com casino free] [http://kleinerachel.blogspot.com valium ativan] [http://cmubroadway.blogspot.com casino poker] [http://evil-gummiworm.blogspot.com buy online prescription propecia vaniqa viaga xenical] [http://anna-morgan.blogspot.com propecia patent] [http://unseenoyster.blogspot.com propecia effectiveness] [http://brokenbond.blogspot.com cheap phentermine online] [http://princesskariboo.blogspot.com propecia rogaine] [http://im-really-cool.blogspot.com propecia patent expiration] [http://dashulya.blogspot.com casino casino] [http://0x009.blogspot.com casino online top] [http://lovejuliet3.blogspot.com casino winner] [http://khawkslaxfan51.blogspot.com propecia hair loss treatment] [http://amino-vera.blogspot.com generic propecia canada] [http://brightflashes.blogspot.com casino wager] [http://theillegalcause.blogspot.com loss propecia] [http://sinbiom.blogspot.com casino las vegas] [http://azur3skye.blogspot.com best casino] [http://mayphyoe.blogspot.com buy no online prescription xanax] [http://kaizokukitsune.blogspot.com propecia alternative] The '''Random Generator''' is BPS's name for the algorithm used to generate the sequence of [[tetromino]]es in ''Tetris'' brand [[game]]s that follow the [[Tetris Guideline]].
[[File:Random_Generator_physical_example.png|thumb|right|200px|The seven tetrominoes are shuffled and drawn from the bag one by one.]]


Random Generator generates a sequence of all seven one-sided tetrominoes (I, J, L, O, S, T, Z) permuted randomly, as if they were drawn from a bag. Then it deals all seven tetrominoes to the piece sequence before generating another bag. There are [http://en.wikipedia.org/wiki/Factorial 7!], or 5,040, permutations of seven elements, and it is believed that ''Tetris'' assigns a nearly equal probability to each of these, making it much less likely that the player will get an obscenely long run without a desired tetromino. It can produce a maximum of 12 tetrominoes between one I and the next I, and a run of S and Z tetrominoes is limited to a maximum of 4.
The '''Random Generator''', also popularly known as '''7-bag''', is the algorithm used to generate the sequence of [[tetromino]]es in ''Tetris''-branded games that follow the [[Tetris Guideline]]. Despite its generic appearance, presumed employees of [[BPS]] are known to treat the term "Random Generator" as a unique name which refers only to this particular algorithm.
Exception: In Random Generator as implemented in [[Tetris The Grand Master Ace]], the first piece of the first bag is always I, J, L, or T, just as in the traditional [[TGM randomizer]].


Despite the generic sounding name, presumed employees of BPS are known to treat the term "Random Generator" as a unique name, referring only to this particular algorithm.
The Random Generator generates a sequence of all seven tetrominoes (I, J, L, O, S, T, Z) in a random order, as if the pieces were drawn from a bag. The resulting sequence of seven tetrominoes is added to the queue, and another bag is then generated. There are [http://en.wikipedia.org/wiki/Factorial 7!], or 5,040, permutations of seven elements, and it is believed that ''Tetris'' assigns a nearly equal probability to each of these. The result is that "droughts", in which a particular piece does not appear for an extended period, are limited in severity and less likely to occur than if all pieces were equally likely to be the next piece at all times. The Random Generator can produce a run of no more than 12 tetrominoes between one I piece and the next, and runs of S and Z tetrominoes are limited to a length of 4. (As an exception, in the [[Tetris The Grand Master Ace]] implementation of the Random Generator, the first piece of the first bag is always I, J, L, or T, just as in the traditional [[TGM randomizer]].)


== Snake sequences ==
While the number of tetrominoes in a single Random Generator bag is canonically 7, some games use bag algorithms with other bag sizes. The public beta of [[Tetris Online (Japan)]], for example, used an 8-bag randomizer. Additionally, not all Guideline-compliant games use the Random Generator in all modes. ''[[Tetris Worlds]]'' and ''[[Tetris Green]]'', for instance, use a different randomizer in their [[The New Tetris|Square modes]], and ''TGM3'' uses its own [[TGM randomizer#Tetris The Grand Master 3 Terror-Instinct|35-bag variant of the TGM randomizer]] even under World Rule.  
There are two "snake" tetrominoes, called S and Z. As only two snakes will be in a given bag, a sequence of more than two snakes must cross the "seam" between bags. The probability of the next two bags having a sequence of four consecutive snakes, the maximum possible, is 1/(7*6*7*6) for SZSZ and likewise for SZZS, ZSSZ, and ZSZS, for a total of 1/441. But the probability of these being your three next pieces are 1/441 times the probability of being at position 6 in a bag, so the probability of the next four pieces being SZSZ are 1 in 3087.


Define a "2|1 combo" as chosen sixth and seventh pieces in one bag and first piece in next bag, and a "1|2 combo" as chosen seventh piece in one bag and first and second pieces in next bag. Define a "snake" as the S tetromino or the Z tetromino.
The Random Generator was originally developed for ''The New Tetris''. This early version of the algorithm used a bag size of 63—nine of each piece—to allow for streaks to assist in square building, and to ensure players need not wait too long to receive pieces needed to complete squares.


The probability of any 2|1 combo (e.g. SZ|Z) is 1/(7*6*7) = 1/294. There are four different 2|1 combos containing all snakes (SZ|Z, SZ|S, ZS|Z, and ZS|S), so the probability of getting a 3-snake 2|1 in your next two bags is 4/294. But the probability of being at the sixth piece in a bag, where your next three pieces are a 2|1, is 1/7, making the probability of being at a three-snake 2|1 equal to 4/(294*7) = 2/1029. By symmetry, the 1|2 probabilities are exactly the same: 2/1029. So for Random Generator, this makes a 1 in 257 chance of your next three tetrominoes being snakes.
== "Snake" sequences ==
There are two "snake" tetrominoes, S and Z. As only two snakes will be in a given bag, a sequence of more than two snakes necessarily crosses the "seam" between bags. The probability of the next two bags having a sequence of four consecutive snakes, the maximum possible, is 1/(7*6*7*6) for each of SZSZ, SZZS, ZSSZ, and ZSZS, for a total of 1/441. Meanwhile, the probability of these being the three next pieces in the queue are 1/441 times the probability of being at position 6 in a bag, and so the probability of the next four pieces being SZSZ is 1/3087.


:''To do: compare with odds for [[TGM randomizer]]''
Let "AB|C" represent the final two pieces of one bag and the first piece of the next bag, and similarly, let "A|BC" represent the final piece of one bag and the first two of the next bag. The probability of any given AB|C (e.g., SZ|Z) is 1/(7*6*7) = 1/294.
 
There are four unique AB|C combos containing only snakes (SZ|Z, SZ|S, ZS|Z, and ZS|S), so the probability of getting a three-snake AB|C in two consecutive bags is 4/294. However, because such a sequence can only occur starting at the sixth position (out of seven) in a bag, the probability of such a sequence constituting the next three pieces at any point in the game is equal to 4/(294*7) = 2/1029. By symmetry, the A|BC probabilities are the same, and so for the Random Generator, the overall probability of any three consecutive pieces being snakes is 1/257.
 
<!-- ''To do: compare with odds for [[TGM randomizer]]'' -->


== References ==
== References ==
*[http://www.tetrisconcept.com/forum/viewtopic.php?p=822#822 Randomizer discussion on forum]
*[https://tetrisconcept.net/threads/the-tetris-guidelines-random-generator-is-apparently-simple.349/ Randomizer discussion on forum]
**[http://www.tetrisconcept.com/forum/viewtopic.php?p=2030#2030 Name of Random Generator revealed]
**[https://tetrisconcept.net/threads/the-tetris-guidelines-random-generator-is-apparently-simple.349/#post-16554 Name of Random Generator revealed]
 
== See also ==
== See also ==
*[[Blackjack]]
*[[Blackjack]]
*[[Playing forever]]


[[Category:Game Mechanics]]
[[Category:Gameplay Components]]
[[Category:Randomizers]]
[[Category:Randomizers]]

Latest revision as of 02:47, 27 May 2025

The seven tetrominoes are shuffled and drawn from the bag one by one.

The Random Generator, also popularly known as 7-bag, is the algorithm used to generate the sequence of tetrominoes in Tetris-branded games that follow the Tetris Guideline. Despite its generic appearance, presumed employees of BPS are known to treat the term "Random Generator" as a unique name which refers only to this particular algorithm.

The Random Generator generates a sequence of all seven tetrominoes (I, J, L, O, S, T, Z) in a random order, as if the pieces were drawn from a bag. The resulting sequence of seven tetrominoes is added to the queue, and another bag is then generated. There are 7!, or 5,040, permutations of seven elements, and it is believed that Tetris assigns a nearly equal probability to each of these. The result is that "droughts", in which a particular piece does not appear for an extended period, are limited in severity and less likely to occur than if all pieces were equally likely to be the next piece at all times. The Random Generator can produce a run of no more than 12 tetrominoes between one I piece and the next, and runs of S and Z tetrominoes are limited to a length of 4. (As an exception, in the Tetris The Grand Master Ace implementation of the Random Generator, the first piece of the first bag is always I, J, L, or T, just as in the traditional TGM randomizer.)

While the number of tetrominoes in a single Random Generator bag is canonically 7, some games use bag algorithms with other bag sizes. The public beta of Tetris Online (Japan), for example, used an 8-bag randomizer. Additionally, not all Guideline-compliant games use the Random Generator in all modes. Tetris Worlds and Tetris Green, for instance, use a different randomizer in their Square modes, and TGM3 uses its own 35-bag variant of the TGM randomizer even under World Rule.

The Random Generator was originally developed for The New Tetris. This early version of the algorithm used a bag size of 63—nine of each piece—to allow for streaks to assist in square building, and to ensure players need not wait too long to receive pieces needed to complete squares.

"Snake" sequences

There are two "snake" tetrominoes, S and Z. As only two snakes will be in a given bag, a sequence of more than two snakes necessarily crosses the "seam" between bags. The probability of the next two bags having a sequence of four consecutive snakes, the maximum possible, is 1/(7*6*7*6) for each of SZSZ, SZZS, ZSSZ, and ZSZS, for a total of 1/441. Meanwhile, the probability of these being the three next pieces in the queue are 1/441 times the probability of being at position 6 in a bag, and so the probability of the next four pieces being SZSZ is 1/3087.

Let "AB|C" represent the final two pieces of one bag and the first piece of the next bag, and similarly, let "A|BC" represent the final piece of one bag and the first two of the next bag. The probability of any given AB|C (e.g., SZ|Z) is 1/(7*6*7) = 1/294.

There are four unique AB|C combos containing only snakes (SZ|Z, SZ|S, ZS|Z, and ZS|S), so the probability of getting a three-snake AB|C in two consecutive bags is 4/294. However, because such a sequence can only occur starting at the sixth position (out of seven) in a bag, the probability of such a sequence constituting the next three pieces at any point in the game is equal to 4/(294*7) = 2/1029. By symmetry, the A|BC probabilities are the same, and so for the Random Generator, the overall probability of any three consecutive pieces being snakes is 1/257.


References

See also