Let's say we were on a 2 bit processor and we had a 2-bit PRNG. There could only be 22 starting points (seeds).

But the (non-repeating) sequences it could produce are any permutation of the following 24 permutations of the 4 basic values it can produce:

{0, 1, 2, 3}  |  {0, 1, 3, 2}  |  {0, 2, 1, 3}  |  {0, 2, 3, 1}  |  
{0, 3, 1, 2}  |  {0, 3, 2, 1}  |  {1, 0, 2, 3}  |  {1, 0, 3, 2}  |  
{1, 2, 0, 3}  |  {1, 2, 3, 0}  |  {1, 3, 0, 2}  |  {1, 3, 2, 0}  |  
{2, 0, 1, 3}  |  {2, 0, 3, 1}  |  {2, 1, 0, 3}  |  {2, 1, 3, 0}  |  
{2, 3, 0, 1}  |  {2, 3, 1, 0}  |  {3, 0, 1, 2}  |  {3, 0, 2, 1}  |  
{3, 1, 0, 2}  |  {3, 1, 2, 0}  |  {3, 2, 0, 1}  |  {3, 2, 1, 0}

[download]

Hence, the 32-bit, Mersenne Twister MT19937 can produce 219937 - 1 values (from any given starting point) before it repeats itself exactly.

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The start of some sanity?

In reply to Re^4: How likely is rand() to repeat? by BrowserUk
in thread How likely is rand() to repeat? by desertrat

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