Weasel Ware
[ Introduction | GUI Description | The Math | The GUI | Atom tha Immortal ]
The Math
First, let's look at partitioned search used by Dr. Dawkins. Assuming uniformity, the probability of successfully identifying a specified letter with sample replacement at least once in Q queries is
.
The probability of identifying all L characters in Q queries is therefore
Solving for
gives
Setting
gives the median number of queries required for success using partitioned search. This is the number displayed on the Weasel GUI under partitioned search. If we ran a large number of simulations, half the number of queries needed to achieve success would be above the median and half below.
For L = 28 and N = 27, we obtain a median number of queries for partitioned search equal to .
For example, the display below lists this number as 98.
For unassisted random search, the probability of success in Q queries is
Solving for
gives
The number
,
however, can be so small that most computers will calculate
as being identically zero. We thus find useful the approximation that, for
we can write
.
The number of queries for unassisted random search then becomes
Setting
gives the median number of queries required for success using unassisted random search. For L = 28 and N = 27, we obtain a median number of queries for partitioned search equal to
For example, the display below lists this number as 8.30e+39.
For deterministic search, the probability of success for a single letter in Q queries is
The probability of that all L letters being correct in Q queries is therefore
Solving for
gives
For L = 28 and N = 27, we obtain a median number of queries for the deterministic search is equal to
In the GUI, this is displayed as 26 queries.
In the binary and nucleotide modes, the same formulas are used except that N = 2 and N = 4 , respectively.
