Binary Refresher
We now know that the number we want for BA = 011, but this number is in binary.
In binary, we're working in base 2, so each digit represents an on/off switch for a certain power of two.
In binary, we're working in base 2, so each digit represents an on/off switch for a certain power of two.
So, in the decimal system, BA = 3.
Final Step
So, we have found BA already. The algorithm also needs the calculation of AA, AB, and BB which we work out using ths same steps described above. Keep in mind that the order of the sequences is important.
Given two (2) triplet sequences, A and B, the odds of Player B winning are given by:
Given two (2) triplet sequences, A and B, the odds of Player B winning are given by:
In our example:
AA = 111 (in binary) = 7
AB = 000 (in binary) = 0
BB = 100 (in binary) = 4
BA = 100 (in binary) = 3
AA = 111 (in binary) = 7
AB = 000 (in binary) = 0
BB = 100 (in binary) = 4
BA = 100 (in binary) = 3
We take this as meaning the following:
The odds of Player B winning over Player A are given by 7:1.
OR
The probability of Player B winning over Player A is given by 7/8.
The odds of Player B winning over Player A are given by 7:1.
OR
The probability of Player B winning over Player A is given by 7/8.