· Black Derman Toy Option Pricing Model
· Vasicek Option Pricing Model
MASTERMIND STRATEGIES
In the classical Mastermind game where the secret code is a 4 digit repeatable combination of 6 different colours, there are in fact just 5 unique types of first guesses to the game. And a player’s guess will be scored according its correct (colour and position) and semicorrect (correct colour but wrong position) digits. If we multiply correct number of digits by 10 and add to that number semicorrect digits in the guess, we can show each score by a 2digit number: 00, 01, 02, ……, 30, and 40. Note that 31 is not a valid score. The table below shows the number of remaining valid possibilities after the first guess for each of the possible combinations and for each possible score:

1111 
1112 
1122 
1123 
1234 
00 
625 
256 
256 
81 
16 
01 
0 
308 
256 
276 
152 
02 
0 
61 
96 
222 
312 
03 
0 
0 
16 
44 
136 
04 
0 
0 
1 
2 
9 
10 
500 
317 
256 
182 
108 
11 
0 
156 
208 
230 
252 
12 
0 
27 
36 
84 
132 
13 
0 
0 
0 
4 
8 
20 
150 
123 
114 
105 
96 
21 
0 
24 
32 
40 
48 
22 
0 
3 
4 
5 
6 
30 
20 
20 
20 
20 
20 
40 
1 
1 
1 
1 
1 
Total: 
1296 
1296 
1296 
1296 
1296 
Simple 
1 
2 
8 
9 
52 
Worst Case 
625 
317 
256 
276 
312 
Entropy 
1.5 
2.7 
2.9 
3.0 
3.1 
Expected Size 
512.0 
235.9 
204.5 
185.3 
188.2 
Most Parts 
5 
11 
13 
14 
14 
From this table, you can see which game strategy picks which first guess and why by looking at the highlighted cells (these are the first guesses of each classical Mastermind strategy). This table below shows the game solution tree averages for all the classical strategies as well as the Optimal Strategy.
Strategy 
Total Moves 
Average 
Max Moves 
6+ Moves 
Author 
Year 
Simple 
7471 
5.76466 
9 
853 
Shapiro 
1983 
Worst case 
5801 
4.47608 
5 
0 
Knuth 
1977 
Entropy 
5722 
4.41512 
6 
12 
Neuwirth 
1982 
Expected Size 
5696 
4.39506 
6 
3 
Irving 
1979 
Most parts 
5668 
4.37346 
6 
7 
Kooi 
2005 
Optimal (Max: 5) 
5626 
4.34105 
5 
0 
Lai 
1993 
Optimal (Max: 6) 
5625 
4.34028 
6 
1 
Lai 
1993 