· 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 to 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 it does so 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 Guesses  Average  Maximum Guesses  6 or more Guesses  Author  Year  
Optimal (Max: 6)  5625  4.34028  6  1  Lai  1993  
Optimal (Max: 5)  5626  4.34105  5  0  Lai  1993  
Weighted Entropy  5646  4.35648  6  3  Gur  2021  
Most parts  5668  4.37346  6  7  Kooi  2005  
Expected Size  5696  4.39506  6  3  Irving  1979  
Entropy  5722  4.41512  6  12  Neuwirth  1982  
Worst Case (MinMax)  5801  4.47608  5  0  Knuth  1977  
Simple  7471  5.76466  9  853  Shapiro  1983 