How about 0978?
0978 has no bulls and two cows.
| Guess # | poster | guess | Bulls | Cows |
|---|---|---|---|---|
| 1 | Prof.Pepperwinkle | 1234 | 0 | 2 |
| 2 | Prof.Pepperwinkle | 5678 | 0 | 1 |
| 3 | Prof.Pepperwinkle | 3478 | 1 | 2 |
| 4 | PlaceboTarget | 0978 | 0 | 2 |
Let’s continue with 3978. 
3978 has no bulls, three cows.
| Guess # | poster | guess | Bulls | Cows |
|---|---|---|---|---|
| 1 | Prof.Pepperwinkle | 1234 | 0 | 2 |
| 2 | Prof.Pepperwinkle | 5678 | 0 | 1 |
| 3 | Prof.Pepperwinkle | 3478 | 1 | 2 |
| 4 | PlaceboTarget | 0978 | 0 | 2 |
| 5 | PlaceboTarget | 3978 | 0 | 3 |
My guess is 8493 this time. 
Congratulations, PlaceboTarget! You have guessed the right number.
| Guess # | poster | guess | Bulls | Cows |
|---|---|---|---|---|
| 1 | Prof.Pepperwinkle | 1234 | 0 | 2 |
| 2 | Prof.Pepperwinkle | 5678 | 0 | 1 |
| 3 | Prof.Pepperwinkle | 3478 | 1 | 2 |
| 4 | PlaceboTarget | 0978 | 0 | 2 |
| 5 | PlaceboTarget | 3978 | 0 | 3 |
| 6 | PlaceboTarget | 8493 | 4 | 0 |
Thank you.
They say smart cows yield strong bulls. 

I have already picked the next number. Here it is:

Please submit your best guesses. 
3456?
Thank you for your guess. 
| guess # | player | guess | bulls | cows |
| 1 | Prof.Pepperwinkle | 3456 | 0 | 1 |
7890?
Thank you. 
| guess # | player | guess | bulls | cows |
| 1 | Prof.Pepperwinkle | 3456 | 0 | 1 |
| 2 | Prof.Pepperwinkle | 7890 | 0 | 2 |
9056?
8931?
| guess # | player | guess | bulls | cows |
| 1 | Prof.Pepperwinkle | 3456 | 0 | 1 |
| 2 | Prof.Pepperwinkle | 7890 | 0 | 2 |
| 3 | Prof.Pepperwinkle | 9056 | 0 | 2 |
| 4 | Tinmansd | 8931 | 1 | 2 |
1965?
| guess # | player | guess | bulls | cows |
| 1 | Prof.Pepperwinkle | 3456 | 0 | 1 |
| 2 | Prof.Pepperwinkle | 7890 | 0 | 2 |
| 3 | Prof.Pepperwinkle | 9056 | 0 | 2 |
| 4 | Tinmansd | 8931 | 1 | 2 |
| 5 | Monty | 1965 | 0 | 3 |
My decision tree has decided that it’s 8619.
| guess # | player | guess | bulls | cows |
| 1 | Prof.Pepperwinkle | 3456 | 0 | 1 |
| 2 | Prof.Pepperwinkle | 7890 | 0 | 2 |
| 3 | Prof.Pepperwinkle | 9056 | 0 | 2 |
| 4 | Tinmansd | 8931 | 1 | 2 |
| 5 | Monty | 1965 | 0 | 3 |
| 6 | bibliophage | 8619 | 4 | 0 |
Congratulations @bibliophage! You have won again and it is your turn to do the honors. 
OK, I have a four-digit number. You may begin guessing.
First, 0864. 