Thirty-One:
Last weekend, 77 recommended me to watch a TV shows, High Intelligent Players, ้ซ่ฝ็ฉๅฎถ.
Among the games they played, there is a game of 31, I think it is very interesting.
Game Rules:
There are 4 sets of 1 to 6.
1๐ค |
2๐ค |
3๐ค |
4๐ค |
5๐ค |
6๐ค |
1โค |
2โค |
3โค |
4โค |
5โค |
6โค |
1๐ |
2๐ |
3๐ |
4๐ |
5๐ |
6๐ |
1๐ท |
2๐ท |
3๐ท |
4๐ท |
5๐ท |
6๐ท |
- Player A and Player B take turns to pick a card and annouce
the running total - Continue playing until the player makes the total 31 wins
- If the player goes over 31 loses.
Can we search for a Winning Strategy for 31?
a player‘s strategy is any of the options which he or she chooses in a setting where the outcome depends not only on their own actions but on the actions of others. A player’s strategy will determine the action which the player will take at any stage of the game.

geralt / Pixabay
Solution:
Thought Progress:
After exploring the game, we notice if the play A arrives 24, then no matter which number(1-6) player B put down, player A can definitely call out 31, and wins the game. Continuing the same fashion, 17,10 are also the critical points for this game.
Question: MUST we call our 10,17,24 in order to win 31?
Answer: Not necessarily because there are only 4 sets of numbers.
Example 1:
Player A |
5 |
2 |
2 |
2 |
Player B |
5 |
5 |
5 |
x |
In this Game Player B has 10, 17, 24, theoretically, Player B can call out 31, however, the game ran out of 5 (only 4 set of numbers), so Player B has to either call 6, the sum will be 32, the game exploded. Player B can call anything smaller than 5, then play A will call (7-x), Player A wins.
Example 2:
Player A |
2 |
4 |
4 |
4 |
x |
Player B |
4 |
3 |
3 |
3 |
|
In this round, The player A in order to call 10, 17,24 used all the 4s. therefore, Player A either exploded in the 5th term or pick another number smaller than 4, either way, Player B will win this game.
Similarly, in this case:
Player A |
3 |
3 |
3 |
3 |
x |
Player B |
4 |
4 |
4 |
4 |
|
or :
Player A |
1 |
1 |
1 |
Player B |
1 |
6 |
6 |
It seems like in the above 4 cases, Player B has a better chance of winning, however, the game of 31 does Favor Player A (First Mover), if player A chooses the correct first number, and be aware of consuming too many of the same number.
Happy Studying while playing games ๐!