Game of 31
Thirty-One:
Last weekend, 77 recommended me to watch a TV shows, High Intelligent Players, 高能玩家.
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.
- 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.
[caption id=”attachment_1422" align=”alignnone” width=”750"]
geralt / Pixabay[/caption]
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.
