Lay out sixteen cards: the Ace, Two, Three and Four of all four suits (hearts, clubs, diamonds, and spades). Two players alternately turn down a card and add it to the common score, and the player who makes the score 22, or forces his or her opponent to go beyond 22, wins. To ensure that they win, which payer should go first and why?
Start with a sure-win problem, it's your opponent's turn to choose, the busting number is 5 (i.e. the player who chooses a card to add to to 6 wins).
So your objective is to force a 5 on your opponent. What about 22? Wait...
If the busting number is 10, you can force a 5 on your opponent using the following strategy: whatever he chooses, you choose the complement of 5, that will leave him 5 to go.
Similarly, force your opponent to get a 15, 20,... and you will assure of a win.
Now you'll decide who starts, and what the overall strategy. Play the game with a friend of yours to test your strategy. If you don't guarantee a win, post again.
Good luck.
(i.e. the player who chooses a card to add to to 5 wins).
To determine which player should go first to ensure a win in this card game, we need to analyze the possible outcomes for each player's turn.
Let's consider the scenario where Player A goes first:
1. Player A's Turn: Player A turns down a card and adds it to the common score. Regardless of the card value, the common score will be at least 1 (if Player A turns down the lowest card, the Ace).
2. Player B's Turn: Player B turns down a card and adds it to the common score. The common score can now be 2 or higher, depending on the card values chosen by both players.
Now let's consider the scenario where Player B goes first:
1. Player B's Turn: Player B turns down a card and adds it to the common score. Regardless of the card value, the common score will be at least 1 (if Player B turns down the lowest card, the Ace).
2. Player A's Turn: Player A turns down a card and adds it to the common score. The common score can now be 2 or higher, depending on the card values chosen by both players.
Based on the analysis above, we can observe that regardless of who goes first, the common score after the first turn will always be 1. Therefore, there is no advantage or disadvantage to either player in terms of the starting position.
The outcome of the game will ultimately depend on the strategy and card choices made by the players during subsequent turns, rather than the initial turn order.