Shuffle one deck of Fraction Bars deal each player eight bar

Shuffle one deck of Fraction Bars, deal each player eight bars, and set the unused bars aside. Player A lays down one bar face up and names the fraction on his or her bar. Player B lays down a bar and names the fraction on his or her bar. If the shaded amount of Player B\'s bar is greater than or equal to that on Player A\'s bar. Player B wins both bars (and sets them aside). Otherwise, Player A wins the bars. This is the end of the first play. The player who won the two bars begins the next play. When the players have both used their eight bars, deal eight more bars from the unused bars to continue the game. After all of the bars have been played, the player with the most bars wins. Variation: For 3 players, deal five bars to each player and adjust the rules accordingly. For the bars shown here, the second player can win two bars by playing any of the bars for the fractions 3/4, 7/12, 3/3, or 3/6. a. Play at least one full Buy Cheap game. b. What is the best bar for the second player to play in the example above? c. Suppose Player 2 in the example started the game. Explain why it might not be a good strategy to start the game by laying down the zero bar.

Solution

a) to be played in person.

b) Though I can hardly make out the parts shaded in the picture you uploaded, however, if player A has played the fraction bar with 1/2 shaded portion, then the probable fraction bars for the player B to win can be (3/4), (7/12), (3/3) or (5/6), since all of these fractions are higher than (1/2).

To be playing with proper diligence, player B should choose the fraction which is the lowest , so that he still has left with the higher shaded fractions with him for the further chances of the game.

3/4= 0.75

7/12=0.583

3/3=1

5/6=0.833

Therefore, player B should lay down the fraction bar with 7/12, since it is the lowest among the bar which could make him win and he is still left with fraction bar with higher chances of winning.

c) If Player 2 has started the game, then he should not choose the zero bar to start the game because he should save it for those instances where he has no chance of winning. for example, if player 1 plays a bar with 3/3 or so, then player B has no chance of putting any bar,he should save it for instances like that so that he can make the player 1 waste his higher fractioned bar against his lowest zero bar.

Thats how the trick should go.