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Hearts Tips and Strategies |
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| Hearts Column of the Month – July 2001 | |
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| By Joe Andrews | |
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| June Hearts Challenge
Last month, this mathematical puzzle was presented:
Assuming no moons, four players, no Jack of diamonds rule, and a 100 -point limit, what is the greatest number of hands that can be played in a game? The fewest number of hands is four, and someone would have to take 25 points in each of four consecutive hands!
Well, to begin with, nearly 500 people took a shot at this puzzle! The vast majority of entries were correct and stated that 16 hands was the maximum. The winner (with the earliest e-mail date), was ptompot , whose solution was very clear. If 26 points are distributed in every hand, then 26 x 15 = 390, and someone must go over the top on the 16th hand. Another method is to multiply 99 x 4 = 396 and divide by 26. This equals 15.23 hands and thus, 16 deals are necessary. Ptompot's scores after hand #15 were 96, 97, 98, and 99, and the next hand ended the game.
Most participants built a chart, which resulted in all four players having a score of 78 points, each after twelve hands. The typical layout (and there are several variations), was:
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| Hand | Player 1 | Player 2 | Player 3 | Player 4 | |
#1 | 13 | 13 | 0 | 0 |
#2 | 0 | 0 | 13 | 13 |
#3 | 13 | 13 | 0 | 0 |
#4 | 0 | 0 | 13 | 13 |
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Note that everyone has 26 points after four hands. If you continue this for three more cycles of 4 hands, with the same pattern of point distribution you will arrive at 78 points for each player after 12 hands. Now we reach hand # 13.
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| Hand | Player 1 | Player 2 | Player 3 | Player 4 | |
#13 | 21 | 0 | 0 | 5 |
#14 | 0 | 21 | 0 | 5 |
#15 | 0 | 0 | 21 | 5 |
Totals | 99 | 99 | 99 | 93 |
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This adds up to 390 and the next hand wraps up the game. There are other combinations that also come to 390 (15 deals).
ENTER EMERIL THE COOK! (INFINITY STRIKES AGAIN!)
One very ingenious person (heartsmeister01), submitted this scenario. Let's go to the 78-points/person matrix after 12 hands. I will identify the points taken by each player with parentheses (13) and the cumulative total in the next column.
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| Hand | Player 1 | Player 2 | Player 3 | Player 4 | |
#12 | 78 | 78 | 78 | 78 |
#13 | (13) 91 | (13) 91 | (0) 78 | (0) 78 |
#14 | (0) 91 | (0) 91 | (13) 91 | (13) 91 |
#15 | (13) 104 | (13) 104 | (0) 91 | (0) 91 |
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Yes, we have a two-way tie for first place! In "live" events, any such tie is played off. On the computer, an additional hand (or more!) would be necessary to break the tie, especially in a tourney. What happens if hand # 16 ends with this result?
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| Hand | Player 1 | Player 2 | Player 3 | Player 4 | |
#16 | (0) 104 | (0) 104 | (13) 104 | (13) 104 |
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Such a pattern could continue forever, as long as the two low players had the same score. A very bizarre aspect of this scenario is the fact that the high and low players alternate positions every third hand!
And to further muddy the waters, I present to you another entry that I call "Lennon's Purple Cow" - an improbable, but still possible result with a THREE-WAY tie for first place.
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| Hand | Player 1 | Player 2 | Player 3 | Player 4 | |
#12 | 78 | 78 | 78 | 78 |
#13 | (19) 97 | (0) 78 | (0) 78 | (7) 85 |
#14 | (0) 97 | (0) 97 | (0) 78 | (7) 92 |
#15 | (0) 97 | (0) 97 | (19) 97 | (7) 99 |
#16 | (13) 110 | (5) 102 | (5) 102 | (3) 102 |
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A very neat finish! And hand # 17 might finish in this manner:
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| Hand | Player 1 | Player 2 | Player 3 | Player 4 | |
#17 | (14) 124 | (4) 106 | (4) 106 | (4) 106 |
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As long as Player # 1 continues to take the Queen of Spades, and the others take an EQUAL number of points (1,2,3, or 4), the game can go on forever with a perpetual three-way tie for first place!
THE PASS IN HEARTS - REVIEW – (ANSWERS TO BE POSTED IN THE NEXT COLUMN).
Here are some passing situations to help hone your game skills:
Assume that you are playing online on Zone.com (where else?)
Scenario A - First deal of a new game. Pass to the left. What would you pass with each of these holdings?
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| Hand #1
 K J 10
 AQ 3
 K 5 2
 A 8 4 3
| Hand #2
 A Q J 9
 K J
 A K 9 7
 K Q 7
| Hand #3
 Q J 9 3
 7 4 2
 6 4 3
 A 4 3
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Scenario B - Sixth hand of a game. Pass to the right. You are in 2nd place (12 points in arrears of the "low" player, and the "low" person is seated directly across from you). What do you pass with each of these holdings?
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| Hand #4
 A Q 3
 K 10 3
 A 10 5 4 2
 7 3 | Hand #5
 VOID
 A K Q 10 7
 9 7 6
 A K J 8 2 | Hand #6
 Q 9 7 6 2
 A
 A J 4 2
 A 6 4 | |
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Scenario C -The game is nearing its conclusion. You are passing across. You find yourself in third place with 71 points. Eleven points behind the 2nd place person, and 21 points out of first place. Your opponent sitting directly across from you is in fourth place with a score of 81 points.
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| North
 Q J
 A 5 3 2
 K Q 6 3
 A 5 4 | North
 K Q 9 8 2
 Q 9 7
 A 10 8
 3 2 | North
 J 8 2
 A 5 3
 A K Q J 7 4
 Q | |
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