5. Examples

5a. Example Game - Multiple Players

This game should illustrate as many rules as possible. There are four players, Zak with a rating of 1125, Katie with a rating of 1076, Jen with a rating of 1011, and Derek with a rating of 958.

Zak is the highest rated player, so he is first declarer. The players sit as follows:

Jen

Katie Derek

Zak

Zak deals out the cards and looks at his hand. Here's the listing of hands.

2C,3C,7C,9C,AC,5S,8S,2H,2D,4D 4C,8C,QC,KC,3S,7S,JS,10H,KH,AD JC,KS,AS,QH,AH,9D,10D,QD,Red Joker, Black Joker 5C,6C,2S,4S,6S,9S,10S,3H,6H,3D

Try setting this up with playing cards to get a feel for the game.

Zak declares that he is playing low, so he discards his 9 and 10 of Spades. Then he draws the 10 of clubs and the Queen of spades - ow! After some muffled cursing, declaration passes to Katie.

Katie’s hand is not too hot, but she decides it is best played high, especially since one player already declared low. She discards 4 of clubs and 3 of spades, drawing the 7 and Jack of diamonds to replace them.

Jen declares low, discarding the Ace of clubs and 8 of spades. She draws the 8 and Jack of hearts.

Derek has not been forced, since there are more low hands than high, but if he declares high, it will be even. He decides to declare high - his hand is frankly awesome. He should be able to win the hand even though he is the least skilled player at the table. Let’s look at the actual play now.

Zak declared first, so he will lead the first trick. He decides that the best way to get rid of the Queen is to lead it first, so he leads QS (Queen of Spades if you didn’t figure out the abbreviations yet.) Katie has spades, so she must play one. However, she can’t beat the Queen (she would need a King or Ace.) So she plays the 7 - that Jack is higher and therefore more valuable to her. Jen’s only choice is the 5 of spades - it’s her only card in the suit. Finally, Derek looks at the cards and decides to take it with his King. He could have used either K or A to take the trick.

It’s Katie’s lead, and she decides to see if she can smoke out a high card from Derek. She leads her Ace of diamonds. Jen throws down the 4D - she wants to get rid of high cards. Derek has diamonds, so he can only play a diamond - or the red Joker since it’s the same color. He could only play the black Joker if he had no diamonds (a "void.") He decides to take the trick with the red Joker. Zak throws down the three.

Now it’s Jen’s turn to lead. She decides to give herself a void in diamonds and leads the 2D. Derek thinks a while and plays the 9D - he doesn’t want to risk the Queen when Katie might have the King. Zak has no diamonds, so he can throw any card onto the table without taking the trick. He gets rid of the 10C. Katie smirks a bit and takes the trick with the JD.

Derek decides to play it safe, so he leads the Ace of hearts. He knows Katie can’t take it because both Jokers are accounted for - one in his hand and one already used. Zak plays his 6H, Katie drops the 10H, and Jen the JH. Now each player has led once - let’s update how it looks on paper.

Jen - low, 0 tricks 2C,3C,7C,9C,2H,8H Katie - high, 1 trick Derek - high, 3 tricks 8C,QC,KC,JS,KH,7D JC,AS,QH,10D,QD,Black Joker Zak - low, 0 tricks 5C,6C,2S,4S,6S,3H

It’s Zak’s turn to lead again. Clubs are untouched, so he leads the 6C. Since Katie has a King anyway, she plays her QC without worrying about throwing away a trick. Jen gets rid of the 9C, and Derek takes the whole thing with that Black Joker.

Now Katie looks at her options. Since Derek used the Black Joker, he probably doesn’t have the Ace of Clubs, and both the Red Joker and Ace of Hearts are gone. Therefore both her kings can take tricks - if in the right suit. She has one lead left after this, so she plays the King of hearts. This way, she leaves her options open for which card to play in the event of a club lead, since she has two clubs. Jen is happy to get rid of the worrisome 8H. Now it’s Derek’s turn. He only has one heart - and it’s one less than the lead! He’s not happy about playing his Queen of hearts, but he has no choice. Zak plays the 3H and Katie takes the trick.

Jen decides to lead the 2C - it loses to any other club. Derek’s only club is the Jack, so he has no choice but to play it. Zak has to play 5C. Then Katie uses the KC to nab another trick. Now we see why she used the KH to lead last trick - that 8 will now take a trick!

Derek thinks awhile and then plays the QD. Zak throws his highest card, the 6S, and Katie must use 7D. Jen throws her highest card, the 7C.

Zak plays safe and leads the 2S. Katie puts down the JS (no choice again), Jen the 3C (high card), and Derek takes the trick with the AS. For the last trick, Katie leads, and since all the players have different suits, her 8H takes the trick. She certainly outplayed Derek this round, but his hand was just to good to beat. Ok, now how do they score this hand?

Derek declared high and took 6 tricks, so his raw score is 6.

Katie declared high and took 4 tricks, so her raw score is 4.

Jen and Zak both declared low and took no tricks. The value of N (section 3a) for 4 players is 6, so their raw scores are 6-0=6.

Since there is a tie for second and third, but fourth is different than second, the penalty is the fourth place score - 4 points. Hence the refined scores for Zak, Jen, and Derek are 2, and for Katie 0. Nobody was forced, so the final scores are 0 for Katie and 2 x 2 = 4 for the others. The score sheet now looks like this:

Zak | Katie | Jen | Derek |

LD,6-4:2 | HD,4-4:0 | LD,6-4:2 | HD,6-4:2 |

4 | 0 | 4 | 4 |

The form for each entry is:

Declaration, Raw Score - Penalty : Refined Score

Total Score (add final score to previous total)

Next round, Katie is first declarer since she is to Zak’s left. She gets a better deal this round - she’s the only high hand. She takes 8 tricks, and Jen and Derek get stuck with one. In the next game, she and Zak both go low taking no tricks, and the other two split even. In the fourth hand, Katie gets an awesome hand and takes 8 out of 10 tricks - and Jen who was also high only got two! Here’s the scoresheet:

Zak | Katie | Jen | Derek |

LD,6-4:2 | HD,4-4:0 | LD,6-4:2 | HD,6-4:2 |

4 | 0 | 4 | 4 |

LD,6-5:1 | HD,8-5:3 | LD,5-5:0 | LD,5-5:0 |

6 | 6 | 4 | 4 |

LD,6-5:1 | LD,6-5:1 | HD,5-5:0 | HD,5-5:0 |

8 | 8 | 4 | 4 |

LD,6-2:4 | HD,8-2:6 | HD,2-2:0 | LD,6-2:4 |

16 | 20 | 4 | 12 |

Since they agreed to play to 20, this ends the game. Now for an explanation of how I rate this:

For 4 players, first the rating change is counted for each player beating the last place player. After these adjustments are made, I adjust ratings for the 1^{st} and 2^{nd} place beating 3^{rd}, and finally for the 1^{st} beating 2^{nd}. However, the change for each individual is less than that for a duel. It’s also less than it would have been had they played to 25 or more.

The ratings start out as follows: Katie 1076, Zak 1125, Derek 958, Jen 1011.

Since Jen was last place, Katie steals 7 points, Zak 5, and Derek 9.

Now the ratings look like this: Katie 1083, Zak 1130, Derek 967, Jen 990.

Jen is no longer adjusted - now Katie takes 5 points from Derek, and Zak also takes 5.

Now - Katie 1088, Zak 1135, Derek 957, Jen 990.

Finally, Katie takes 9 points from Zak, so she moves up to 1097 and Zak falls to 1126. Chances are, after the sheets arrive in my Hotmail mailbox, Katie’s a pretty happy camper - 21 points up this game! If they had played to 25 or more, all the changes would have doubled.

Overall, all the players had similar ratings, so the top two moved up and the bottom two moved down. The changes were based on the assumption that one of the players has shown to me that he or she knows the rules cold - otherwise they would have changed only half as much.

The two players involved in this duel are Zak, with a rating of 1126, and Katie with 1097. Zak deals first, since his rating is higher, and draws a hand with AC, 5S, 7S, QS, AS, 3H, 8H, KH, 6D, AD, and the Red Joker. This hand is quite capable high, so he places three face-up cards behind his arm, where Katie can’t see them. Katie now looks at 3C, 5C, 6C, 8C, 8S, 10S, 5H, 2D, 3D, and JD and bids two low. Zak’s bid of three is stronger, so Katie takes three tricks, and Zak discards 3H and 6D, drawing 7D and QD.

Here’s a quick run of the hand:

Zak | Katie | Winner |

AD | 2D | Zak |

AC | 8C | Zak |

AS | 8S | Zak |

Joker | 5C | Zak |

QS | 10S | Zak |

7D | 6C | Katie |

KH | 5H | Zak |

5S | 3C | Katie |

7S | 3D | Zak |

8H | JD | Katie |

Zak took seven tricks to Katie’s three, but Katie had three free tricks from Zak’s bid. Therefore Zak only had one trick more and scores two points. You can see that this could take a while! In reality, most duels don’t go this slowly, but I’ve had streaks of twos.