Six-Handed Bridge

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A six suited deck was spotted at http://www.rightfast.com/empire/, as reported to me on November 2, 2002 by P. Genszler. (Cost is about $40 U.S. as of January 2010.)
Back in the eighth decade of the twentieth century, while I was a student at the University of Waterloo in Ontario, we had a large number of people who played bridge. We played bridge during lunch breaks. Once or twice a week, we played duplicate bridge in the evening at the local clubs. About once a month, we travelled many miles to get to sectional, regional and national tournaments. (Around the year 2000, I started playing duplicate again, usually once a week, sometimes less, sometimes more. As of January 2010, I'm an A.C.B.L. Life Master closing in on 600 masterpoints. My other hobby is judo.)

Since we had an ample supply of bridge players, and since students like to experiment, we also played other games. We played Diplomacy in my residence and Dungeons and Dragons in the mathematics student society offices.

We also played a six-handed version of bridge. Since I've not seen this described elsewhere on the web, I'll try to set down some rules and statistics.


Making a Six-Suit Deck: Take two normal packs of playing cards, with the same backing. Take the clubs and diamonds form the second pack and set the rest of that pack aside. Use a marker to replace the diamonds by red circles and the clubs by black circles. Now, with the first deck added, you have six suits. With our great imaginations, we called the new suits Red Rounders and Black Rounders. I don't remember who came up with the idea for this game, or if it was a group idea. I know I made myself a deck like that. (For more history, perhaps see: http://en.wikipedia.org/wiki/Suit_(cards)#Six-suit_decks.)

A few people have written to me recently and stated that they have seen six-handed decks, with the two extra suits called bells and stars, or called anchors and eagles. I do not have such a deck in my possession, nor do I know where one can purchase such a deck at this time (January 2010, except as noted above). Of course if you do find out where to buy one, I'd be happy to get one as a curiosity if it is not too expensive ($40 is too much -- I'm a cheapskate). It has been over twenty years (nearer thirty?) since I actually played the game. I don't recall that we had a scoring mechanism. If there was one, Red Rounders and Black Rounders would presumably have been worth 20 points each. We did order the suits Red Rounders, Black Rounders, Clubs, Diamonds, Hearts, Spades, No Trump. This preserved the perceived red-black-black-red-red-black symmetry.

Bidding would proceed as in normal bridge. Players bid for six tricks in addition to the number stated. Doubles and Redoubles are still permitted. There are two teams of three players, seated alternately. The contract is played by the first player (the declarer) who bid the trump suit on the team that wins the bidding. The player to the left of the declarer makes the opening lead. The other two members of the declaring side turn their hands face up (double-dummy play on every hand).


The two dummies make for some differences from ordinary bridge. For example, with hearts as trump:

Declarer Dummy 1 Dummy 2
AK
-
xx
xx
-
-
-
xx
xx
xx
-
-
-
xx
xx
xx
-
-

Declarer leads the Ace and King of Spades, discarding the diamonds from the first dummy and the clubs from the second. Now, declarer can cross-ruff the clubs and diamonds between the two dummies.

If the defenders had been on lead, they could have taken two clubs and two diamonds.

There are obvious other differences. In normal bridge, declarer can choose to lead from the dummy or from the closed hand (by taking the previous trick in the appropriate place). Now, declarer has three choices. It might be best to focus on which hand you'd like to play last. (A finesse towards the AQ in the second dummy would succeed 2/3 of the time, towards the first dummy only 1/3.)

One might argue that declarer has more power in this version, since he plays three hands, and each defender is at the mercy of two others. I don't recall that bothering us.
Bidding and Conventions. As I remember, when we played, which might have been for a total time span measured in hours, we bid rather "seat-of-the-pants". If one were to seriously play such a game, one might want to play a few dozen games to get a feel what the game is like, and then preset certain conventions for your team to follow. Some form of high card points (HCP) as in normal bridge seem an obvious idea. Now, there are 60 HCP in the deck, but the average hand is still 10 HCP. However, the points distribution should be flatter than it is for a four-suit deck.

Perhaps opening one in a suit promises four or more in that suit and at least 10 HCP. The first responder to show support should have three of the proposed trump suit and the second perhaps two. The first responder to show support might be exected to have about 10 HCP also, although some allowance for distribution might be proper.

I'd think that opening two of a suit with a five card suit and not many HCP could work the same as weak twos in duplicate bridge. If you have five cards in the suit and if the suit splits evenly among the other five players, the distribution among those five would be 2-2-2-1-1. It hardly matters if your partners each have one or two.

One no trump might be a "flat" hand (all suits of length less than or equal to three) of 13 HCP to 16 HCP. I'd bet suit contracts will tend to score more tricks. Some experimentation might be needed to see what the score for one no trump should be as compared to suit contracts.


Distributions: (short version)

70% of all hands have a suit of 4 cards or longer.
21% of all hands have a suit of 5 cards or longer.
3.6% of all hands have a suit of 6 cards or longer.
0.4% of all hands have a suit of 7 cards or longer.

40% of all hands have a void.
97% of all hands have a singleton or void.

This last fact, might lead one to believe that to really make a good version of six-handed bridge, we should be using decks in which each suit has about 19.5 cards. Perhaps one could make a good six-handed, four-suited, bridge deck, in which each suit has 21 cards. Then, each player would have 14 cards, so hands would be about the same size. Take two decks, modify the cards 2 through 9 in the second deck so that they read 12 through 19, so the sequence in each suit is 2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,J,Q,K,A.

Contacts would be for seven tricks plus the number bid -- although making contracts for six tricks plus the number bid has the allure of finally being able to bid 8NT.


Distributions:
13-0-0-0-0-06
12-1-0-0-0-05070
11-2-0-0-0-0182520
11-1-1-0-0-0790920
10-3-0-0-0-02453880
10-2-1-0-0-034800480
10-1-1-1-0-037700520
9-4-0-0-0-015336750
9-3-1-0-0-0319004400
9-2-2-0-0-0261003600
9-2-1-1-0-016965234000.001%
9-1-1-1-1-0612633450
8-5-0-0-0-049691070
8-4-1-0-0-014355198000.001%
8-3-2-0-0-034452475200.002%
8-3-1-1-0-0111970544400.005%
8-2-2-1-0-0183224527200.008%
8-2-1-1-1-0264657650400.012%
8-1-1-1-1-128671245460.001%

7-6-0-0-0-088339680
7-5-1-0-0-034452475200.002%
7-4-2-0-0-0114841584000.005%
7-4-1-1-0-0373235148000.017%
7-3-3-0-0-084217161600.004%
7-3-2-1-0-01791528710400.081%
7-3-1-1-1-01293881846400.059%
7-2-2-2-0-0488598739200.022%
7-2-2-1-1-03175891804800.144%
7-2-1-1-1-11146849818400.052%

6-6-1-0-0-022968316800.001%
6-5-2-0-0-0206714851200.009%
6-5-1-1-0-0671823266400.030%
6-4-3-0-0-0421085808000.019%
6-4-2-1-0-04478821776000.203%
6-4-1-1-1-03234704616000.147%
6-3-3-1-0-03284469302400.149%
6-3-2-2-0-05374586131200.243%
6-3-2-1-1-023289873235201.056%
6-3-1-1-1-14205116000800.191%
6-2-2-2-1-012703567219200.576%
6-2-2-1-1-113762197820800.624%

5-5-3-0-0-0284232920400.013%
5-5-2-1-0-03023204698800.137%
5-5-1-1-1-02183425615800.099%
5-4-4-0-0-0394767945000.018%
5-4-3-1-0-012316759884000.559%
5-4-2-2-0-010077348996000.457%
5-4-2-1-1-043668512316001.980%
5-4-1-1-1-17884592501500.358%
5-3-3-2-0-014780111860800.670%
5-3-3-1-1-032023575698401.452%
5-3-2-2-1-0104804429558404.753%
5-3-2-1-1-175692088014403.433%
5-2-2-2-2-014291513121600.648%
5-2-2-2-1-161929890193602.809%

4-4-4-1-0-02851101825000.129%
4-4-3-2-0-020527933140000.931%
4-4-3-1-1-044477188470002.017%
4-4-2-2-1-072780853860003.301%
4-4-2-1-1-152563950010002.384%
4-3-3-3-0-010035878424000.455%
4-3-3-2-1-0213490504656009.682%
4-3-3-1-1-177093793348003.496%
4-3-2-2-2-0116449366176005.281%
4-3-2-2-1-13784604400720017.164%
4-2-2-2-2-1103216483656004.681%

3-3-3-3-1-026093283902401.183%
3-3-3-2-2-085396201862403.873%
3-3-3-2-1-1185025104035208.391%
3-3-2-2-2-13027683520576013.731%
3-2-2-2-2-249543912154882.247%
Total220495674290430


Splits of one suit in the other three hands:

There are 84478098072866400 ways to distribute 39 cards in 3 hands.

As in regular bridge, the most likely splits are the ones that are nearest to even, without being even.

7 cards outstanding
3-2-22867066904723840033.939%
4-2-12389222420603200028.282%
3-3-11752096441775680020.740%
4-3-067388324683680007.977%
5-1-135838336309048004.242%
5-2-033081541208352003.916%
6-1-0751453601856000.870%
7-0-0282748215456000.033%

6 cards outstanding
3-2-14505390850280320053.332%
2-2-21228742959167360014.545%
4-1-1938623093808400011.111%
4-2-0866421317361600010.256%
3-3-063537563273184007.521%
5-1-025992639520848003.077%
6-0-01332955872864000.158%

5 cards outstanding
2-2-13481438384307520042.211%
3-1-12127545679299040025.185%
3-2-01963888319352960023.247%
4-1-081828679973040009.686%
5-0-05665062459672000.671%

4 cards outstanding
2-1-14061678115025440048.080%
3-1-02291203039245120027.122%
2-2-01874620668473280022.191%
4-0-022030798454280002.608%

3 cards outstanding
2-1-05623862005419840066.572%
1-1-12030839057512720024.040%
3-0-079310874435408009.388%

2 cards outstanding
1-1-05780080394459280068.421%
2-0-02667729412827360031.579%


Department of Mathematical Sciences
Florida Atlantic University
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Boca Raton, Florida 33431-0991
USA

Office: Room 286, Science & Engineering
Phone: (561) 297-3350
Fax: (561) 297-2436
URL: http://math.fau.edu/locke/Bridge6.htm


Last modified January 27, 2010, by S.C. Locke.