This Hand Occurs Once in Every 130,000 Deals ... (According to a Google Query Posted by a Mathematician)
#1
Posted Yesterday, 16:17
Recently I was playing in an open duplicate club game with a group of (mostly) Life Masters when this hand occurred. (East-West were vulnerable and I was sitting in the North chair. South was the dealer.) My pickup partner is a very good bridge player with over 16,000 master points. (I have approximately 20.)
The cards were distributed as follows:
South: J-7-6 of spades, K-9-7-4-2 of hearts, T-9-6-3-2 of diamonds, Club Void
West: 5 of spades, Q-8-3 of hearts, 8-7-4 of diamonds, Q-8-7-6-5-3 of clubs
North: A-K-Q-T-9-8-4-3-2 of spades, Hearts - Void, A-Q of diamonds, J-9 of clubs
East: Void in Spades, A-J-T-6-5 of hearts, K-J-5 of diamonds, A-K-T-4-2 of clubs
The bidding on my table went as follows:
South: Pass
West: Pass
North: 2 Clubs
East: Pass
South: 2 Diamonds
West: Pass
North: ???
Long story short ... After over a minute of agonizing over what to bid, I went with 4 spades which was passed out and played. As soon as the dummy was laid down it was painfully obvious that 6 spades was cold. Six other North-South pairs bid the same cards. Three of them stopped in 4 spades (making six) and two bid 5 spades making six. One North-South pair let East-West play a heart contract that was doubled and set one trick for a bottom board.
Initially I was dejected to have missed the cold slam. My much-more-experienced partner's initial assessment was that we [probably] had a "bad board" as at least some of the other North-South pairs would surely find (and bid) the slam. Prior to sitting down to play, my partner and I spent all of ten minutes discussing conventions and treatments and filling out our convention card. (We were basically winging it. We certainly didn't discuss how to bid a hand like this!)
Naturally, there was a lot of post-session discussion about this hand - and various opinions as to how it should have been bid. The thought occurred to me that with both my partner (and myself) having voids in two different suits, this must be a very rare hand. I thought the odds against a hand like this coming up at the table might be several-million-to-one against. My "guesstimate" was a bit high as the actual odds are more like 130,000-to-1 - according to a post by a mathematician via a Google query.
Given the exact same circumstances, how would you (and your partner) have bid this hand?
Former_DJ (with a fearsome total of 20 Master Points. Ha! Ha!)
#2
Posted Yesterday, 20:01

With East generously staying quiet, I would have jumped to 3♠ which sets spades as trumps and invites my partner to start cuebidding - though having said that I'm not sure of how to actually find out the right info - maybe 4♣ - 4♦ - 4♥ - 4♠ and see if partner wants to keep going. Though this isn't my strong point either, so will see what others say..
#3
Posted Yesterday, 20:38
Your auction could start like this playing common methods (3♠ as stronger than 4♠; first and second round controls):
Once North bids 4♦, South won't sign off below slam - having a void in the right place and a king.
As for who should make which move after that, without fancy agreements it's awkward for both hands to conceive of a way to confidently reach 7♠ holding a void that they haven't revealed yet.
North might use Keycard anyway, expecting that grandslam is out unless parter shows up with both keycards and a king (extremely unlikely). That'd be my blunt approach in a random partnership with an experienced partner.
If South had the same hand with a singleton club, not a void, I'd say it's a great candidate for a 4♣ splinter over 2♠. With a void, I'd feel like I haven't done the hand justice and that I might be wasting too much bidding space.
#4
Posted Yesterday, 21:18
#5
Posted Yesterday, 22:03
After I bid 4 spades, (which sounds like a signoff bid), it's possible my partner might have considered a 5 clubs cue bid to show his void, but he might have been thinking "My inexperienced partner with less than 25 master points might be confused or misunderstand my bid and leaver me there!" so he passed.
Two of the North-South pairs apparently smelled a slam in the air as they bid it up to 5 spades and stopped. I chose not to initiate a 4 NT Blackwood inquiry as I had read that you don't use Blackwood with a void. I don't know if regular partnerships discuss how to handle "freaky" hands like this, but there were six other experienced partnerships who bid and played the same cards and they all missed the slam, so what do I know?
I've queried Google about this [again] and they now say the odds are approximately 1 in 100,000 of being dealt a hand like that.
https://www.google.c...nt=gws-wiz-serp
I haven't been playing bridge very long, but this is an interesting game. Ha!
#6
Posted Yesterday, 22:34
Former_DJ, on 2025-July-21, 22:03, said:
https://www.google.c...nt=gws-wiz-serp
AI is entirely hopeless at questions like this; don't rely on it being correct about anything. It mainly just mimics things other people have said, replacing numbers with unrelated ones and making it sound real. 1 in 130,000 is the probability all four players have a void in different suits.
#7
Posted Today, 00:06
Similarly, 2♠-then-4♠ is a mistake. It does not explain your hand to partner - how is partner to know that we have two losers in clubs but that hearts are waste paper?
Bid slowly and explain your hand if you want partner to think along with the bidding.
Lastly there are already several mentions of Blackwood on this auction. There's a lot more to slam bidding than ace asking, especially on tricky deals like this with multiple voids. I think the focus on the gadget is misplaced on this deal.
#8
Posted Today, 01:32
DavidKok, on 2025-July-22, 00:06, said:
Similarly, 2♠-then-4♠ is a mistake. It does not explain your hand to partner - how is partner to know that we have two losers in clubs but that hearts are waste paper?
Bid slowly and explain your hand if you want partner to think along with the bidding.
Lastly there are already several mentions of Blackwood on this auction. There's a lot more to slam bidding than ace asking, especially on tricky deals like this with multiple voids. I think the focus on the gadget is misplaced on this deal.
David:
Taking in to account your comments and observations, would a more accurate bidding sequence go something like this.
South: Pass
West: Pass
North: 2 Clubs
East: Pass
South: 2 Diamonds
West: Pass
North: 2 Spades - Forcing
East: Pass
South: 3 Spades (or show the club void by jumping to 4 clubs?)
West: Pass
North: 4 Hearts (Showing my heart void)
East: Pass
South: 6 Spades! (South, with his club void and his partner's [suggested] first or second round control of hearts, figures there must be a spade slam.)
The only problem with this [optimal?] bidding sequence is that a perceptive East, sitting on 16 HCPs including two Ace-King combinations and a void in Spades, will probably recognize that this is a good time to risk a sacrifice in either clubs or hearts. (One East-West partnership did jump in and bid a [doubled] heart contract that was set by only one trick. For that bravery, they were rewarded with a top board.) I'm admittedly not that experienced, but something tells me if you and partner proceeded with a "slow arrival" bidding sequence, unless East is not paying attention or is not very experienced, he/she will almost surely suggest a hearts or clubs sacrifice to partner.
One friend I asked about this hand commented that with very "freaky" type hands - like this one - "scientific bidding methods" don't always work. These type hands are infrequent, but they make for lively discussion at the bar after the game is over.
#9
Posted Today, 01:59
Actually I would open 1♠ rather than 2♣, but that's probably beyond the scope of this discussion.
In my opinion there are four flaws in your closing paragraphs:
- Perceptive East-West players won't wait for the 7-level to investigate a sacrifice. It is much better for them to enter the auction immediately, over 2♣ (or even before North's opening bid! Though that is very aggressive). You also can't learn nearly as much as it may seem from this particular auction, North does not announce club shortage or the extreme spade length. Once EW pass the first round the risk of the opponents entering the auction has gone down significantly.
- I expect to set E-W by two tricks in 7♣X, or three in 7♥X, if they take out our 6♠. The three tricks are better than 4♠+2, though I fully expect that if E-W find the sacrifice it is good for them.
- Fear of the opponents learning more than partner from our bids is a terrible habit. Be very careful with justifying unilateral action based on some hypothetical moves by the opponents. Much more often partner is the one with the problem, not the opponents, and we should be helping as much as possible. On balance it is beneficial to explain our hand, even with the opponents listening in. On slam auctions this is even more true than normal. It is possible but unlikely that this is an exception, but the burden of proof is quite high.
- Science does work on this hand, though in general a good system will primarily cater to more common hands before the rare ones. There's simply more points to be gained on the common ones. In general a lot of people make mistakes on their slam bidding, burning valuable bidding space and resorting to gadgets too much and too soon.
#10
Posted Today, 02:34
Also does E really pass over 2♣, I know I don't
#11
Posted Today, 02:54
#12
Posted Today, 04:16
I believe that the USA currently hold only the World Championship For People Who Still Bid Like Your Auntie Gladys - dburn
dunno how to play 4 card majors - JLOGIC
True but I know Standard American and what better reason could I have for playing Precision? - Hideous Hog
Bidding is an estimation of probabilities SJ Simon
#13
Posted Today, 04:28
I used to have an alternative playing two-under preempts that also could contain 4- loser one or two suiters, the second bid would then show the exact number of loser + the exact suit(s). That worked fine, but it was a heavy burden on memory as well as a very low occurence, so we stopped with it.
Not having such options, you have to pick 1♠ or 2♣ both of them are fine. When you open 2♣ though, don't auto preempt the next round by bidding 4♠ if 3♠ mandates cueing that'd be the thing to do however it remains a gamble as after mandatory cues you may know of the void, but does your partner have 2 trumps to ruff 2 ♣ or 3 if they lead ♠? I'd bid 2♠ is forcing after all, give your partner the opportunity to do something useful after which partner would bid 3♠ and promising a first round control somewhere.
Apart from that, relating to the title here; Every single bridge hand has the same chance of occurring, once in 635,013,559,600 the total number of hands possible you can club groups of hands together, but is that correct? On this actual had for instance par would be EW playing 7♣ doubled -2. I'm sure that's not the case for the entire group this mathematician came up with.