[jerdonald]

BBO forum,

Playing in a local club today where we shuffled and
made the boards by hand, I picked up this hand on the
first board, which by the way I had made myself.

S KQxxx
H -
D KQx
C KQxxx

I opened 1 spade, LHO passed, partner bid 2 spades
and after some hesitation RHO passed. 2 spades
was passed out.

A low diamond was led and dummy boarded:

S ATx
H Qxxxxx
D Jxxx
C -

I played a low diamond from dummy and RHO trumped.
RHO then led a heart which I trumped. When I led a
trump LHO showed out so every hand had a void!

What are the odds?

jerryd

[Cascade]

At least one void in each suit

Probability = 0.0000192756954796046

A little less often than once in 50000 deals.

[kfay]

Sorry to be that guy but...

RHO tanked with 5 spades?
I passed 2♠?
LHO underled ♦Axxxxx?

What a club!

[Cascade]

Four Voids
0.0000192757 1 in 51878.80
Four stiffs (no voids)
0.010795069 1 in 92.63
Four doubletons (no singletons or voids)
0.092372353 1 in 10.83
Four tripletons (no doubletons or singletons or voids)
0.00093142 1 in 1073.63

Relaxing the constraint on shorter suits the numbers become
Four stiffs
0.01133135 88.25073974
Four doubletons
0.176378388 5.669628861
Four tripletons
0.316146724 3.163088289

[BunnyGo]

Cascade, on 2011-November-30, 01:38, said:

Relaxing the constraint on shorter suits the numbers become
Four tripletons
0.316146724 3.163088289

Somewhere you made a mistake. I can say with no calculations at all that this is occurs every hand.

Edit: Rethinking, I understood what you were saying to be "every hand has a suit 3 cards or shorter". What you meant was "Every hand has a tripleton, and may have a shorter suit as well." My mistake.

This post has been edited by BunnyGo: 2011-November-30, 02:09

[Cascade]

BunnyGo, on 2011-November-30, 02:07, said:

Edit: Rethinking, I understood what you were saying to be "every hand has a suit 3 cards or shorter". What you meant was "Every hand has a tripleton, and may have a shorter suit as well." My mistake.

That is what I intended.

[Cascade]

Cascade, on 2011-November-29, 20:32, said:

At least one void in each suit

Probability = 0.0000192756954796046

A little less often than once in 50000 deals.

Just to be clear. I calculated the probability of each suit being void. By symmetry the probability of each hand having a void is the same.

I have also calculated the probability that each hand has a void and the four voids are in different suits which is the smaller number:

0.00000930619869138331

[phil_20686]

kfay, on 2011-November-29, 21:18, said:

Sorry to be that guy but...

RHO tanked with 5 spades?
I passed 2♠?
LHO underled ♦Axxxxx?

What a club!

Its bridge, but not as we know it. You can make 4S despite the 5-0 break maybe? You will need lho to have - AKx Axxxxx Axxx - then you can play K of clubs, covered or run, ruff a club low if necessary, ruff a heart, ruff a club, ruff a heart. ruff a 4th round of clubs (Assuming you cashed your club winner at some point), and play the now good heart Q. ten in the bag.

Obviously this is impossible for lots of reasons, but seems like a strange club so who knows.....

[Statto]

The chances quoted above will be close. However, the probability of one hand having a void is not independent of whether another hand does. E.g. given that West has a void, it's more likely another hand has a void in another suit, due to there being fewer cards in the other suits to share around. It's quite complicated to work out accurately (so I haven't ), but it could be quite significantly more likely than the independent calculation suggests.

[Cascade]

Statto, on 2011-December-01, 20:50, said:

The chances quoted above will be close. However, the probability of one hand having a void is not independent of whether another hand does. E.g. given that West has a void, it's more likely another hand has a void in another suit, due to there being fewer cards in the other suits to share around. It's quite complicated to work out accurately (so I haven't ), but it could be quite significantly more likely than the independent calculation suggests.

I didn't do an independent calculation. I looked at every possible distribution of four hands and added the probabilities.

[Statto]

Cascade, on 2011-December-01, 22:11, said:

I didn't do an independent calculation. I looked at every possible distribution of four hands and added the probabilities.

Ah, sry, just checking