Two consecutive 7 No Trumps contracts!

I don’t play bridge very often these days. But last night six of us boxed and coxed after dinner to play 15 or so hands. Four played while the other two casually glimpsed play or tidied up the dinner things. The two non-players showed more interest in the play when the bidding on one hand reached the unusual crescendo of “7 No Trumps”. This was clearly worth watching. The bidding sequence was 1NT, 4NT, 5 Diamonds, 7NT.

Above: the two bridge hands from the first consecutive 7 No Trumps deal.

The hand was extremely well bid, and the play was not difficult, despite the inevitable nerves, with winners both in hand and on table. That was exciting. A very rare contract and one which inevitably had a profound effect on the scorecard, not to mention the people involved. This was very special and unlike the rather patchy hands which preceded it.

After a breather, and plenty of discussion and congratulations, play resumed with a couple of changes of personnel. I had kibitzed the first contract but stood in as a player, and dealer, on the next hand. The second pack, shuffled as normal, was dealt and I had no option but to pass. The bidding then proceeded as follows: One diamond (left hand opponent), 4NT, 5 diamonds, 5NT, 7NT.

Above: the two bridge hands from the second consecutive 7 No Trumps deal.

I led a random card from my Jack-high hand and, as on the previous deal, 7 No Trumps was achieved without alarm.

This was clearly an extraordinary event. Two consecutive contracts of 7 no trumps – the highest possible contract – both bid and made. Six accomplished bridge players^[1] were stunned in trying to come to terms with what had just happened.

What are the odds of such a thing happening? As my maths achievements are limited to a grade 3 “O-level” in 1964, I asked the advice of Copilot. (Other AIs are available.) According to Copilot the probability of a cold^[2] 7NT on a random deal is 1 in 220,000. Different sources quote figures ranging from 1 in 200,000 to 1 in 300,000 so 1 in 220,000 seems a reasonable estimate.

Not every such hand is bid as 7NT. Even expert partnerships miss or stop short. A generous estimate would be that, say, 25% of makeable 7NT contracts are actually bid so

As the two consecutive deals were independent, we can square the probability thus:

So, in summary, the odds of our two consecutive bridge hands each resulting in a 7NT contract that were both bid and made are approximately

1 in 8 × 10¹¹ or about 1 in 800 billion

The fact that this was experienced by six of us last evening during an after-dinner bridge game is nothing short of mind-blowing. After this, our next bridge encounter is likely to feel rather dull by comparison.

Footnotes

1. Well, five plus me. ←
2. “Cold” means that the contract is achieved against any defence. ←