Best hand ever

At my school bridge club last week somebody dealt themselves this hand. My first thought was that she'd rigged the deck, but I don't think that's possible because I shuffled and gave her the pack of cards to deal, which she did while I stood beside her writing something on the board.

What I was writing on the board was point ranges for opening bids. I didn't cover opening 36 point hands. In the end she settled for a 6NT opening bid and played there. This was the full deal and auction:

♠ A K Q ♥ A K Q ♦ A K Q ♣ A K Q 2

♠ 6 4 ♥ J 5 4 ♦ 7 5 3 2 ♣ T 5 4

W N E S 6NT - - -

I was the dummy and did not have the vital ♣J (and my ♥J is useless) and Clubs only produced three tricks, so declarer claimed her twelve top tricks for 6NT=. I like it when they claim early, as it shows they are aware of what is required for the contract and know how many winners they have.

I hope that the pupils will not be expecting another hand like this, as it could take many lifetimes. It's very rare to have above 20 points, as the table below shows (adapted from RP Bridge).

Points	Probability
19	1.0%
20	0.7%
21	0.4%
22	0.2%
23	0.1% (1 in 1000)
...
29	0.00066% (1 in 150,000)
...
35	0.00000009827% (1 in 1 billion)
36	0.00000000945% (1 in 10 billion)
37	0.00000000063% (1 in 1600 million)

Since the probabilities fall off so quickly you're in fact more likely to get a hand of 21 points than any hand with more than 21 points. Or to put it another way, more than half of 21+ point hands have exactly 21 points.

And what about that massive 36 point hand? The probability of getting one of those is a staggering 1 in 10 billion. That's more than the number of people on Earth. So the probability of getting a 36 point hand is less than the likelihood of lining up everybody in the World randomly and you happening to be at the front. Or, alternatively, if you deal yourself one hand a second night and day it would take on average about 300 years before you saw one this good. If you deal yourself a more modest thirty hands a day it will take about a million years.

My best ever hand was a balanced 29 count. The bidding went like this:

2♣1	2♦2
5NT3	7NT4

1: 23+
2: Weak or waiting
3: Showing 29-30 (on the logic that 2NT rebid is 23-24, 3NT rebid 25-26, 4NT rebid 27-28, 5NT rebid 29-30)
4: Actually had about 10 points and six good clubs

7NT made with about 18 top tricks. What's your best ever hand?