[daveharty]

Played in a two-session pairs game on Wednesday at the local regional, and it wasn't until after the session was over that I realized I hadn't declared a single hand during the second session. ZERO. Then I looked back at the first session and realized I had only declared four times during the first session. So out of 54 boards I declared a grand total of four times. I am not the world's most aggressive bidder, but I am more aggressive than most. And I held my fair share of high cards, too. For reference, my partner declared a total of 18 times, nine in each session. Anyone else had a game like that recently?

[wyman]

It looks like (if you just randomly choose a declarer -- obviously there's asymmetry in 54 boards with respect to dealer and vul, so that will skew things), you'll declare 13.5 hands on average, with a std deviation of sqrt(10.125) ~= 3.18 hands. So declaring 4 or fewer hands or 23 or more hands is about a 3sigma event, which you expect to occur only about 0.27% of the time. Declaring exactly 4 you'd expect to occur in 7 out of 10000 54-bd sessions, or once in every 1429 sessions.

[helene_t]

wyman, on 2010-October-22, 13:47, said:

It looks like (if you just randomly choose a declarer -- obviously there's asymmetry in 54 boards with respect to dealer and vul, so that will skew things), you'll declare 13.5 hands on average, with a std deviation of sqrt(10.125) ~= 3.18 hands. So declaring 4 or fewer hands or 23 or more hands is about a 3sigma event, which you expect to occur only about 0.27% of the time. Declaring exactly 4 you'd expect to occur in 7 out of 10000 54-bd sessions, or once in every 1429 sessions.

Why use the normal-distribution approximation when the computer can do the (exact) binomial distribution

The probability of exactly 4 events out of 54 with p=0.25 is 0.0699%
At most 4 events has probability 0.0896%

[Fluffy]

the statisticals experts focus on mathematics, yet they fail to understand the real fenomenom lol.

He palyed a session with 0 declarer play from 27, I don't need much math to know it is the most unexpected fenomem of the 3 he mentioned .

[wyman]

helene_t, on 2010-October-22, 16:13, said:

Why use the normal-distribution approximation when the computer can do the (exact) binomial distribution

The probability of exactly 4 events out of 54 with p=0.25 is 0.0699%
At most 4 events has probability 0.0896%

I thought about this -- sheer laziness is really the answer.