What are the odds?
Yarboroughs don't occur that often but what are the odds of two turning up in the same set of three? Have a look at last night's boards 22 and 24 at Patcham BC. I was the unfortunate East. Boards 12 and 25 are also a bit of a surprise.
http://www.bridgewebs.com/cgi-bin/bwom/bw.cgi?pid=display_rank&event=20190516_1&club=patcham
Comments
If you were 'unfortunate' (100% and 87%), I would hate to play you when you are lucky!
Odds of a Yarborough 1827:1 (approx)
Odds of ExactlyTwo Yarboroughs = 1 in [1827^2] * 3 (there are three combinations 1:2, 1:3, 2:3)
or one in 1,112,643 approx. This assumes random-number generator in hand generation.
If Three Yarboroughs incude two Yarboroughs then you have to add on a very small extra.
Guess what - playing at Patcham last night I sat North and on boards 2 & 3 I had consecutive Yarboroughs. I think the Bridge Gods are conspiring against me.
https://www.bridgewebs.com/cgi-bin/bwom/bw.cgi?pid=display_rank&event=20190627_1&club=patcham
"Odds of Exactly Two Yarboroughs = 1 in [1827^2] * 3 ...... or one in 1,112,643 approx."
I think these are the odds for either two or three Yarboroughs for a given player in a given set of three random hands, and this is going to be the statistic we are most likely to be interested in.
To exclude a third Yarborough, we have to specify that the third hand can't be a Yarborough and thus multiply the 1/1,112,643 by 1826/1827.
The worst hand I've ever had was no card higher than a 7 and a void in spades, yet I had the critical decision of opening lead against 4 !s!
Barrie Partridge - CTD for Bridge Club Live