you can be dealt
. Every card must be less than or equal to a nine
, and distribution
must be 3-3-3-4, for zero honors points
and zero distribution points
Named after a certain Lord Yarborough, who once offered 1000 pounds to every player who was dealt a whist hand in which no card was higher than a nine, on the condition that they paid him one pound for every hand they played. This was a winning proposition for Yarborough, as the probability of this happening is equal to (32 choose 13)/(52 choose 13), or (32!*39!)/(52!*19!), or about one in 1,828. (I'm using microsoft calculator here).
The Bridge Yarborough is more rare, occurring only (4*((8 choose 3)^3)*(8 choose 4))/(52 choose 13) = ((8!^4)*13!*39!)/(6^4*(5!^3)*4!*52!) = about once every 12,900 hands.