SO far in this series I have got away without giving
you lots of percentages. However you do need to
have some idea about how likely certain breaks are
because sometimes you have to choose between
lines of play that depend on breaks.
Missing 2 cards:
1-1 break = 52%; 2-0 break = 48%.
Missing 3 cards:
2-1 break = 78%; 3-0 break = 22%.
Missing 4 cards:
2-2 break = 40.7%; 3-1 break = 49.7%;
4-0 break = 9.6%.
Missing 5 cards:
3-2 break = 67.8%; 4-1 break = 28.3%;
5-0 break = 3.9%.
Missing 6 cards:
3-3 break = 35.5%; 4-2 break = 48.5%;
5-1 break = 14.5%; 6-0 break = 1.5%.
Missing 7 cards:
4-3 break = 62.2%; 5-2 break = 30.5%;
6-1 break = 6.8%; 7-0 break = 0.5%.
A word of warning here. These percentages assume
that the cards have been perfectly shuffled, as would
be the case if a duplimate machine is used. If players
shuffle and deal they rarely shuffle properly and the
good breaks become far more likely. Indeed research
done several years ago suggest that some players
shuffle so badly that at least at one club a 3-3 break
occurred more than 50% of the time. If you are
playing bridge where a 3-3 break is more likely than
a finesse the nature of bridge is fundamentally
altered. I cannot possibly know what happens at
your club; all I can do is write on the assumption
that your boards are duplimated.
It is worth noting at this stage that if you are missing
an odd number of cards in a suit the odds of the
best break are greater than a finesse, whereas if you
are missing an even number of cards the odds of the
best break are worse than a finesse (with the
marginal exception of the 1-1 break when missing
On the deal below plan your play in 3NT by
South on the lead of the ´3.
Would your decision be different if you replaced
the t6 in dummy with the ®6?
Game All. Dealer South.
´ A 8
™ 8 7 3 2
t 7 6 5 4
® 7 5 4
´ 9 6
™ A K Q
t A Q 3 2
® A K Q 2
You have eight top tricks. Your ninth trick will have
to come from either the diamond finesse or a 3-3
club break. You would have liked to test the clubs
first, and fall back on the diamond finesse if clubs
broke unfavourably, but the opening lead has
removed your only entry to dummy so if you don't
take the diamond finesse now you will not have
another chance. So you must decide between the
two options. The diamond finesse is about 50%.
The 3-3 club break is 35.5%. So take the diamond
finesse at trick two.
If you had the ®6 in dummy instead of the t6,
you would be comparing the probability of a 3-2
club break (67.8%) against the 50% diamond
finesse. So now it would be incorrect to take the
Sadly life is not always so clearcut. On the next
deal you are in 6´. West leads the ™K, taken by your
™A. When you cash dummy's ´A, East follows with
48 English Bridge December 2015 www.ebu.co.uk
Combining Chances by Andrew Kambites