The Value of a Ten
The so-called Standard American point count system — invented
by Milton Work in contract bridge's formative
years — has
proved immensely popular if only for its utter simplicity. Although
Ely Culbertson's Honor-Trick Table was considered de rigeur
in the 1930s, counting all those half-tricks and quarter-tricks
was tedious — and largely inaccurate. In 1936, Charles Goren
began developing and popularizing a point-count method in his own books,
which instigated a 15-year battle between those titans of bridge.
Because the new 22.214.171.124 valuation scheme was much
easier on the brain and more accurate as well, it ultimately supplanted the
old system and remains the favorite some seven decades later.
The old Honor-Trick table overvalued kings and A-K combinations, much to
the dismay of countless declarers going set in notrump contracts that should
have been fulfilled according to their charts. Conversely, today's expert
consensus is that the higher honors are undervalued by the
count. New valuations have been suggested for the ace, king, queen, and
jack. For example, one programmer's research on balanced hands suggests
a rating system of 6½-4½-2½-1. Some players
add ½ point for a ten or other plus-value;
Others would prefer to employ their homemade alternative schemes at the table;
however, experimentation with new evaluations is partly stymied by the the
tunnel-visioned ACBL, which laws mandate certain bidding agreements
(such as the range for a Weak-Two-Bid) to conform to Work-Points
I believe that sufficiently comprehensive simulations could establish a
valid numeric ratio among the honors, by comparing their frequencies of
double-dummy trick totals over a great number of
deals. Although this seems like a straightforward analysis, I have seen
no such results published as yet. SIM will get
the ball rolling here.
Today the spotlight is on the "forgotten honor" — the lowly
sure — every player talks about
having "good fillers" or "no spots" or the like, but the
common quick-evaluation methods make no accommodation for other than the
top four honors. This oversight is a significant error, as the following
data will show.
For this simulation, North and South were dealt
13 hcp each.
Four different hand-pattern combinations are compared. For added
interest (and because the feature is built into SIM),
each scenario arbitrarily compares the results of a contract of
1NT with a game bid of 3NT.
So! It seems that the presence of tens can be worth quite a bit.
Note from the Bid/Pass data that with two "spotless"
hands, game is made barely half the time despite the
total; yet nearly 80% of the ten-rich games succeed.
Let's compress the trick data for readability:
Fascinating! Although the actual increments between boxes vary
somewhat due to the relatively small sampling of these studies
deals each), the tendencies are clear: possession of supporting
ten-spots is a big deal.
The difference between having no ten and possessing them all
is approximately .6 to .8 tricks, which translates roughly to
one-sixth of a trick per card. On average,
the offensive side will possess nearly half of the ten-spots anyway;
but when all are working together, that's an additional trick on every
third hand that you play. Those tricks are golden at matchpoints,
and they score up a lot of extra game and slam bonuses as well.
In terms of total points, the numbers are equally astounding.
This chart condenses the
assuming that game is bid on every hand:
Wow! It seems that a ten is worth
approximately 13 points non-vulnerable, and about 20 points when
ten-rich hands generate fully 70-80%
more total points than their substance-bereft counterparts!
Compared to the average holding of a pair of tens, having all four is worth
about 20% additional total points.
The bottom line: Within our test framework of balanced hands with
13 hcp opposite 13:
** Each ten is worth roughly
of a trick.
** Each ten adds an average of 10-15% points to the final score!
Translating a ten's worth into an equivalent high-card-point value is
more difficult, but eventually SIM will determine
The Way It Is. We also will evaluate tens
in comparison to other high-card-point combinations; the worth of
lesser spot-cards might be examined as well.
Note from the graphs that the hands with opposing
fared better than when 4-4-3-2 patterns were included.
Why? Also, declarers with but a single 5-card
suit to work with handily out-scored those in which both hands had a
5-card suit. Why? That seems non-intuitive,
and the literature offers little if any insight into this phenomenon.
I believe, however, that SIM already has suggested
the answer — to be detailed in an upcoming study.