The Value of a Ten
The so-called Standard American point count system — invented by
Milton Work in contract bridge's formative
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 184.108.40.206 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
220.127.116.11 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 only.
I believe that sufficiently comprehensive simulations could establish a valid
numeric ratio among the honors, by comparing their frequencies of occurrence with
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
(1,000 deals each),
the tendencies are clear: possession of supporting ten-spots is a
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 vulnerable.
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
The bottom line: Within our test framework of balanced hands with
** Each ten is worth roughly
1/6 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
4-3-3-3 patterns 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.