Improving Hand Evaluation Part 4

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tys...@yahoo.com

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Jun 29, 2004, 8:00:29 PM6/29/04
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[Improving Hand Evaluation Part 1]
http://tinyurl.com/25huc

[Improving Hand Evaluation Part 2]
http://tinyurl.com/383e6

[Improving Hand Evaluation Part 3]
http://tinyurl.com/2xhdf

How should you change your hand evaluation when the opponents enter
the bidding? Common sense tells you that if your opponents show a
suit, your hand goes up in value if you are short in that suit and
down in value if you are long. But how many points should you adjust
by? 1? Half a point? Similarly we've been told that AQ or Kx goes
up in value if RHO bids this suit, but down in value if LHO bids it.
Again, how much should you adjust? Maybe a point but probably less?
This article quantifies some of these adjustments. Read on, I bet you
aren't adjusting enough.

First let's look at how many points you should adjust based on
distribution. I've defined the pattern convention 2=5-4-2 to be a
hand with 2 cards in a key suit (in these examples your opponent's
suit) and 5-4-2 in the remaining suits (any order). I'll give
adjustments in terms of tricks (for finer adjustments), but I've also
given the equivalents in terms of normal MWC points and also in TSP
(my evaluation method based on a 6-4-2-1 honor count described in Part
3). The adjustments are different if your RHO made the bid or if
LHO did it. If your opponent just named a 5+ card suit (let's say he
opened 1S) then you should make the following adjustments to your
original hand valuation:

Tricks MWC TSP
Pattern RHO LHO RHO LHO RHO LHO
0=5-4-4 0.86 0.75 2 2 4 3
0=5-5-3 0.75 0.67 2 2 3 3
0=6-4-3 0.75 0.65 2 2 3 3
0=6-5-2 0.77 0.62 2 2 3 3
0=7-4-2 0.74 0.59 2 2 3 2
1=4-4-4 0.51 0.49 1 1 2 2
1=5-4-3 0.46 0.44 1 1 2 2
1=5-5-2 0.50 0.42 1 1 2 2
1=6-3-3 0.43 0.40 1 1 2 2
1=6-4-2 0.48 0.35 1 1 2 1
1=6-5-1 0.45 0.40 1 1 2 2
1=7-3-2 0.35 0.30 1 1 1 1
1=7-4-1 0.38 0.29 1 1 2 1
2=4-4-3 0.11 0.20 0 1 0 1
2=5-3-3 0.11 0.20 0 1 0 1
2=5-4-2 0.14 0.18 0 0 1 1
2=5-5-1 0.15 0.24 0 1 1 1
2=6-3-2 0.10 0.12 0 0 0 0
2=6-4-1 0.14 0.15 0 0 1 1
2=6-5-0 0.15 0.13 0 0 1 1
2=7-2-2 0.00 0.04 0 0 0 0
2=7-3-1 0.06 0.04 0 0 0 0
3=4-3-3 -0.01 0.04 0 0 0 0
3=4-4-2 -0.01 0.01 0 0 0 0
3=5-3-2 -0.04 0.00 0 0 0 0
3=5-4-1 -0.04 0.01 0 0 0 0
3=5-5-0 -0.03 -0.04 0 0 0 0
3=6-2-2 -0.12 -0.08 0 0 0 0
3=6-3-1 -0.10 -0.07 0 0 0 0
3=6-4-0 -0.15 -0.06 0 0 -1 0
3=7-2-1 -0.16 -0.21 0 -1 -1 -1
4=3-3-3 -0.19 -0.29 -1 -1 -1 -1
4=4-3-2 -0.24 -0.36 -1 -1 -1 -1
4=4-4-1 -0.32 -0.35 -1 -1 -1 -1
4=5-2-2 -0.36 -0.43 -1 -1 -1 -2
4=5-3-1 -0.34 -0.42 -1 -1 -1 -2
4=5-4-0 -0.32 -0.36 -1 -1 -1 -1
4=6-2-1 -0.41 -0.52 -1 -1 -2 -2
4=6-3-0 -0.36 -0.41 -1 -1 -1 -2
5=3-3-2 -0.67 -0.84 -2 -2 -3 -3
5=4-2-2 -0.73 -0.89 -2 -2 -3 -4
5=4-3-1 -0.77 -0.87 -2 -2 -3 -4
5=5-2-1 -0.86 -0.98 -2 -3 -4 -4

So for distribution it doesn't make as much of a difference if the
opponent was LHO or RHO. For MWC points, the adjustment is almost
always +2 for void, +1 for singleton, -1 for 4 cards, and -2 for 5.
In your recent games have you been subtracting 2 points when you have
5 cards in the opponent's suit? Maybe you should.

Now let's look at how your HCP should change if your opponent bids.
This time it matters more if it was LHO or RHO. But something is
going on with these numbers, they are all losing value:

Tricks MWC TSP
RHO LHO RHO LHO RHO LHO
x 0.00 0.00 0 0 0 0
T -0.01 -0.06 0 0 0 0
J -0.07 -0.05 0 0 0 0
Q -0.09 -0.08 0 0 0 0
K -0.15 -0.14 0 0 -1 -1
A -0.05 -0.07 0 0 0 0

xx 0.00 0.00 0 0 0 0
Tx -0.03 -0.03 0 0 0 0
Jx -0.04 -0.09 0 0 0 0
JT -0.12 -0.15 0 0 0 -1
Qx -0.09 -0.16 0 0 0 -1
QT -0.10 -0.21 0 -1 0 -1
QJ -0.22 -0.20 -1 -1 -1 -1
Kx -0.03 -0.23 0 -1 0 -1
KT -0.13 -0.30 0 -1 -1 -1
KJ -0.09 -0.25 0 -1 0 -1
KQ -0.24 -0.29 -1 -1 -1 -1
Ax -0.03 -0.14 0 0 0 -1
AT -0.04 -0.17 0 0 0 -1
AJ -0.05 -0.19 0 -1 0 -1
AQ 0.00 -0.27 0 -1 0 -1
AK -0.16 -0.20 0 -1 -1 -1

xxx 0.00 0.00 0 0 0 0
Txx -0.04 -0.09 0 0 0 0
Jxx -0.07 -0.16 0 0 0 -1
JTx -0.16 -0.18 0 0 -1 -1
Qxx -0.12 -0.26 0 -1 0 -1
QTx -0.21 -0.32 -1 -1 -1 -1
QJx -0.25 -0.33 -1 -1 -1 -1
QJT -0.30 -0.38 -1 -1 -1 -2
Kxx -0.08 -0.33 0 -1 0 -1
KTx -0.16 -0.40 0 -1 -1 -2
KJx -0.16 -0.44 0 -1 -1 -2
KJT -0.17 -0.40 0 -1 -1 -2
Axx -0.08 -0.12 0 0 0 0
KQx -0.30 -0.43 -1 -1 -1 -2
ATx -0.09 -0.23 0 -1 0 -1
KQT -0.20 -0.48 -1 -1 -1 -2
KQJ -0.43 -0.38 -1 -1 -2 -2
AJx -0.09 -0.34 0 -1 0 -1
AJT -0.17 -0.38 0 -1 -1 -2
AQx -0.08 -0.37 0 -1 0 -2
AQT 0.02 -0.49 0 -1 0 -2
AQJ -0.12 -0.45 0 -1 0 -2
AKx -0.20 -0.30 -1 -1 -1 -1
AKT -0.19 -0.40 -1 -1 -1 -2
AKJ -0.17 -0.40 0 -1 -1 -2
AKQ -0.33 -0.56 -1 -2 -1 -2

xxxx 0.00 0.00 0 0 0 0
Txxx -0.01 -0.10 0 0 0 0
Jxxx -0.12 -0.11 0 0 0 0
JTxx -0.17 -0.10 0 0 -1 0
Qxxx -0.15 -0.21 0 -1 -1 -1
QTxx -0.18 -0.27 0 -1 -1 -1
QJxx -0.24 -0.32 -1 -1 -1 -1
QJTx -0.34 -0.26 -1 -1 -1 -1
Kxxx -0.17 -0.36 0 -1 -1 -1
KTxx -0.21 -0.44 -1 -1 -1 -2
KJxx -0.25 -0.54 -1 -2 -1 -2
KJTx -0.30 -0.52 -1 -1 -1 -2
Axxx -0.13 -0.17 0 0 -1 -1
KQxx -0.39 -0.49 -1 -1 -2 -2
ATxx -0.15 -0.26 0 -1 -1 -1
KQTx -0.44 -0.50 -1 -1 -2 -2
KQJx -0.45 -0.50 -1 -1 -2 -2
KQJT -0.35 -0.44 -1 -1 -1 -2
AJxx -0.23 -0.36 -1 -1 -1 -1
AJTx -0.27 -0.42 -1 -1 -1 -2
AQxx -0.18 -0.40 0 -1 -1 -2
AQTx -0.15 -0.43 0 -1 -1 -2
AQJx -0.31 -0.41 -1 -1 -1 -2
AKxx -0.34 -0.36 -1 -1 -1 -1
AQJT -0.51 -0.55 -1 -2 -2 -2
AKTx -0.38 -0.41 -1 -1 -2 -2
AKJx -0.41 -0.49 -1 -1 -2 -2
AKJT -0.43 -0.40 -1 -1 -2 -2
AKQx -0.51 -0.46 -1 -1 -2 -2
AKQT -0.39 -0.69 -1 -2 -2 -3
AKQJ -0.40 -0.88 -1 -2 -2 -4

xxxxx 0.00 0.00 0 0 0 0
Txxxx -0.04 -0.04 0 0 0 0
Jxxxx 0.01 -0.07 0 0 0 0
JTxxx -0.06 -0.11 0 0 0 0
Qxxxx -0.13 -0.27 0 -1 -1 -1
QTxxx -0.12 -0.21 0 -1 0 -1
QJxxx -0.20 -0.29 -1 -1 -1 -1
QJTxx -0.26 -0.22 -1 -1 -1 -1
Kxxxx -0.27 -0.34 -1 -1 -1 -1
KTxxx -0.26 -0.45 -1 -1 -1 -2
KJxxx -0.33 -0.56 -1 -2 -1 -2
KJTxx -0.41 -0.42 -1 -1 -2 -2
Axxxx -0.20 -0.18 -1 0 -1 -1
KQxxx -0.43 -0.51 -1 -1 -2 -2
KQTxx -0.59 -0.61 -2 -2 -2 -3
ATxxx -0.11 -0.27 0 -1 0 -1
KQJxx -0.50 -0.60 -1 -2 -2 -2
KQJTx -0.44 -0.67 -1 -2 -2 -3
AJxxx -0.26 -0.38 -1 -1 -1 -2
AJTxx -0.25 -0.40 -1 -1 -1 -2
AQxxx -0.20 -0.57 -1 -2 -1 -2
AQTxx -0.24 -0.57 -1 -2 -1 -2
AQJxx -0.25 -0.64 -1 -2 -1 -3
AKxxx -0.43 -0.47 -1 -1 -2 -2
AQJTx -0.41 -0.24 -1 -1 -2 -1
AKTxx -0.41 -0.74 -1 -2 -2 -3
AKJxx -0.53 -0.56 -1 -2 -2 -2
AKJTx -0.52 -0.65 -1 -2 -2 -3
AKQxx -0.59 -0.64 -2 -2 -2 -3
AKQTx -0.48 -0.66 -1 -2 -2 -3
AKQJx -0.58 -0.56 -2 -2 -2 -2
AKQJT 0.06 -0.30 0 -1 0 -1

I'd ignore the values for the stronger 5-card suits. There just
weren't enough samples to make a statistically valid approximation of
their worth.

Pretty much every single holding loses value. This is another effect
of the honor devaluation + a constant that we saw in Part 2. What we
saw there was that if partner bid a 5+ suit, we lost HCP in all of our
outside suits, but we added a constant. A good approximation was that
we subtract 1/3 of all our HCP outside of partner's suit, but we add a
constant of 3 points (4 for TSP). This was because partner is more
likely to be unbalanced than an average hand and so high cards become
less important while shape becomes more important. Weak hands become
stronger while strong hands become weaker. I've looked into this
effect in a little more detail and found that when partner promises a
balanced hand, the opposite is true. In that case our HCP actually
become worth more than they did before. This overall effect of the
changing weight of honor cards depending on the balanced/unbalanced
nature of the other hands is going to need more investigation. It
might be the subject of Part 5 of this series. At the table, we've
generally just assigned a constant value to high cards and gotten by,
but in reality, they change a lot.

We saw that when partner has a 5+ suit, points outside his suit lose
1/3 of their value (multiply by 0.67). What's the factor when the
opponents bid? For honors *outside* their suit it actually gets
multiplied by the same number (0.67)! And again we add the constant
of 3 points (4 for TSP). It doesn't matter much if it was RHO or LHO
and all holdings devalue approximately by this same factor of 0.67.
Honors in the opponent's suit are trickier. The average multiplier is
0.90 for RHO and 0.81 for LHO. But while in the other cases almost
all cards were devalued by the same factor, when the opponents bid,
Aces aren't devalued as much and there are some other holding
combinations that defy straight factoring. Also longer suits tend to
devalue more. So Kxxx will lose more value than Kx. If we ignore
this and just multiply by this factor, we'd get the following
additional adjustments:

Tricks MWC TSP
RHO LHO RHO LHO RHO LHO
x 0.00 0.00 0 0 0 0
T -0.01 -0.05 0 0 0 0
J -0.05 -0.02 0 0 0 0
Q -0.06 -0.03 0 0 0 0
K -0.10 -0.05 0 0 0 0
A 0.09 0.18 0 1 0 1

xx 0.00 0.00 0 0 0 0
Tx -0.02 -0.02 0 0 0 0
Jx -0.02 -0.05 0 0 0 0
JT -0.09 -0.10 0 0 0 0
Qx -0.05 -0.09 0 0 0 0
QT -0.05 -0.13 0 0 0 -1
QJ -0.16 -0.10 0 0 -1 0
Kx 0.07 -0.05 0 0 0 0
KT -0.02 -0.12 0 0 0 0
KJ 0.03 -0.03 0 0 0 0
KQ -0.10 -0.04 0 0 0 0
Ax 0.12 0.15 0 0 1 1
AT 0.12 0.13 0 0 1 1
AJ 0.13 0.13 0 0 1 1
AQ 0.21 0.11 1 0 1 0
AK 0.09 0.25 0 1 0 1

xxx 0.00 0.00 0 0 0 0
Txx -0.03 -0.07 0 0 0 0
Jxx -0.05 -0.11 0 0 0 0
JTx -0.12 -0.11 0 0 -1 0
Qxx -0.06 -0.16 0 0 0 -1
QTx -0.14 -0.19 0 -1 -1 -1
QJx -0.16 -0.18 0 0 -1 -1
QJT -0.20 -0.21 -1 -1 -1 -1
Kxx 0.03 -0.13 0 0 0 -1
KTx -0.04 -0.18 0 0 0 -1
KJx -0.02 -0.19 0 -1 0 -1
KJT -0.02 -0.12 0 0 0 -1
Axx 0.09 0.18 0 1 0 1
KQx -0.13 -0.12 0 0 -1 -1
ATx 0.09 0.10 0 0 0 0
KQT -0.02 -0.15 0 0 0 -1
KQJ -0.24 -0.04 -1 0 -1 0
AJx 0.12 0.02 0 0 0 0
AJT 0.05 0.01 0 0 0 0
AQx 0.15 0.05 0 0 1 0
AQT 0.27 -0.05 1 0 1 0
AQJ 0.14 0.02 0 0 1 0
AKx 0.07 0.19 0 1 0 1
AKT 0.10 0.11 0 0 0 0
AKJ 0.14 0.14 0 0 1 1
AKQ -0.01 0.02 0 0 0 0

xxxx 0.00 0.00 0 0 0 0
Txxx 0.01 -0.07 0 0 0 0
Jxxx -0.08 -0.05 0 0 0 0
JTxx -0.13 -0.02 0 0 -1 0
Qxxx -0.09 -0.10 0 0 0 0
QTxx -0.10 -0.14 0 0 0 -1
QJxx -0.15 -0.15 0 0 -1 -1
QJTx -0.24 -0.07 -1 0 -1 0
Kxxx -0.06 -0.16 0 0 0 -1
KTxx -0.08 -0.21 0 -1 0 -1
KJxx -0.10 -0.28 0 -1 0 -1
KJTx -0.14 -0.23 0 -1 -1 -1
Axxx 0.04 0.13 0 0 0 1
KQxx -0.21 -0.18 -1 -1 -1 -1
ATxx 0.03 0.07 0 0 0 0
KQTx -0.26 -0.16 -1 0 -1 -1
KQJx -0.25 -0.15 -1 0 -1 -1
KQJT -0.14 -0.08 0 0 -1 0
AJxx -0.02 0.01 0 0 0 0
AJTx -0.05 -0.02 0 0 0 0
AQxx 0.06 0.02 0 0 0 0
AQTx 0.10 0.03 0 0 0 0
AQJx -0.05 0.07 0 0 0 0
AKxx -0.07 0.14 0 0 0 1
AQJT -0.23 -0.05 -1 0 -1 0
AKTx -0.09 0.11 0 0 0 0
AKJx -0.11 0.06 0 0 0 0
AKJT -0.12 0.16 0 0 0 1
AKQx -0.19 0.12 -1 0 -1 1
AKQT -0.06 -0.09 0 0 0 0
AKQJ -0.06 -0.26 0 -1 0 -1

xxxxx 0.00 0.00 0 0 0 0
Txxxx -0.02 -0.01 0 0 0 0
Jxxxx 0.03 -0.02 0 0 0 0
JTxxx -0.02 -0.03 0 0 0 0
Qxxxx -0.08 -0.17 0 0 0 -1
QTxxx -0.05 -0.08 0 0 0 0
QJxxx -0.11 -0.13 0 0 0 -1
QJTxx -0.16 -0.04 0 0 -1 0
Kxxxx -0.17 -0.15 0 0 -1 -1
KTxxx -0.14 -0.23 0 -1 -1 -1
KJxxx -0.19 -0.31 -1 -1 -1 -1
KJTxx -0.26 -0.15 -1 0 -1 -1
Axxxx -0.03 0.12 0 0 0 1
KQxxx -0.26 -0.21 -1 -1 -1 -1
KQTxx -0.41 -0.29 -1 -1 -2 -1
ATxxx 0.07 0.06 0 0 0 0
KQJxx -0.31 -0.25 -1 -1 -1 -1
KQJTx -0.24 -0.30 -1 -1 -1 -1
AJxxx -0.06 -0.01 0 0 0 0
AJTxx -0.03 0.00 0 0 0 0
AQxxx 0.03 -0.15 0 0 0 -1
AQTxx 0.01 -0.12 0 0 0 0
AQJxx 0.02 -0.16 0 0 0 -1
AKxxx -0.16 0.02 0 0 -1 0
AQJTx -0.13 0.25 0 1 -1 1
AKTxx -0.12 -0.22 0 -1 0 -1
AKJxx -0.22 -0.01 -1 0 -1 0
AKJTx -0.21 -0.08 -1 0 -1 0
AKQxx -0.26 -0.06 -1 0 -1 0
AKQTx -0.14 -0.06 0 0 -1 0
AKQJx -0.24 0.06 -1 0 -1 0
AKQJT 0.41 0.33 1 1 2 1

So what can we get from this? I'm not sure. =) It's a lot more
complicated than simple rules can accommodate. But seriously, I'm
trying to get a feel for the actual quantitative size of adjustments
that good card players make all the time. I'm not sure that a lot of
us are really making enough adjustments. When your LHO opens 1S,
these two hands become about the same strength:

- Kxxxx
xxxxx vs. Kxx
xxxx QJT
xxxx KT

Are you adjusting enough?

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