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# High Card Points Versus Binky Points

In Binky Points, the difference between 'xxx' and 'AKQ' is 4.29 tricks in notrump and 3.08 tricks in suit contracts. If AKQ is 9 points, then 1 point is worth about 1/2 a trick in notrump and 1/3 a trick in a suit contract.

Similarly, 'xxxx' and 'AKQJ' differ by 4.55 tricks in notrump and 3.31 tricks in suit contracts. So, if AKQJ is ten points, then a point is close to 1/2 a trick in notrump and 1/3 a trick in a suit contract.

In five-card suits, 'xxxxx' and 'AKQJT' differ by 4.91 tricks in notrump and 3.39 tricks in suit contracts. Again, we are close to 1/2 trick per HCP in notrump, and 1/3 trick per HCP in suit.

So, let's take that as our definition of a point.

We'll look at the values scaled to 1/5 of a point, because we have five values to add together (shape and the values for each suit.) For values not exactly equal to an integer number of points, we use the terms 'good', 'very good', 'bad', and 'very bad.'

ValueName
2.2Good 2 points
2.4Very good 2 points
2.6Very bad 3 points
2.8Bad 3 points

The scaling of Binky Points provided by in these tables makes it necessary to have 27 points to expect nine tricks in notrump, and 30 points to make ten tricks in a suit. That does not mean these should be our bidding goals - at 29 points or 28 points or even 27 points, we have a good chance of making game in a suit. We also need to look into the value of fits.

In notrump, where the variance is higher for the Binky Points, we might want to bid games with 24 or 25 points.

I'll be looking into these questions at a later date.

# The Values

## Example

Suppose you are dealt the hand:

```♠ K Q 9 6 5 2
♥ K 10 7
♦ A 8
♣ J 4
```

The value of this hand in notrump is 0.2 points for the 6-3-2-2 shape, 4.4 points for K-Q-9-X-X-X, 3.6 points for K-10-X, 4.6 points for A-X, and 0.6 points for J-X. Totaled, that equals 13.4 points, or a 'very good' 13 points.

The value of this hand in suit contracts is 2.6 for the 6-3-2-2 shape, 4.6 points for K-Q-9-X-X-X, 3.6 points for K-10-X, 4.6 points for A-X, and 0.6 points for J-X. That totals 16.0 points.

Most of the difference between these two evaluations come from the shape value in suit contracts, the other values almost being identical.

I picked this hand because in each case, the suit value is a 'very bad' value. So if we rounded to the nearest integer for each of the components, we'd get a value of 3 + 5 + 4 + 5 + 1 = 18 points. So using only integers for these values would overvalue this hand by a whole two points. That is the extreme case, but it shows that there is a risk of using integer values for each suit. Fractional values make sense even if we round to the nearest integer after the sum.

## Patterns

As is to be expected, the notrump values for patterns are fairly small - the only large values are possibly due to statistical sampling errors.

In suit contracts, we see that 4-3-3-3 is a 'bad zero point.' 4-4-3-2 is a 'bad one point.'

Data wrong - will fix real soon
```             NT Suit
4-3-3-3 -0.2 -0.2
4-4-3-2 -0.2  0.8
5-3-3-2  0.0  1.0
5-4-2-2  0.0  2.0
6-3-2-2  0.2  2.6
4-4-4-1  0.0  2.2
5-4-3-1  0.0  2.6
6-3-3-1  0.2  3.2
7-2-2-2  0.4  4.4
6-4-2-1  0.2  4.0
5-5-2-1  0.2  3.8
7-3-2-1  0.4  4.8
5-4-4-0  0.0  4.2
8-2-2-1  0.6  6.8
6-4-3-0  0.2  4.8
5-5-3-0  0.2  4.6
7-3-3-0  0.4  5.6
6-5-1-1  0.2  5.8
7-4-1-1  0.6  6.2
8-3-1-1  0.6  7.2
7-4-2-0  0.6  6.4
8-3-2-0  0.6  7.4
6-5-2-0  0.2  6.2
9-2-1-1 -1.4  6.8
9-3-1-0 -1.8  7.2
9-2-2-0 -1.0  7.4
8-4-1-0  0.6  8.8
7-5-1-0  0.6  8.4
6-6-1-0  0.0  8.2
9-4-0-0 -1.0  8.8
7-6-0-0  0.8 10.2
8-5-0-0  0.4 10.6
```

## Holdings

First, notice that the values for suit and notrump tend to be very close. Rarerly is there more than a 3/5 point difference in suits of length 5 or lower.

```             NT Suit   HCP
x  0.0  0.0     0
9  0.0  0.0     0
T  0.2  0.2     0
J  0.4  0.4     1
Q  1.0  0.8     2
K  1.8  1.4     3
A  4.2  4.0     4
```

A stiff king is therefore worth a 'bad 2 points' in notrump, but is worth a 'very good' one point in suits. A stiff ace is worth a good four points in notrump and a straight four points in suit contracts.

```        xx  0.0  0.0     0
9x  0.0  0.0     0
Tx  0.2  0.2     0
T9  0.4  0.2     0
Jx  0.6  0.6     1
J9  0.8  0.6     1
JT  0.8  0.8     1
Qx  1.4  1.2     2
Q9  1.4  1.2     2
QT  1.6  1.4     2
QJ  1.8  1.6     2
Kx  3.0  2.8     3
K9  3.0  3.0     3
KT  3.2  3.0     3
KJ  3.8  3.4     4
KQ  4.2  4.0     5
Ax  4.6  4.6     4
A9  4.6  4.6     4
AT  4.8  4.8     4
AJ  5.2  5.2     5
AQ  6.2  6.0     6
AK  7.2  7.2     7
```

Note that doubleton honors tend to evaluate as better in notrump than in suit contracts. This is not the truth if one of those cards is an ace - then only AQ is slightly better in notrump than in suit contracts.

Remember that the playing strength of the doubleton in suits is contained in the value for the pattern.

```       xxx  0.0  0.0    0
9xx  0.0  0.0    0
Txx  0.2  0.2    0
T9x  0.4  0.4    0
Jxx  0.8  0.8    1
J9x  1.0  0.8    1
JTx  1.2  1.2    1
JT9  1.2  1.2    1
Qxx  1.8  1.6    2
Q9x  2.0  1.8    2
QTx  2.4  2.0    2
QT9  2.4  2.2    2
QJx  2.8  2.4    3
QJ9  3.0  2.4    3
QJT  3.2  2.8    3
Kxx  3.2  3.2    3
K9x  3.2  3.4    3
KTx  3.6  3.6    3
KT9  3.8  3.8    3
KJx  4.2  4.2    4
KJ9  4.4  4.2    4
KJT  4.6  4.4    4
Axx  4.6  4.8    4
KQx  4.8  4.8    5
KQ9  5.0  5.0    5
A9x  4.8  5.0    4
ATx  5.0  5.2    4
KQT  5.2  5.2    5
AT9  5.2  5.4    4
KQJ  5.4  5.4    6
AJx  5.6  5.8    5
AJ9  5.8  6.0    5
AJT  6.0  6.2    5
AQx  6.4  6.8    6
AQ9  6.6  6.8    6
AQT  6.8  7.0    6
AQJ  7.2  7.4    7
AKx  7.4  7.8    7
AK9  7.6  8.0    7
AKT  7.8  8.2    7
AKJ  8.2  8.6    8
AKQ  8.6  9.2    9
```

Here we see that AKQ is worth a 'very bad' nine points in notrump and a 'good' nine points in suit contracts. Here we see big differences when the highest card in the holding is the queen. One value, for QJ9, is 3/5 points higher in notrump than suits.

```      xxxx  0.0  0.0    0
9xxx  0.2  0.2    0
Txxx  0.6  0.4    0
T9xx  0.6  0.6    0
Jxxx  1.0  1.0    1
J9xx  1.2  1.0    1
JTxx  1.6  1.2    1
JT9x  1.6  1.4    1
Qxxx  1.8  1.8    2
Q9xx  2.2  2.0    2
QTxx  2.4  2.2    2
QT9x  2.6  2.4    2
QJxx  2.8  2.6    3
QJ9x  3.0  2.8    3
QJTx  3.2  3.0    3
QJT9  3.4  3.2    3
Kxxx  3.0  3.2    3
K9xx  3.2  3.4    3
KTxx  3.6  3.8    3
KT9x  3.8  3.8    3
KJxx  4.2  4.2    4
KJ9x  4.4  4.4    4
KJTx  4.4  4.6    4
KJT9  4.4  4.6    4
KQxx  4.8  5.0    5
KQ9x  4.8  5.0    5
KQTx  5.2  5.4    5
KQT9  5.2  5.2    5
Axxx  4.6  4.8    4
A9xx  4.8  5.0    4
ATxx  5.0  5.4    4
AT9x  5.2  5.6    4
KQJx  5.4  5.6    6
KQJ9  5.6  6.0    6
KQJT  5.8  5.8    6
AJxx  5.6  6.0    5
AJ9x  5.8  6.2    5
AJTx  6.0  6.4    5
AJT9  6.2  6.6    5
AQxx  6.4  6.8    6
AQ9x  6.6  7.0    6
AQTx  6.8  7.2    6
AQT9  7.0  7.6    6
AQJx  7.2  7.6    7
AQJ9  7.2  7.6    7
AQJT  7.4  8.0    7
AKxx  7.2  7.8    7
AK9x  7.4  8.2    7
AKTx  7.6  8.4    7
AKT9  7.8  8.4    7
AKJx  8.2  8.8    8
AKJ9  8.4  9.0    8
AKJT  8.2  9.0    8
AKQx  8.6  9.4    9
AKQ9  8.8  9.8    9
AKQT  9.0  9.6    9
AKQJ  9.2 10.0   10
```

Note that the holdings with AK are significantly more valuable in suit contracts than in notrump - usually by 3/5 a point or more. (I think the value of 9.8 for AKQ9 is a statistical anomoly, however, since it doesn make sense that it would be better than AKQT.)

```     xxxxx  0.0  0.0
9xxxx  0.2  0.2
Txxxx  0.4  0.4
T9xxx  0.4  0.6
Jxxxx  1.0  0.8
J9xxx  1.2  1.2
JTxxx  1.2  1.2
JT9xx  1.4  1.4
Qxxxx  1.6  1.6
Q9xxx  2.0  2.0
QTxxx  2.0  2.0
QT9xx  2.2  2.2
QJxxx  2.6  2.6
QJ9xx  2.6  2.6
QJTxx  2.8  2.8
QJT9x  3.0  3.0
Kxxxx  2.8  3.0
K9xxx  3.0  3.4
KTxxx  3.4  3.6
KT9xx  3.6  3.8
KJxxx  3.8  4.0
KJ9xx  4.0  4.2
KJTxx  4.2  4.4
KJT9x  4.4  4.6
Axxxx  4.4  4.8
A9xxx  4.6  5.0
ATxxx  4.8  5.2
AT9xx  5.2  5.4
KQxxx  4.6  4.8
KQ9xx  4.6  5.0
KQTxx  5.0  5.2
KQT9x  5.0  5.4
KQJxx  5.2  5.6
KQJ9x  5.4  5.8
KQJTx  5.6  5.8
KQJT9  5.6  5.8
AJxxx  5.4  6.0
AJ9xx  5.6  6.0
AJTxx  6.0  6.4
AJT9x  6.0  6.6
AQxxx  6.2  6.6
AQ9xx  6.4  7.0
AQTxx  6.8  7.2
AQT9x  6.8  7.2
AQJxx  7.0  7.6
AQJ9x  7.2  7.8
AQJTx  7.4  8.0
AQJT9  7.4  8.0
AKxxx  7.2  7.8
AK9xx  7.4  8.0
AKTxx  7.6  8.2
AKT9x  7.8  8.4
AKJxx  8.2  8.8
AKJ9x  8.2  8.8
AKJTx  8.4  9.0
AKJT9  8.2  8.8
AKQxx  8.8  9.4
AKQ9x  8.8  9.6
AKQTx  9.2  9.8
AKQT9  9.4  9.8
AKQJx  9.6 10.0
AKQJ9 10.0 10.2
AKQJT  9.8 10.2
```
```    xxxxxx  0.0  0.0
9xxxxx  0.0  0.0
Txxxxx  0.4  0.4
T9xxxx  0.4  0.4
Jxxxxx  0.8  0.8
J9xxxx  0.8  0.8
JTxxxx  1.0  1.2
JT9xxx  1.2  1.2
Qxxxxx  1.6  1.6
Q9xxxx  1.6  1.6
QTxxxx  2.0  2.0
QT9xxx  2.0  2.0
QJxxxx  2.4  2.4
QJ9xxx  2.4  2.6
QJTxxx  2.4  2.8
QJT9xx  2.6  2.8
Kxxxxx  2.8  3.0
K9xxxx  2.8  3.0
KTxxxx  3.2  3.4
KT9xxx  3.4  3.4
KJxxxx  3.8  3.8
KJ9xxx  3.8  3.8
KJTxxx  4.0  4.2
KJT9xx  4.0  4.2
KQxxxx  4.4  4.6
KQ9xxx  4.4  4.6
KQTxxx  4.8  4.8
KQT9xx  4.8  5.0
KQJxxx  5.2  5.4
KQJ9xx  5.2  5.4
KQJTxx  5.4  5.6
KQJT9x  5.4  5.8
Axxxxx  4.4  4.6
A9xxxx  4.4  4.6
ATxxxx  5.0  5.0
AT9xxx  5.0  5.2
AJxxxx  5.4  5.6
AJ9xxx  5.6  5.6
AJTxxx  5.8  6.0
AJT9xx  5.8  6.0
AQxxxx  6.2  6.2
AQ9xxx  6.2  6.4
AQTxxx  6.8  6.8
AQT9xx  6.8  6.8
AQJxxx  7.2  7.2
AQJ9xx  7.2  7.2
AQJTxx  7.2  7.4
AQJT9x  7.4  7.4
AKxxxx  7.4  7.6
AK9xxx  7.6  7.8
AKTxxx  7.8  8.0
AKT9xx  7.8  8.0
AKJxxx  8.4  8.4
AKJ9xx  8.4  8.6
AKJTxx  8.6  8.8
AKJT9x  8.8  8.8
AKQxxx  9.2  9.0
AKQ9xx  9.2  9.2
AKQTxx  9.6  9.4
AKQT9x  9.6  9.4
AKQJxx  9.8  9.6
AKQJ9x  9.8  9.6
AKQJTx 10.2  9.8
AKQJT9 10.2  9.8
```
```   xxxxxxx  0.0  0.0
9xxxxxx  0.0  0.0
Txxxxxx  0.0  0.0
T9xxxxx  0.2  0.2
Jxxxxxx  0.6  0.8
J9xxxxx  0.6  0.8
JTxxxxx  0.6  0.8
JT9xxxx  0.8  1.0
Qxxxxxx  1.2  1.6
Q9xxxxx  1.4  1.6
QTxxxxx  1.4  1.6
QT9xxxx  1.4  1.6
QJxxxxx  2.0  2.2
QJ9xxxx  2.0  2.2
QJTxxxx  2.0  2.4
QJT9xxx  2.0  2.4
Kxxxxxx  2.6  2.6
K9xxxxx  2.6  2.6
KTxxxxx  2.8  2.8
KT9xxxx  2.8  2.8
KJxxxxx  3.4  3.6
KJ9xxxx  3.4  3.6
KJTxxxx  3.6  3.6
KJT9xxx  3.6  3.6
KQxxxxx  4.2  4.4
KQ9xxxx  4.2  4.4
KQTxxxx  4.2  4.4
KQT9xxx  4.2  4.4
KQJxxxx  4.6  5.0
KQJ9xxx  4.6  5.0
KQJTxxx  4.8  5.0
KQJT9xx  4.8  5.2
Axxxxxx  4.4  4.4
A9xxxxx  4.4  4.6
ATxxxxx  4.6  4.6
AT9xxxx  4.6  4.6
AJxxxxx  5.4  5.4
AJ9xxxx  5.6  5.4
AJTxxxx  5.6  5.4
AJT9xxx  5.6  5.4
AQxxxxx  6.2  6.0
AQ9xxxx  6.4  6.0
AQTxxxx  6.4  6.2
AQT9xxx  6.4  6.2
AQJxxxx  7.2  6.8
AQJ9xxx  7.2  7.0
AQJTxxx  7.4  7.0
AQJT9xx  7.4  7.0
AKxxxxx  7.6  7.2
AK9xxxx  7.6  7.2
AKTxxxx  7.8  7.4
AKT9xxx  7.8  7.4
AKJxxxx  8.4  8.0
AKJ9xxx  8.6  8.0
AKJTxxx  8.6  8.0
AKJT9xx  8.6  8.0
AKQxxxx  9.4  8.6
AKQ9xxx  9.4  8.8
AKQTxxx  9.6  8.8
AKQT9xx  9.6  8.8
AKQJxxx 10.0  9.0
AKQJ9xx 10.0  9.0
AKQJTxx 10.0  9.2
AKQJT9x 10.0  9.2
```

Notice that the value of solid honors is never more than a good nine points in suit contracts. That's because the value of AKQxxxx is already nearly all of the tricks in the suit.

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