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After Partner Opens 1♠ And You Have a Fit

Binky Points are a first round evaluation technique, but we all know that when your partner bids, that bid will change your hand's evaluation.

For example, playing a Standard American 5-card major system, how do you re-evaluate your hand if your partner opens 1♠ and you have at least three card support?

I ran quite a few deals of this sort, and tried to figure out how much the difference was between the raw Binky Points estimation of tricks and the expected number of tricks if spades is the contract.

Responder Hand Pattern

Let's look at responder's shapes first. We sort the suits other than spades, so if you are deal a 3-4-1-5 shape, we will list that as 3-5-4-1, because we don't, in this simulation, really differentiate between the other suits. (There is a degree to which this assumption is false - partner will open with more hands that have long hearts and spades. But for now, this is our assumption.)

```             3-8-1-1  -1.097
3-8-2-0  -0.971
3-7-2-1  -0.568
3-7-3-0  -0.529
3-6-4-0  -0.366
3-5-5-0  -0.322
3-6-3-1  -0.180
3-6-2-2  -0.164
3-5-4-1  -0.084
4-7-1-1  -0.016
3-5-3-2  +0.069
3-4-4-2  +0.091
3-4-3-3  +0.193
4-6-2-1  +0.277
5-6-1-1  +0.349
4-6-3-0  +0.352
4-5-2-2  +0.418
7-3-2-1  +0.423
6-5-1-1  +0.429
4-5-4-0  +0.433
5-6-2-0  +0.443
4-5-3-1  +0.450
4-4-3-2  +0.470
4-4-4-1  +0.478
4-3-3-3  +0.495
5-5-2-1  +0.505
6-3-2-2  +0.514
6-4-2-1  +0.522
5-4-2-2  +0.533
6-5-2-0  +0.542
5-3-3-2  +0.552
6-3-3-1  +0.580
5-4-3-1  +0.586
5-5-3-0  +0.594
6-4-3-0  +0.607
5-4-4-0  +0.653
```

The key is to realize that these adjustments are to your intiial Binky suit evaluation. A 6-4-3-0 pattern is probably better than a 5-4-4-0 pattern, but we've already counted a lot of the strength of the spade length of the 6-4-3-0 pattern. This measures the *additional* value once you know that partner has a 1♠ opening.

Also, since we are only evaluating here the value of playing in spades. the 3-8-1-1 pattern actually loses value, because it had a lot of natural playing strength in the 8-card suit that gets potentially lost when playing in a suit control.

If we use the idea that a "point" is a third of a trick in a suit contract, this means that, after partner opens, we get an additional two points if we have a 5-4-4-0 pattern. On the other hand, a 4-3-3-3 hand is worth 1 1/2 additional suit contract points, while the 3-4-3-3 hand has just a little more than 1/2 a point added to its value.

```  3 card fits
S:xxx -0.060
S:AQx -0.050
S:AQJ -0.044
S:KQx -0.037
S:AKx -0.015
S:KQJ -0.009
S:AKJ -0.007
S:KJx +0.012
S:Kxx +0.016
S:AJx +0.020
S:Axx +0.025
S:Jxx +0.053
S:Qxx +0.067
S:QJx +0.075
S:AKQ +0.077
```
There is very little adjustment to the values here - a total swing of a little more than 1/3 a trick. Hard to tell if the differences are noise due to sample size or actual values.
```
S:AQJx -0.265
S:KQJx -0.208
S:AKQJ -0.207
S:AKQx -0.184
S:AQxx -0.174
S:AKJx -0.162
S:KQxx -0.162
S:KJxx -0.142
S:AKxx -0.108
S:AJxx -0.100
S:QJxx -0.026
S:Kxxx -0.024
S:Axxx +0.008
S:Qxxx +0.029
S:Jxxx +0.059
S:xxxx +0.084
```

Again, we see that lots of honors is a negative. This is essentially a duplication of values issue - when you have a nine card fit, there isn't much value to all of those honors. The total range of adjustments for the four card fit is an entire point.

That doesn't mean xxxx is better than AQJx, only that finding out partner opens 1S, you adjust your evaluation of xxxx up, while you've over-valued AQJx with a blind Binky evaluation.

```             S:AQJxx -0.289
S:AKJxx -0.240
S:AQxxx -0.224
S:KQJxx -0.224
S:KQxxx -0.205
S:AKQxx -0.171
S:AKxxx -0.167
S:AKQJx -0.145
S:KJxxx -0.139
S:AJxxx -0.138
S:Kxxxx -0.019
S:QJxxx -0.019
S:Axxxx +0.018
S:Qxxxx +0.054
S:Jxxxx +0.124
S:xxxxx +0.229
```

Now a range of about a point and a half. Again, this evaluates up or none if the five card suit has zero or one honors, and down if the hand has two or more honors.

```            S:AKQJxx -0.242
S:AKJxxx -0.232
S:AQxxxx -0.213
S:KQxxxx -0.180
S:AQJxxx -0.179
S:AKQxxx -0.158
S:KQJxxx -0.148
S:AKxxxx -0.127
S:KJxxxx -0.114
S:AJxxxx -0.103
S:QJxxxx -0.008
S:Kxxxxx -0.004
S:Axxxxx +0.064
S:Qxxxxx +0.126
S:Jxxxxx +0.180
S:xxxxxx +0.315
```

Longer spade fits don't have reliable data, but seem to follow the same pattern.

Responder side suits

In some of these tables, there is a N/A in the data. This just means, I don't have nearly enough data to really estimate.

Also, note that x below includes nines and tens.

```Length 1
Avg   3 Fit   4 Fit   5 Fit   6 Fit
Q  -0.045  -0.013  -0.065  -0.071  -0.124
K  -0.026  +0.029  -0.067  -0.094  -0.097
J  -0.022  -0.026  -0.022  -0.004  -0.047
x  +0.008  -0.007  +0.019  +0.025  +0.043
A  +0.016  +0.106  -0.040  -0.100  -0.176
```

Just a note. This means that if we have a stiff ace and a four card fit, we adjust our hand evaluation by -0.040. If we have a stiff ace and a three-card fit, the adjustment is +0.106.

Note the adjustment here is negligable - our raw Binky Point suit evaluation was good.

The stiff ace with three-card support is the only holding with a big positive adjustment - about a third of a point. This is because, with three-card support, it is not clear that you are going to get ruffs in the suit, but the ace gives you a timing advantage - you never need to lose a trick in the suit to set up a ruff.

```Length 2
Avg   3 Fit   4 Fit   5 Fit   6 Fit
KQ  -0.162  -0.120  -0.201  -0.243  -0.258
AQ  -0.133  -0.047  -0.194  -0.291  -0.321
KJ  -0.124  -0.046  -0.208  -0.178  -0.258
AK  -0.110  +0.008  -0.217  -0.302  -0.293
Kx  -0.076  -0.032  -0.118  -0.143  -0.143
AJ  -0.047  +0.016  -0.110  -0.120  -0.107
Qx  -0.044  -0.024  -0.058  -0.083  -0.057
QJ  -0.036  -0.011  -0.071  -0.054  +0.070
Jx  -0.009  -0.013  -0.008  +0.004  -0.001
Ax  +0.010  +0.073  -0.045  -0.090  -0.120
xx  +0.039  +0.006  +0.069  +0.089  +0.091

```
```Length 3
Avg   3 Fit   4 Fit   5 Fit   6 Fit
AKQ  -0.250  -0.174  -0.318  -0.539     N/A
KQJ  -0.217  -0.159  -0.282  -0.362     N/A
AKJ  -0.201  -0.109  -0.301  -0.403     N/A
AQJ  -0.168  -0.088  -0.241  -0.386     N/A
KQx  -0.166  -0.125  -0.212  -0.260  -0.321
AKx  -0.145  -0.072  -0.226  -0.312  -0.348
AQx  -0.135  -0.080  -0.196  -0.259  -0.291
KJx  -0.115  -0.081  -0.142  -0.209  -0.302
AJx  -0.071  -0.027  -0.117  -0.183  -0.204
Kxx  -0.054  -0.028  -0.083  -0.118  -0.106
QJx  -0.053  -0.043  -0.070  -0.073  -0.073
Qxx  -0.010  -0.010  -0.012  -0.006  -0.019
Jxx  +0.018  -0.001  +0.038  +0.067  +0.098
Axx  +0.022  +0.053  -0.011  -0.049  -0.074
xxx  +0.070  +0.036  +0.107  +0.148  +0.162
```

We start to see a pattern in side-suits. The value of honors goes down in side suits for the most part. Especially queens and jacks with higher honors. That's not so surprising - in suit contracts, queens and jacks take fewer tricks, replaced by ruffs.

```Length 4
Avg   3 Fit   4 Fit   5 Fit   6 Fit
AKQJ  -0.314  -0.221  -0.478     N/A     N/A
AKQx  -0.305  -0.213  -0.454  -0.524     N/A
KQJx  -0.233  -0.199  -0.267  -0.387     N/A
AKJx  -0.220  -0.149  -0.336  -0.405     N/A
AQJx  -0.176  -0.116  -0.252  -0.405     N/A
AKxx  -0.152  -0.085  -0.257  -0.343  -0.418
KQxx  -0.151  -0.117  -0.201  -0.245  -0.306
KJxx  -0.116  -0.093  -0.153  -0.185  -0.198
AQxx  -0.110  -0.064  -0.173  -0.277  -0.344
AJxx  -0.054  -0.018  -0.110  -0.165  -0.202
QJxx  -0.040  -0.046  -0.029  -0.022  +0.032
Kxxx  -0.029  -0.019  -0.042  -0.056  -0.060
Qxxx  +0.016  +0.005  +0.031  +0.044  +0.092
Axxx  +0.044  +0.064  +0.016  -0.028  -0.105
Jxxx  +0.055  +0.024  +0.098  +0.158  +0.167
xxxx  +0.127  +0.084  +0.191  +0.258  +0.322

Length 5
Avg   3 Fit   4 Fit   5 Fit   6 Fit
AKQJx  -0.362  -0.285  -0.474     N/A     N/A
AKQxx  -0.289  -0.202  -0.476  -0.626     N/A
KQJxx  -0.222  -0.196  -0.281  -0.302     N/A
AKJxx  -0.219  -0.152  -0.364  -0.462     N/A
AQJxx  -0.135  -0.081  -0.239  -0.290     N/A
KQxxx  -0.133  -0.111  -0.175  -0.228     N/A
AKxxx  -0.120  -0.076  -0.208  -0.306     N/A
AQxxx  -0.068  -0.031  -0.148  -0.229     N/A
KJxxx  -0.064  -0.055  -0.087  -0.103     N/A
QJxxx  -0.027  -0.042  +0.007  +0.006     N/A
AJxxx  -0.016  +0.000  -0.052  -0.086     N/A
Kxxxx  +0.014  +0.010  +0.021  +0.029  -0.026
Qxxxx  +0.041  +0.024  +0.081  +0.114  +0.197
Axxxx  +0.094  +0.099  +0.087  +0.054     N/A
Jxxxx  +0.094  +0.053  +0.174  +0.277  +0.376
xxxxx  +0.183  +0.137  +0.273  +0.400  +0.440

Length 6
Avg   3 Fit   4 Fit   5 Fit   6 Fit
AKQJxx  -0.349  -0.263  -0.582     N/A     N/A
AKQxxx  -0.257  -0.191  -0.449     N/A     N/A
KQJxxx  -0.227  -0.218  -0.257  -0.370     N/A
AKJxxx  -0.169  -0.113  -0.336     N/A     N/A
KQxxxx  -0.108  -0.095  -0.149  -0.222     N/A
AQJxxx  -0.056  -0.017  -0.171  -0.318     N/A
QJxxxx  -0.049  -0.078  +0.071  +0.198     N/A
KJxxxx  -0.048  -0.058  -0.037  -0.045     N/A
AKxxxx  -0.048  -0.014  -0.145  -0.292     N/A
AQxxxx  +0.013  +0.038  -0.068  -0.107     N/A
AJxxxx  +0.050  +0.062  +0.029  -0.056     N/A
Qxxxxx  +0.055  +0.023  +0.159  +0.266     N/A
Kxxxxx  +0.081  +0.058  +0.170  +0.141     N/A
Jxxxxx  +0.122  +0.086  +0.217  +0.467     N/A
Axxxxx  +0.187  +0.182  +0.202  +0.216     N/A
xxxxxx  +0.230  +0.189  +0.330  +0.548     N/A

```