Partner's view is that a fourth in hand weak two should be within a trick of making, i.e. 6.5 to 7.5 playing tricks. I gave him4
A K Q 6 5 4
J 10 3
7 6 3
and his reaction was "Pass in a nanosecond. What else?"
I contend that this hand is worth 2after three passes. My reasoning: on the evidence so far, my expectation would be that we have 8/9 hearts between us, and oppo have 8/9 spades. So by LTT this is likely to be a 17-trick hand. By virtue of the concentration of hearts in my hand, and the absence of a 2
Thanks for the question! This shouldn't be too difficult to do. We'll deal out three hands which wouldn't open the bidding and fix ours. For simplicity we'll assume that the opposition's third seat style is the same as their first seat style. Let's say they open all 12-counts and all 7-loser hands. As explained in this post, it doesn't matter much that this criteria will exclude some genuine hands and let through some false ones — the overwhelming majority will be miles from the borderline.
In order to gather this data I actually wrote some new functions for Deal which makes it all a lot simpler. This lets me produce lovely big tables like this puppy (from a sample size of 10,000 deals):
E/W Spade Fit N/S Heart Fit DD Tricks
NSH <8s =8s =9s >9s <8h =8h =9h >9h 2H+ 2S+ tot
7 478 371 172 1021 595 430 1021
8 1597 2102 1313 105 5117 4221 3147 5117
9 896 1299 937 280 3412 3205 2229 3412
10 48 171 172 55 446 438 396 446
11 3 1 4 4 4 4
EWS <8s =8s =9s >9s <8h =8h =9h >9h 2H+ 2S+ tot
5 14 1 10 3 8 14
6 533 136 281 115 1 392 3 533
7 2472 341 1306 778 47 1983 441 2472
8 3943 371 2102 1299 171 3313 2908 3943
9 2597 172 1313 937 175 2349 2426 2597
10 426 104 271 51 404 413 426
11 15 1 9 5 14 15 15
Htks <8s =8s =9s >9s <8h =8h =9h >9h 2H+ 2S+ tot
5 12 6 15 3 6 18
6 151 86 33 2 110 154 8 163 272
7 473 538 215 21 301 739 199 8 856 1247
8 1193 1341 811 102 378 2004 958 107 3447 2220 3447
9 872 1422 1032 216 185 1721 1430 206 3542 2217 3542
10 291 486 422 81 32 432 703 113 1280 655 1280
11 26 64 74 16 58 106 16 180 78 180
12 1 10 3 6 8 14 11 14
Stks <8s =8s =9s >9s <8h =8h =9h >9h 2H+ 2S+ tot
1 17 14 3 16 17
2 14 8 6 7 14
3 7 2 1 2 5 1 8 9
4 59 13 15 30 1 49 59
5 319 4 79 131 105 8 265 323
6 976 107 4 2 187 555 331 16 938 1089
7 1183 922 167 11 311 1245 703 24 1999 2283
8 408 1857 957 111 279 1862 1082 110 2891 3333 3333
9 35 921 1089 201 133 1097 828 188 1811 2246 2246
10 1 124 340 100 18 173 283 91 432 565 565
11 6 38 14 15 33 10 43 58 58
12 2 2 3 1 4 4 4
<8s =8s =9s >9s <8h =8h =9h >9h 2H+ 2S+ tot
tot 3019 3943 2597 441 1021 5117 3412 450 8463 6206 10k
The labels along the top should be self-explanatory. <8s means that East/West have less than 8 spades between them. 2H+ means that we can make 8 or more tricks in hearts, double-dummy.
Along the left side, NSH means North/South combined hearts; EWS means East/West combined spades; Htks means the number of tricks North/South can make in hearts and Stks is the number East/West can make in spades.
I started to do some analysis of when hearts isn't our best fit or when spades isn't the oppo's best fit but these are actually very unlikely and so I didn't pursue the matter. The fact is that we have a 10 count and nobody has opened yet. Therefore, the points are distributed fairly evenly between the other three hands. And since nobody has opened at the one level or with a preempt, it must mean that they don't have much distribution.
The good thing about nice big tables like this is I can just dump it to the screen and let you all do the conclusions! But I'll throw some points at you for free.
- (highlighted blue) 2 will make about 85% of the time. Can you really afford to pass this opportunity up?
- (red) Of the 6206 times where 2 makes, 3 will make 2961 times.
- (green) You'll make game in hearts a full 15% of the time!
- (purple) There's no guarantee that oppo have a spade fit at all. Even if they manage to find (and this is unlikely) every 5-3 and every 4-4 fit then it only comes to about 70% of cases. And well over half of these are 8 card fits where the suit breaks 4-1.
Update: Another Table
Sorry, I forgot to run stats on when both sides make exactly 9 tricks — a good time to pass this out. Here is the full double-dummy cross table (using 10,000 new deals).
Htks 2H- 2S- 2H= 2S= 3H= 3S= 4H+ 4S+ tot
5 26 10 8 5 3 26
6 230 95 54 46 35 230
7 1348 450 385 355 158 1348
8 1138 3350 1012 917 283 3350
9 1361 1290 3535 748 136 3535
10 614 451 202 1303 36 1303
11 117 58 15 192 2 192
12 13 3 16 16
Stks 2H- 2S- 2H= 2S= 3H= 3S= 4H+ 4S+ tot
1 1 14 4 8 1 14
2 3 11 7 1 11
3 1 9 3 2 3 9
4 12 55 12 14 17 55
5 49 335 92 140 54 335
6 149 1067 316 385 217 1067
7 340 2294 704 811 439 2294
8 447 1012 3271 1290 522 3271
9 406 917 748 2291 220 2291
10 179 255 122 37 593 593
11 16 28 13 1 58 58
12 1 1 2 2
2H- 2S- 2H= 2S= 3H= 3S= 4H+ 4S+ tot
tot 1604 3785 3350 3271 3535 2291 1511 653 10k
The important bit is highlighted red. This shows that, of the 3535 times when 3
made exactly, 3 made 884 times — about a quarter of the time.
