[jogs]

simulation needed

Can anyone help? TIA

Conditions. Both sides hold 20 HCP.
NS has 5-4 spades. EW has 9 hearts.
Restrict patterns for NS to
5233 // 4243 and
5233 // 4234

100 iterations.
List tricks made by NS with spades as trumps.
Need list of distribution. I will calculate the variance.
12 -
11 -
10 -
9 -
8 -
7 -
6 -
5 -
4 -

thanks, jogs

[inquiry]

I did 200 simulations and then double dummy on them from the north seat (hand with 5 spades) and south seat

North
12 = 1
11 = 4
10 = 13
9 = 53
8 = 83
7 = 39
6 = 7

South
12 = 1
11 = 3
10 = 13
9 = 53
8 = 80
7 = 43
6 = 7

[jogs]

inquiry, on 2013-July-25, 20:23, said:

I did 200 simulations and then double dummy on them from the north seat (hand with 5 spades) and south seat

North
12 = 1
11 = 4
10 = 13
9 = 53
8 = 83
7 = 39
6 = 7

Thanks, inquiry.

average tricks = 8.000
standard deviation = 1.794

Quote

South
12 = 1
11 = 3
10 = 13
9 = 53
8 = 80
7 = 43
6 = 7

ave trks = 7.965
std dev. = 1.787

Was surprised by the high std dev.
Notice that 9 trumps produced only 8 tricks.
8 tricks was what I found from my small sample.
Lawrence/Wirgren was right. Flat patterns
produce fewer tricks.
This blind bid up to the level of your
trumps is wrong. Bergen raises aren't
protected by any physical law.

Should add that there is a minor bias favoring
the defense in double dummy. In live play
declarer may do 1/4 of a trick better.

[inquiry]

I think I miss-understood the contraints you wanted... The south hand was only restricted to 4=2 in the majors so could have five or six card minors.... so I reran it where north has to 5=2=3=3 and south can be 4=2=4=3 or 4=2=3=4. Those number are given below. Sorry for the extra work this puts on you

North
12 = 0
11 = 0
10 = 6
9 = 27
8 = 77
7 = 72
6 = 16
5 = 2

South
12 = 0
11 = 0
10 = 6
9 = 28
8 = 75
7 = 74
6 = 14
5 = 3

[jogs]

inquiry, on 2013-July-25, 21:39, said:

I think I miss-understood the contraints you wanted... The south hand was only restricted to 4=2 in the majors so could have five or six card minors.... so I reran it where north has to 5=2=3=3 and south can be 4=2=4=3 or 4=2=3=4. Those number are given below. Sorry for the extra work this puts on you

Thanks, no problem. Have app in excel to solve variance.
Averaged only 7.15 tricks. This is much lower than I
expected. The bias for the defense in double dummy must
be huge. I was expecting 8 to 8.25 tricks.

Quote

North
12 = 0
11 = 0
10 = 6
9 = 27
8 = 77
7 = 72
6 = 16
5 = 2

ave trks = 7.115
std dev. = 2.365

Quote

South
12 = 0
11 = 0
10 = 6
9 = 28
8 = 75
7 = 74
6 = 14
5 = 3

ave trks = 7.150
std dev. = 2.312

[inquiry]

I am not sure how you did your averages and standard deviation, but there is no way the newest set of data can have double the stnd dev of the first sample that won from 6 to 12 tricks. I also doubt that your averages are right. Just looking at the numbers suggest the average would be above 7.5. Why? There are more 10 tricks than five tricks, there are more 9 tricks than 6 tricks and there are more 8 tricks than 7 tricks. There is no way for the average to be something like the 7.15 tricks. I would think it would be 7.6 or 7.7 range, but am too lazy to type in all the 10's, and 9's. and 8's and run the stats myself. Also the Stnd dev looks like it would be in the 0.8 to 0.9 range... maybe up to 1.0 but no where near two.

[gwnn]

I get 7.645 with a std dev 0.961 for the last one.

[inquiry]

jogs, on 2013-July-25, 20:54, said:

inquiry, on 2013-July-25, 20:23, said:

I did 200 simulations and then double dummy on them from the north seat (hand with 5 spades) and south seat

North
12 = 1
11 = 4
10 = 13
9 = 53
8 = 83
7 = 39
6 = 7

Thanks, inquiry.

average tricks = 8.000
standard deviation = 1.794

Quote

South
12 = 1
11 = 3
10 = 13
9 = 53
8 = 80
7 = 43
6 = 7

ave trks = 7.965
std dev. = 1.787

Was surprised by the high std dev.
Notice that 9 trumps produced only 8 tricks.
8 tricks was what I found from my small sample.
Lawrence/Wirgren was right. Flat patterns
produce fewer tricks.
This blind bid up to the level of your
trumps is wrong. Bergen raises aren't
protected by any physical law.

Should add that there is a minor bias favoring
the defense in double dummy. In live play
declarer may do 1/4 of a trick better.

Now that I think about it, you have to be wrong here on several fronts. First, you say the first group averages 8.000 (quite precise). However, there are 46 numbers smaller than 8.00 in the test, 39 of them one trick less, 7 of them two tricks less. There are 70 numbers higher (53 one trick higher, 13 two trick higher, and others higher still). There is no way on god's green earth this averages 8.000. If you throw out the 39 of the 53 one trick higher and 7 of the one two tricks higher, you can readily (those average together to get 8), you will see why the entire population can not average 8.000.

The same holds true for when South was declarer. That has to average more than 8.0.

As far as proving or disproving LOTT, this as presented says nothing. The law of total tricks states that the total tricks equals the sum of your trump fit plus the sum of opponents. So the total tricks here would be (according to the law) 9 + 9 = 18. All this suggest is that with your two balanced hands and unrestricted opponents hands, there will be a total of 18 tricks. Since your average is just better than 8.0, their should be just less than 10. Until and unless you simulate the opponents tricks, this doesn't tell you nearly as much as you are claiming. However, no one doubts with shape you will win more tricks than without shape.

[barmar]

Detailed discussions of the LOTT describe a number of adjustments that should be made to get better accuracy. Minor honors in the opponent's suit reduce the total tricks, more distributional hands increase them.

Do you think you're the first one to attempt to verify the LOTT with a statistical analysis like this? Wasn't the original paper that described it based on statistics?

[jogs]

gwnn, on 2013-July-26, 08:24, said:

I get 7.645 with a std dev 0.961 for the last one.

Sample size = 200
total tricks = 1430
ave tricks = 7.15

[gwnn]

jogs, do you have inquiry on your ignore list? Please read his post.

[jogs]

inquiry, on 2013-July-26, 08:43, said:

Now that I think about it, you have to be wrong here on several fronts. First, you say the first group averages 8.000 (quite precise). However, there are 46 numbers smaller than 8.00 in the test, 39 of them one trick less, 7 of them two tricks less. There are 70 numbers higher (53 one trick higher, 13 two trick higher, and others higher still). There is no way on god's green earth this averages 8.000. If you throw out the 39 of the 53 one trick higher and 7 of the one two tricks higher, you can readily (those average together to get 8), you will see why the entire population can not average 8.000.

The same holds true for when South was declarer. That has to average more than 8.0.

As far as proving or disproving LOTT, this as presented says nothing. The law of total tricks states that the total tricks equals the sum of your trump fit plus the sum of opponents. So the total tricks here would be (according to the law) 9 + 9 = 18. All this suggest is that with your two balanced hands and unrestricted opponents hands, there will be a total of 18 tricks. Since your average is just better than 8.0, their should be just less than 10. Until and unless you simulate the opponents tricks, this doesn't tell you nearly as much as you are claiming. However, no one doubts with shape you will win more tricks than without shape.

You better add them up. 1600 total tricks. It is
the nature of variance. The outliers have a greater
effect on the variance than those lumped in the middle.

The LoTT statement is too powerful. Total tricks equal
total trumps less than 40% of the time.
Cohen backed off and later stated the average tricks
equal total trumps. He needed to weaken the statement
more. The expected number of tricks equals total
trumps.
Now we 'know' when tricks is less than trumps. And
when tricks is more than trumps. Flat patterns produced
fewer tricks. Skewed patterns, those with singletons,
voids, and long second suits, produce more tricks than
trumps.

[jogs]

gwnn, on 2013-July-26, 08:24, said:

I get 7.645 with a std dev 0.961 for the last one.

I rechecked everything and now have
your numbers.

Sorry.

[jogs]

Quote

North
12 = 0
11 = 0
10 = 6
9 = 27
8 = 77
7 = 72
6 = 16
5 = 2

Recalculated these.

ave trks = 7.645
std dev. = 0.948

[Cyberyeti]

jogs, on 2013-July-26, 10:56, said:

You better add them up. 1600 total tricks. It is
the nature of variance. The outliers have a greater
effect on the variance than those lumped in the middle.

It was 1600 before adding the 6x7 when I added it up.

[johnu]

If you are interested in LOTT, Steve Bloom had a thought provoking series of articles on Bridgewinners.com Theory of Total Tricks

[inquiry]

jogs, on 2013-July-26, 10:56, said:

You better add them up. 1600 total tricks. It is the nature of variance. The outliers have a greater effect on the variance than those lumped in the middle.

The LoTT statement is too powerful. Total tricks equal total trumps less than 40% of the time. Cohen backed off and later stated the average tricks equal total trumps. He needed to weaken the statement more. The expected number of tricks equals total trumps.

Now we 'know' when tricks is less than trumps. And when tricks is more than trumps. Flat patterns produced fewer tricks. Skewed patterns, those with singletons, voids, and long second suits, produce more tricks than trumps.

Maybe you should look again. The total tricks is not 1600. Nor in this case was total trick less than calculate 40% of the time. In fact, here the total tricks was less than 16 only 4 times (2%). Quite a difference. However, the deck was stacked in EW favor by your conditions. First, Hearts always split 2-2 for them. That would save a trick anytime 3-1 or 4-0 would cost a trick Ior more) sight unseen. Second, their 7 card minor always ran into a 3-3 split NS, while NS's 4-3 minor fit frequently runs into 4-2 or worse split (under the tested conditions). I think this "even" heart and "even" 3-3 minor split for EAST west adds a trick or so to the trick total.

Below are the 200 deal stats, with tricks won by north in spades or West in hearts as well as the total tricks on the hands. As noted, only four of the deals took LESS Than 16 total tricks (See below, a llst of tricks won on all 200 deals as played from north or west). So much for 40% being lower (at least in this case).
Total tricks on all 200 hands....
15 = 4
16 = 58
17 = 89
18 = 41
19 = 8

The only thing this shows is the balanced tricks for NS and their 9 spades subtracted from their 9 card fit numbers but seemed to add to the tricks EW could win with their 9 card fit. There was more than a trick difference between the tricks NS could win on their 9 card fit compared to tricks EW could win (also EW were allowed to have one hand with six or seven hearts... even more perhaps as random dealt for them).

Deal [sp] [he] total
1      8      8      16
2      7      10      17
3      6      9      15
4      8      9      17
5      8      9      17
6      7      9      16
7      7      11      18
8      6      13      19
9      7      9      16
10      8      8      16
11      7      10      17
12      8      10      18
13      7      11      18
14      8      9      17
15      6      10      16
16      8      10      18
17      8      10      18
18      9      8      17
19      8      9      17
20      6      11      17
21      8      9      17
22      6      11      17
23      6      11      17
24      7      11      18
25      7      10      17
26      6      11      17
27      8      10      18
28      9      9      18
29      8      9      17
30      10      8      18
31      8      9      17
32      7      10      17
33      8      9      17
34      8      8      16
35      9      9      18
36      7      9      16
37      8      9      17
38      6      10      16
39      9      8      17
40      8      8      16
41      8      10      18
42      8      9      17
43      6      11      17
44      8      9      17
45      8      9      17
46      7      9      16
47      8      9      17
48      7      9      16
49      9      8      17
50      6      10      16
51      7      9      16
52      8      10      18
53      8      9      17
54      8      10      18
55      8      11      19
56      7      9      16
57      9      8      17
58      8      9      17
59      7      9      16
60      8      10      18
61      8      10      18
62      8      8      16
63      7      9      16
64      7      10      17
65      7      11      18
66      9      8      17
67      7      10      17
68      6      11      17
69      7      9      16
70      10      6      16
71      7      9      16
72      8      9      17
73      7      10      17
74      7      9      16
75      7      9      16
76      7      10      17
77      8      11      19
78      8      9      17
79      9      8      17
80      7      9      16
81      8      11      19
82      7      10      17
83      7      10      17
84      8      9      17
85      7      10      17
86      8      10      18
87      7      10      17
88      7      9      16
89      8      8      16
90      9      9      18
91      6      10      16
92      7      10      17
93      9      8      17
94      7      10      17
95      8      10      18
96      7      10      17
97      8      8      16
98      9      9      18
99      8      9      17
100      7      11      18
101      7      10      17
102      6      10      16
103      8      9      17
104      8      8      16
105      8      10      18
106      7      9      16
107      9      9      18
108      7      10      17
109      7      10      17
110      8      8      16
111      9      9      18
112      5      11      16
113      7      10      17
114      8      8      16
115      8      9      17
116      7      10      17
117      7      10      17
118      8      9      17
119      6      11      17
120      8      10      18
121      8      11      19
122      9      9      18
123      9      8      17
124      7      11      18
125      9      8      17
126      8      7      15
127      8      9      17
128      8      9      17
129      8      10      18
130      8      8      16
131      7      9      16
132      7      10      17
133      7      10      17
134      5      11      16
135      9      9      18
136      8      7      15
137      9      7      16
138      7      9      16
139      10      7      17
140      9      7      16
141      7      10      17
142      9      9      18
143      7      9      16
144      7      11      18
145      8      9      17
146      7      9      16
147      8      9      17
148      7      10      17
149      7      9      16
150      7      11      18
151      7      9      16
152      7      9      16
153      9      10      19
154      8      9      17
155      9      9      18
156      8      9      17
157      8      9      17
158      8      9      17
159      9      9      18
160      8      11      19
161      7      10      17
162      8      10      18
163      10      8      18
164      9      10      19
165      8      9      17
166      7      10      17
167      7      9      16
168      7      9      16
169      7      10      17
170      8      10      18
171      9      8      17
172      7      9      16
173      8      8      16
174      7      10      17
175      8      8      16
176      7      9      16
177      10      7      17
178      7      9      16
179      7      10      17
180      7      10      17
181      10      8      18
182      9      9      18
183      9      8      17
184      7      9      16
185      7      9      16
186      6      11      17
187      8      10      18
188      8      10      18
189      7      10      17
190      8      9      17
191      8      9      17
192      6      10      16
193      7      8      15
194      8      9      17
195      8      8      16
196      7      9      16
197      7      10      17
198      8      8      16
199      8      8      16
200      8      9      17

[jogs]

inquiry, on 2013-July-26, 12:39, said:

Maybe you should look again. The total tricks is not 1600.

Okay, I copied and pasted the app and a line or two disappeared.
Rechecked it after gwnn disagreed with my numbers.

Now it is 1642 total tricks.
8.21 ave tricks.
1.037 std dev.

[jogs]

johnu, on 2013-July-26, 12:35, said:

If you are interested in LOTT, Steve Bloom had a thought provoking series of articles on Bridgewinners.com Theory of Total Tricks

Read his article. Neither Cohen or Bloom posted expected
value or variance for any of their data.

[jogs]

barmar, on 2013-July-26, 08:56, said:

Detailed discussions of the LOTT describe a number of adjustments that should be made to get better accuracy. Minor honors in the opponent's suit reduce the total tricks, more distributional hands increase them.

Do you think you're the first one to attempt to verify the LOTT with a statistical analysis like this? Wasn't the original paper that described it based on statistics?

On Chapter 9 p216 Cohen listed many adjustment factors.
He provided no statistical analysis.
It is really difficult to isolate the effects of
any particular parameter.