[Cascade]

bid_em_up, on Mar 20 2008, 03:37 AM, said:

Cascade, on Mar 18 2008, 07:14 PM, said:

This hand predealt no other constraints.

Spades made:

    7          1
    8         17
    9         71
   10        188
   11        390
   12        269
   13         64

Hearts made :

    4          7
    5         21
    6         57
    7        106
    8        133
    9        118
   10        113
   11        230
   12        172
   13         43

Hearts made more than spades  158/1000

Draw your own conclusion but I think it worth investigating slam and exploring for a heart fit.

If I am reading this table correctly, the number on the left is the number of tricks taken, and the number on the right is the number of times. Right?

Please explain your conclusion that it is worth "exploring" a heart fit, or that Hearts made more than spades 158/1000. Because I sure dont see the same thing.

Assuming my math is right, spades took 10+ tricks a total of 911 times out of 1000 or 91.1% of the time. Hearts tooks 10+ tricks a total of 558 times out of 1000 or 55.8%. (For 9+ tricks the numbers are 98.2% vs. 67.6%)

Hmmm, lets see. 91.1% vs. 55.8%, this is a no-brainer for spades, imo.

Yep you are reading the numbers wrong.

Well most of what you are reading is correct you are just missing one thing.

The 158/1000 is another statistic. That is the number of times (hidden in the rest of the data) that hearts was a better contract than spades.

I feel that 15% is a big enough minority option to at least make some exploration for the alternative contract.

[jdonn]

What are the statistics for hearts and spades specifically when partner has 4+ hearts?

[Cascade]

Rob F, on Mar 20 2008, 12:28 AM, said:

CSGibson, on Mar 19 2008, 01:34 AM, said:

I think I'm opening this 2♣.

I was going to point this out too. Game in hand? Check. Unwilling to open game directly? Check. Must leave 2♣.

Notice that something like 90%+ of the spade simulations are making game or better. This is also without exploring for hearts when they might offer a better strain either.

Actually I did a further simulation and there was a smaller but still around 80% chance of making 4♠ when partner had a hand too weak to respond to 1♠.

Having said that personally I am experimenting with opening at the one-level on stronger and stronger hands. And so far this approach seems to work ok.

Sometimes when partner passes or would have passed the opponents rescue you.

[Cascade]

helene_t, on Mar 20 2008, 03:54 AM, said:

Funny to see that the number of hearts tricks is bimodal. Wonder if this is reproducible.

Not that even if some 15% of deals take more tricks in hearts than is spades, the number of deals on which it would be correct to bid a heart contract may be smaller (or larger for that matter). For example it could be that if p is 1-4, the expected number of spades tricks is always larger than the expected number of heart tricks, but sometimes hearts split more friendly.

I will try and reproduce it. I am not at all surprised though.

If partner has not many hearts we don't rate to make many tricks at all. Whereas if partner has lots of hearts we rate to make lots of tricks.

[TimG]

whereagles, on Mar 19 2008, 04:48 AM, said:

Cascade, on Mar 18 2008, 09:15 PM, said:

Jlall, on Mar 19 2008, 09:56 AM, said:

3H

Isn't there some danger that partner with 1=3 in the majors and one or other minor unstopped will raise to 4♥?

NO NO NO. Statistically, he won't have that hand. And even if he does, he should still bid 3NT because opener, who has a strong hand, probably has a stop anyway.

I believe the correct call with 1-3 in the majors and a hand unsuitable to bid 3N is 3S.

[Cascade]

TimG, on Mar 20 2008, 11:26 AM, said:

whereagles, on Mar 19 2008, 04:48 AM, said:

Cascade, on Mar 18 2008, 09:15 PM, said:

Jlall, on Mar 19 2008, 09:56 AM, said:

3H

Isn't there some danger that partner with 1=3 in the majors and one or other minor unstopped will raise to 4♥?

NO NO NO. Statistically, he won't have that hand. And even if he does, he should still bid 3NT because opener, who has a strong hand, probably has a stop anyway.

I believe the correct call with 1-3 in the majors and a hand unsuitable to bid 3N is 3S.

Yes I like false preference on this sort of auction too. But I am not sure that is standard.

[Cascade]

nick_s, on Mar 20 2008, 03:58 AM, said:

bid_em_up, on Mar 19 2008, 09:37 AM, said:

Cascade, on Mar 18 2008, 07:14 PM, said:

Cool analysis snipped

If I am reading this table correctly, the number on the left is the number of tricks taken, and the number on the right is the number of times. Right?

Please explain your conclusion that it is worth "exploring" a heart fit, or that Hearts made more than spades 158/1000. Because I sure dont see the same thing.

Assuming my math is right, spades took 10+ tricks a total of 911 times out of 1000 or 91.1% of the time. Hearts tooks 10+ tricks a total of 558 times out of 1000 or 55.8%. (For 9+ tricks the numbers are 98.2% vs. 67.6%)

Hmmm, lets see. 91.1% vs. 55.8%, this is a no-brainer for spades, imo.

Following on: I guess what I'd really like to know is when hearts was a better contract than spades, when the same, and when worse etc.

I'm asking a lot, I know.

I hope this makes some sense:

Spade Length (rows - horizontal) versus Heart Length (columns - vertical)
Spades made more tricks than hearts.

              0      1      2      3      4      5      6    Sum
   0          0      7     22     13      0      0      0     42
   1          6     19     85     66      8      1      0    185
   2         13     54    147    139     28      3      1    385
   3          5     56     93     87     26      2      0    269
   4          6     22     34     24      9      2      1     98
   5          1      3      7      5      3      0      0     19
   6          0      0      2      0      0      0      0      2
Sum          31    161    390    334     74      8      2   1000

Spade Length (rows - horizontal) versus Heart Length (columns - vertical)
Spades made the same number of tricks as hearts.

        1      2      3      4      5      6      7    Sum
   0    0     10     21      9      1      0      0     41
   1    2     28     76     73     22      7      1    209
   2    1     19    140    210     74     12      1    457
   3    0      8     93    108     32      3      1    245
   4    0      1     21     20      5      0      0     47
   5    0      0      1      0      0      0      0      1
Sum     3     66    352    420    134     22      3   1000

Spade Length (rows - horizontal) versus Heart Length (columns - vertical)
Spades made fewer tricks than hearts.

          2      3      4      5      6      7      8      Sum
   0      2     46    121     70     18      4      0      261
   1      1    123    241    179     49      6      1      600
   2      0      1     60     51     20      1      0      133
   3      0      0      1      2      2      0      0        5
   4      0      0      0      0      1      0      0        1
Sum       3    170    423    302     90     11      1     1000

[Cascade]

jdonn, on Mar 20 2008, 10:12 AM, said:

What are the statistics for hearts and spades specifically when partner has 4+ hearts?

Partner has exactly four hearts
===============================

Spade Tricks

    7          3
    8         19
    9         91
   10        197
   11        382
   12        267
   13         41

Heart Tricks

    6          4
    7         17
    8         49
    9         88
   10         90
   11        362
   12        319
   13         71

   More heart tricks than spade tricks 276/1000

Partner has five or more hearts
===============================

Spade Tricks

    7          3
    8         19
    9         91
   10        197
   11        382
   12        267
   13         41

Heart Tricks

    6          4
    7         17
    8         49
    9         88
   10         90
   11        362
   12        319
   13         71

   More heart tricks than spade tricks 505/1000


Partner has four or more hearts
===============================

 Spade Tricks

    7          2
    8         16
    9         92
   10        234
   11        390
   12        227
   13         39


 Heart Tricks

    6          2
    7         12
    8         37
    9         64
   10         94
   11        388
   12        336
   13         67

   More heart tricks than spade tricks 364/1000

[Cascade]

Cascade, on Mar 20 2008, 10:35 AM, said:

helene_t, on Mar 20 2008, 03:54 AM, said:

Funny to see that the number of hearts tricks is bimodal. Wonder if this is reproducible.

Not that even if some 15% of deals take more tricks in hearts than is spades, the number of deals on which it would be correct to bid a heart contract may be smaller (or larger for that matter). For example it could be that if p is 1-4, the expected number of spades tricks is always larger than the expected number of heart tricks, but sometimes hearts split more friendly.

I will try and reproduce it. I am not at all surprised though.

If partner has not many hearts we don't rate to make many tricks at all. Whereas if partner has lots of hearts we rate to make lots of tricks.

Ten smaller samples of 100 hands:

       Total
    0     0       0   0   0   0   0   0   0   0   0   0
    1     0       0   0   0   0   0   0   0   0   0   0
    2     0       0   0   0   0   0   0   0   0   0   0
    3     1       1   0   0   0   0   0   0   0   0   0
    4     7       0   0   0   1   0   1   2   0   3   0
    5    34       2   3   2   0   4   3   6   6   3   5
    6    64       8   9   8   7   4   9   4   5   2   8
    7    98       5  11  12   9   8   7  13  15  10   8
    8   104      11  10  13   4  18   7   6   9  17   9
    9   133      10  14   9  18  17  12  13   9  14  17
   10   126      17   9  15  15   9  13  12  14  11  11
   11   226      22  22  24  25  19  22  21  23  24  24
   12   157      18  17  12  16  17  22  17  15  12  11
   13    50       6   5   5   5   4   4   6   4   4   7

A bigger sample. I haven't done the numbers but it might be too close to call as to whether it really is bimodal.

   0          0
   1          0
   2          0
   3          7
   4         76
   5        285
   6        573
   7        915
   8       1233
   9       1250
  10       1169
  11       2312
  12       1781
  13        399

[awm]

Hmm I'm not sure what Cascade's numbers are suggesting. His first post artificially equalizes the number of hands where each contract is better, and the second doesn't seem to count situations where hearts and spades are equal.

I think the relevant question is, suppose that your choices are:

(1) Insist on spades by rebidding 4♠ or something like this. Now you always play in spades.
(2) Introduce hearts, accepting that you will now always play in hearts if partner has 4+♥ and occasionally play in hearts when partner is 1-3 or 0-3 in the majors.

The question is which approach is better. So what we need to know is:

(1) Given that partner has 4+♥, what is the probability that hearts are better than spades relative to the probability that spades are better than hearts? Obviously there will be a substantial amount of the time when either major is equally good -- this doesn't really matter one way or the other.

(2) Given that partner has 3♥ and 0-1♠, what is the probability that hearts are better than spades relative to the probability that spades are better than hearts? What is the frequency of partner having this shape? Can we quantify the frequency of a 4♥ raise with such a hand versus a 3NT bid (which we can correct to 4♠)?

[Cascade]

awm, on Mar 20 2008, 12:29 PM, said:

Hmm I'm not sure what Cascade's numbers are suggesting. His first post artificially equalizes the number of hands where each contract is better, and the second doesn't seem to count situations where hearts and spades are equal.

I am not sure what you mean.

My first simulation made no assumptions other than the we held the hand in the opening post and I calculated double dummy tricks opposite 1000 random hands.

One subsequent series of simulations tried to give information about heart and spade length for the three scenarios:

• More tricks were available in spades then hearts
  
• spades and hearts produced the same number of tricks
  
• more tricks were available in hearts than spades

[awm]

Okay here's what I mean.

Given partner has 4+♥, what are the probabilities that hearts are better, spades are better, or they are equal?

Cascade's first post just generates random hands. But obviously for some (many?) of these random hands we will always end in 4♠. So we need to condition on partner actually raising a heart rebid, which is pretty close to conditioning on partner has 4+♥.

Cascade's second post comes closer to doing this, but he figures out of the hands where 4♥ is better than 4♠, what percentage include various numbers of hearts and spades in partner's hand?. This again is not what we want -- presumably most of the time that hearts are better partner has four or more hearts; the question is how often are hearts better given partner has four or more hearts versus the number of times spades are still better despite partner having four or more hearts.

Cascade's third post actually gives the percentage of times hearts are better given partner has four or more hearts as 276/1000 for exactly four hearts and 505/1000 for five-plus hearts. However, the question is, of the thousand hands where partner has exactly four hearts, how often are the two contracts equal? If hearts are better 276/1000 times and they are the same the other 724/1000 times then introducing hearts is obviously a big win. If hearts are better 276/1000 times and spades are better the other 724/1000 times then introducing the hearts will lead to lots of inferior contracts. Of course the reality is somewhere between the extremes, but we need to know where it is.

[Cascade]

awm, on Mar 20 2008, 12:53 PM, said:

Okay here's what I mean.

Given partner has 4+♥, what are the probabilities that hearts are better, spades are better, or they are equal?

Cascade's first post just generates random hands. But obviously for some (many?) of these random hands we will always end in 4♠. So we need to condition on partner actually raising a heart rebid, which is pretty close to conditioning on partner has 4+♥.

Cascade's second post comes closer to doing this, but he figures out of the hands where 4♥ is better than 4♠, what percentage include various numbers of hearts and spades in partner's hand?. This again is not what we want -- presumably most of the time that hearts are better partner has four or more hearts; the question is how often are hearts better given partner has four or more hearts versus the number of times spades are still better despite partner having four or more hearts.

Cascade's third post actually gives the percentage of times hearts are better given partner has four or more hearts as 276/1000 for exactly four hearts and 505/1000 for five-plus hearts. However, the question is, of the thousand hands where partner has exactly four hearts, how often are the two contracts equal? If hearts are better 276/1000 times and they are the same the other 724/1000 times then introducing hearts is obviously a big win. If hearts are better 276/1000 times and spades are better the other 724/1000 times then introducing the hearts will lead to lots of inferior contracts. Of course the reality is somewhere between the extremes, but we need to know where it is.

Responder has :

• Four or more hearts
  
• Six or more points (perhaps this should be relaxed a little)

Hearts made more tricks 364/1000

Spades made more tricks 95/1000

[hrothgar]

Out of curiousity, what happened at the table on this one?