Ask Jerry (ACBL Bulletin) Are his geeky friends correct?
#1
Posted 2009-July-02, 07:51
He says that 4=4=3=2 shape makes up 1.796% of all hands. (98.204% are not 4=4=3=2.)
He goes on to say that "if you further calculate that a one-level opening bid shows between 12 and 21 HCP (and factor out the 15-17 HCP with this shape that are opened 1NT), the probability of a four-card or longer diamond suit for a 1♦ opener increases to 99.56%."
Won't the percentage of 12-14 and 18-21 point hands that are 4=4=3=2 stay pretty close to the 1.796% of all hands that are 4=4=3=2? (My guess is that slightly more than 1.796% of 18 HCP hands are 4=4=3=2, in part because it is impossible to have 18 HCP in some extreme shapes).
#2
Posted 2009-July-02, 08:17
If the probability of being 4=4=3=2 is 1.8%, then probability of being 4=4=3=2 given that we opened 1♦ must be substantially more.
4=4=3=2 is one of the 11 balanced shapes that open 1♦. If they are all appr. equally frequent and a little less than half of our 1♦ openings are balanced, the probability of being 4=4=3=2 given that we open 1♦ is appr. 4%
#3
Posted 2009-July-02, 10:22
#4
Posted 2009-July-02, 10:38
TimG, on Jul 2 2009, 08:51 AM, said:
He says that 4=4=3=2 shape makes up 1.796% of all hands. (98.204% are not 4=4=3=2.)
He goes on to say that "if you further calculate that a one-level opening bid shows between 12 and 21 HCP (and factor out the 15-17 HCP with this shape that are opened 1NT), the probability of a four-card or longer diamond suit for a 1♦ opener increases to 99.56%."
Won't the percentage of 12-14 and 18-21 point hands that are 4=4=3=2 stay pretty close to the 1.796% of all hands that are 4=4=3=2? (My guess is that slightly more than 1.796% of 18 HCP hands are 4=4=3=2, in part because it is impossible to have 18 HCP in some extreme shapes).
If I'm understanding your post, you're questioning that apparently a disproportionately large percentage of hands are removed, when the 1.8% drops down to 0.4%?
His numbers seem plausible to me, without doing the math. If you get rid of all 0-11 point hands, all 15-17 point hands, and all 22+ point hands, I think you could lose about 75-80% of the hands (1.4% of the 1.8%).
Edit: Was only considering what he was presenting, which, as Helene points out, is a different question that he purports to answer. This all would suggest that 0.4% of hands would be 4-4-3-2 and open 1♦ , but not that a given 1♦ opener has a 0.4% change of being 4-4-3-2.
Call me Desdinova...Eternal Light
C. It's the nexus of the crisis and the origin of storms.
IV: ace 333: pot should be game, idk
e: "Maybe God remembered how cute you were as a carrot."
#5
Posted 2009-July-02, 12:46
An analogy: there are millions of animal species on the planet, and only a tiny fraction of them are dogs that bark. But if you encounter a dog, there's probably at least a 95% chance that it barks. This is a much more extreme difference than the 1♦ opening, but it demostrates how different the two ways of looking at the situation are.
#6
Posted 2009-July-02, 12:58
#7
Posted 2009-July-02, 12:58
I am assuming a Standard American bidding structure.
Having defined the question properly, one then goes on to determine the criteria for opening 1♦ on 3-card diamond suits, 4-card diamond suits, and so on up the line. After defining the criteria, one can attempt to determine how many hands (or what percentage of all hands) match the criteria, and then one can answer the question.
Without going through all of the hoops, I would guess that about 10-20% of all 1♦ openings contain a 3-card diamond suit. This is purely a guess based on my experience.
Certainly, the number of hands which qualify for a 1♦ opening (specificially a 4-4-3-2 distribution and not a 1NT opening (15-17 HCP) and not too strong to open at the one level (20+ HCP)) is very small as a percentage of all hands. But, compared to all hands that would otherwise open 1♦, the percentage is not that small.
Also, one is assuming that one would never open 1♦ on a hand with 4-3-3-3 or 3-4-3-3 distribution because of the relative honor strength of the minor suits. Many players would open 1♦, rather than 1♣ holding KQx Qxxx AKx xxx, but many other players always open 1♣ with this distribution.
#8
Posted 2009-July-02, 13:01
ArtK78, on Jul 2 2009, 01:58 PM, said:
I would have estimated something more like 3%.
#9
Posted 2009-July-02, 13:04
jdonn, on Jul 2 2009, 02:01 PM, said:
ArtK78, on Jul 2 2009, 01:58 PM, said:
I would have estimated something more like 3%.
Maybe 10-20% is an overbid, but it is certainly a lot more than 0.4%.
#10
Posted 2009-July-02, 13:05
aguahombre, on Jul 2 2009, 01:58 PM, said:
I'm just taking the flip side of the 99.56% figure in the original post (rounding down from 0.44%).
Call me Desdinova...Eternal Light
C. It's the nexus of the crisis and the origin of storms.
IV: ace 333: pot should be game, idk
e: "Maybe God remembered how cute you were as a carrot."
#11
Posted 2009-July-02, 13:05
#12
Posted 2009-July-02, 13:08
ArtK78, on Jul 2 2009, 02:04 PM, said:
jdonn, on Jul 2 2009, 02:01 PM, said:
ArtK78, on Jul 2 2009, 01:58 PM, said:
I would have estimated something more like 3%.
Maybe 10-20% is an overbid, but it is certainly a lot more than 0.4%.
The point of the previous posts is that the 0.4% figure (if it's accurate) isn't the percentage of all 1♦ openers (as Helms stated), but the percentage of all hands. (that are specifically 4=4=3=2 and open 1♦).
That is, 1.8% of the time you're dealt ANY hand, you'll be 4=4=3=2. That 1.8% breaks down as follows:
1.4%: You're either too weak to open, or you have a 1NT opener, or you have a 2♣ opener.
0.4% You have a 1♦ opener.
But if you just look at how many 1♦ openers you have, then a much higher percentage of them are 4=4=3=2 (for the reasons given by others, above).
Call me Desdinova...Eternal Light
C. It's the nexus of the crisis and the origin of storms.
IV: ace 333: pot should be game, idk
e: "Maybe God remembered how cute you were as a carrot."
#13
Posted 2009-July-02, 13:09
#14
Posted 2009-July-02, 19:01
TimG, on Jul 2 2009, 08:51 AM, said:
He says that 4=4=3=2 shape makes up 1.796% of all hands. (98.204% are not 4=4=3=2.)
He goes on to say that "if you further calculate that a one-level opening bid shows between 12 and 21 HCP (and factor out the 15-17 HCP with this shape that are opened 1NT), the probability of a four-card or longer diamond suit for a 1♦ opener increases to 99.56%."
Won't the percentage of 12-14 and 18-21 point hands that are 4=4=3=2 stay pretty close to the 1.796% of all hands that are 4=4=3=2? (My guess is that slightly more than 1.796% of 18 HCP hands are 4=4=3=2, in part because it is impossible to have 18 HCP in some extreme shapes).
Playing strong NT, 1D opener with 4-4-3-2 is more frequent than a 2C opener, in my experience. If I play weak NT [sometimes I do] the 1D opening with three is rare since much of the hands are opened 1NT and only 15-19HCP 4-4-3-2 are opened 1D.
Not going into percentages, that is not my strong suit
#15
Posted 2009-July-02, 19:02
I just ran a couple of quick sim that suggests playing a standardish strong nt 5 card major system, but with a very strict balanced nt (no 5422, no 6322) that you'll open 1♦ about 11.23% of the time in first seat. About 0.52% of hands you'll open 1♦ with a 3 card suit. But the more important thing is when you open 1♦ you'll have only 3 diamonds 4.61% of the time. This shifts your expected diamonds for a 1♦ from 4.86 (require 4+) to 4.76 (require 3+).
If instead we make 5m422 and 6m322 hands open 1nt when in range then it shifts up only slightly with us opening 1♦ 11.00% of the time with about 0.53% of hands having you'll open 1♦ with a 3 card suit but now the conditional probability of 1♦ having only 3 is up to 4.81% of the time. And the expected diamonds doesn't really change.
So really, if someone plays 1♦ promises 4+ or 4432 then almost 1 in 20 times when they open 1♦ it is 4432.
I'd, personally, rather have 4432 in the 1♣ because then I know the 1♦ is 4+ and the 2 card club suit since the clubs are always suspect.
#16
Posted 2009-July-02, 19:12
#17
Posted 2009-July-02, 19:19
I ran a simulation with some very basic conditions (44 in minors open 1D and 33 in minors open 1C; 1N = 15=17, 2N = 20-21; opening bid = 12-21; 5M332 always opened 1M, 5m332 always opened NT when in range; 54 and any 6-card suit never opened NT) and came up with 4.28% of 1D openings were 4=4=3=2.
#18
Posted 2009-July-02, 19:53
The conditional probability Pr[1D opener has only 3 diamonds GIVEN responder has 5 diamonds] will unfortunately be substantially higher than the a priori probability. So the "could be only three" situation hurts even more than these statistics would indicate.
a.k.a. Appeal Without Merit
#19
Posted 2009-July-04, 06:02
TimG, on Jul 2 2009, 08:19 PM, said:
I ran a simulation with some very basic conditions (44 in minors open 1D and 33 in minors open 1C; 1N = 15=17, 2N = 20-21; opening bid = 12-21; 5M332 always opened 1M, 5m332 always opened NT when in range; 54 and any 6-card suit never opened NT) and came up with 4.28% of 1D openings were 4=4=3=2.
I did such an analysis on 1♦ openings in a Precision context in 2004. Using a strong NT and 5-card major system my 'adjusted' calculations show that when you open 1♦ it will only be a 3-card suit 5.6 % of the time.
Larry
C3: Copious Canape Club is still my favorite system. (Ultra upgraded, PM for notes)
Santa Fe Precision ♣ published 8/19. TOP3 published 11/20. Magic experiment (Science Modernized) with Lenzo. 2020: Jan Eric Larsson's Cottontail ♣. 2020. BFUN (Bridge For the UNbalanced) 2021: Weiss Simplified ♣ (Canape & Relay). 2022: Canary ♣ Modernized, 2023-4: KOK Canape.
#20
Posted 2009-July-04, 11:02