Bridge:Weak Two styles - frequency estimation

Bridge: Two level preempts

Frequencies for various opening styles

Links to the main file and an index

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I have used Hans van Staveren's superb public domain dealer.exe program to estimate rough Weak Two hand type frequencies. To simpify I have used a common base range of 6-10 points. Clearly in tournament practice a shapely 6520 hand might require less than an stolid Ekren 4432, but there you are! Dropping the points requirement in to account for this would make the type less common. All these shapes are most common around 10 h.c.p

Rather than estimate for {eg} all the Muiderberg 5-4 major-minor possibilities I have gone for a single / type and multiplied up for the four permutations in the group.

Preempt type	Raw freq.	No of perms	Overall freq.	8+ card fit freq.
6 card weak two including 7222 excluding other maj	1.5%	two	3.0%	76.4%
Muiderberg Pure 5-4 2-suiter major/minor	0.86%	four	3.44%	74.4%
.. add say half the 5-5 types below	q.v	four	4.2% approx	80%+
Loose preempts With 5-6 cards excluding 5332 or both majors	n/a	add above	6.4%	75% approx
5-5 two suiters as in Tartan twos (major/minor)	0.39%	four	1.54%	86%
5-5 two suiters as in Wilkosz 2 (all except /)	0.39%	six	2.3%	86%
Ekren as a theoretical pure 4-4	2.2%	one	2.2%	60%
Ekren as a 5-4 or better as per EBU 2	2.6%	one	2.6%	78%
Overall Ekren 4-4 or better in the majors	4.8%	one	4.8%	66% approx

Here is an old DOS printout demonstrating
the dealer.exe parameters and output

# My 6 card weak 2S includes the rather feeble 7222 shape 
#  but excludes 4+ hearts  Voids are OK  Base points 6-10

weak2s = shape(north, 6xxx + 7222 - 64xx - 65xx - 66xx - 6700) 
         and hcp(north) >= 6 and hcp(north) <= 10   
fit    = spades(north)+spades(south) 
condition weak2s  
action
  frequency "points" (hcp(north), 6, 10), 
  frequency "fit" (fit, 6, 13)
  
Frequency points: Frequency fit: ...  
6       2329      6     637    11      387 
7       2900      7     3005   12      50  
8       3233      8     5113   13      0 
9       3408      9     4354   
10      3563      10    1887 
Generated 1000000 hands, produced 15433.


# Muiderberg (Woo/Dutch two) is 5+major 4+minor 

muiderberg = shape(north, 5xx4 - 5404)
              and  hcp(north) >= 6 and hcp(north) <= 10 
spadefit   = spades(north)+spades(south) >= 8 
clubfit    = clubs(north)+clubs(south) >= 8 
fit        = clubfit or spadefit
condition muiderberg 
action   
  frequency "points" (hcp(north), 6, 10), 
  average "spade fit" spadefit, 
  average "club fit" clubfit,   
  average "black fit" fit 
         
Frequency points: 
6       1268    spade fit: 0.545486  
7       1665     club fit: 0.336132 
8       1783    black fit: 0.74376   
9       1964 
10      1894   
Generated 1000000 hands, produced 8574. 


# Estimate stats for specific 55 hand for Tartan Twos, 
# Muiderberg extensions and for the Polish 2D 

tartan   = shape(north, 5xx5 + 6xx5 + 5xx6 + 6xx6 +6007 +7006) 
           and hcp(north) >= 6 and hcp(north) <= 10 
spadefit = spades(north)+spades(south) >= 8   
clubfit  = clubs(north)+clubs(south) >= 8 
fit      = clubfit or spadefit  
condition tartan 
  action  frequency "points" (hcp(north), 6, 10), 
  average "spade fit" spadefit, 
  average "club fit" clubfit,   
  average "black fit" fit 
         
Frequency points:  
6        563    spade fit: 0.57487   
7        738     club fit: 0.582124 
8        875    black fit: 0.861658  
9        840 
10       844   
Generated 1000000 hands, produced 3860. 
         
 
# The Ekren base type is 4-4 in the majors
   
ekren    = shape(north, 44xx) and 
           hcp(north) >= 6 and hcp(north) <= 10  
heartfit = hearts(north) + hearts(south) >= 8 
spadefit = spades(north) + spades(south) >= 8
fit      = heartfit or spadefit 
condition ekren
action  
  frequency "points" (hcp(north), 6, 10), 
  average "major fit" fit   
  
Frequency points:  
 6       3486    major fit: 0.595748 
 7       4239  
 8       4645 
 9       4802  
10       4886 
Generated 1000000 hands, produced 22058. 
 
         
# 'Safe' Ekren demands a 5 card suit 
ekren5   = shape(north, 45xx 54xx 55xx 64xx 46xx 65xx 56xx)  
           and hcp(north) >= 6 and hcp(north) <= 10 
heartfit = hearts(north) + hearts(south) >= 8
spadefit = spades(north) + spades(south) >= 8 
fit      = heartfit or spadefit
condition ekren5 
action
  frequency "points" (hcp(north), 6, 10), 
  average "major fit" fit 
         
Frequency points: 
6       4150    major fit: 0.779127  
7       4974 
8       5516   
9       5844 
10      5943   
Generated 1000000 hands, produced 26427.

dealer.exe can be downloaded free in several formats from Henk Uiterwaal's http://www.dombo.org/henk/dealer.html reference site. It deals and analyses about 70,000 hands per second under DOS/486, or faster in an XP DOS window. I ran a million deals for each type and these results are typical. If you run the Monte Carlo simulation repeatedly you will get about 5% variance in these frequencies.

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Bridge: Two level preempts

Frequencies for various opening styles

Here is an old DOS printout demonstrating the dealer.exe parameters and output

Here is an old DOS printout demonstrating
the dealer.exe parameters and output