 When Top is Not 100% |
Question:
We got an outright top on a board and yet on our personal score card it is shown as 99.54%. Why not 100%?
Answer:
When all boards are not played the same number of times, the match points for the boards played fewer times are factored/increased to allow for this. The Neuberg formula is used to do the factoring. However, the effect of the formula is also to 'downgrade' the match points on these boards a bit to allow for the fact that the 'competition' wasn't as good as on the boards played more times.
The calculation is performed as follows:
| ♦ |
On each traveller match points are allocated to each pair first. This is done by comparing this pair's score with all the other scores on the board. (Adjustments/averages and missing scores are excluded from this comparison.) 2 match points are allocated for each score that is worse than this pair's score and 1 match point for each score equal to it.
Therefore the maximum number of match points anybody can get on a board is:
Top = (2 * Number of Scores on the Board) - 2
Number of Scores on the Board excludes adjustments/missing scores.
So if there are 12 scores on a board and one of them was an adjustment/average, then the top score on this board will be 20, while with 12 'normal' scores, the top score would be 22.
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The Neuberg formula is then applied to the resulting match points.
The Neuberg formula is:
| FMpt = |
| (Mpt * MaxS) + (MaxS - ActS) |
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| ActS |
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where:
FMpt = the factored match points to be given on this board to a specific pair
MPt = the original match points given to the pair as calculated above
MaxS = the maximum number of scores on any board in the event
ActS = the actual number of scores on this board. This excludes adjustments/averages and missing scores.
So, for example, if a pair gets 12 match points on a board that was played 11 times and the maximum number of times any board was played is 12, then this pair will get 13.18 match points after the Neuberg formula was applied or 59.9% (13.18/22) and not 60% (12/20). Equally if a pair gets a top on a board played 11 times and the maximum number of times any board was played is 12, then this pairs score will be 21.9 match points after the Neuberg formula was applied and not 22, which would be the top score for the board played 12 times. In percentage terms this would be 99.54% (21.9/22), and not 100% (20/20). |
Wish you hadn't asked?
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| Makeable Contracts and Points on Hand Diagrams |
Question:
On the results page each hand diagram shows a framed square in the bottom right hand corner, with some numbers in it. What are the numbers?
Also, what are the four numbers in the bottom left hand corner?
Answer:
The numbers in the bottom left hand corner are the high card points for North, South, East and West.
The numbers in the bottom right hand corner show makeable contracts. So, if there is number 6 to the right of N(orth) and underneath the ♥ symbol, this means that small slam in hearts is makeable on this hand, played by North.
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| What is Par Score or Optimum |
Question:
- On Bridgewebs hand diagrams in the top right hand corner it says Optimum followed by contracts and/or scores.
- On our own style hand diagrams in the top left hand corner it says Par Score followed by contracts and scores.
What does this mean?
Answer:
That is the score where neither side can improve their score by bidding further.
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| Computer Dealt Hands |
Question:
Since we started using the card dealing machine, there are a lot of weird distributions, long suits, singletons and voids.
Are the hands truly random or are they fixed? What has happened to our normal hands?
Answer:
These funny computer-dealt hands!!
Well, hand-dealt boards tend to, if not shuffled properly, give more flat distributions than statistically probable. That's because cards of the same suit end up next to each other when the cards are played or when tricks are gathered together. If these aren't separated by shuffling, it ends up that one card in that run of cards of the same suit goes to each player during the deal: voids and singletons become less likely.
When a card dealing machine is used, voids and singletons occur with the correct probability. Hands will now look more distributional, especially if manually dealt hands didn't use to be shuffled thoroughly.
Also see Bridge Probabilities from Wikipedia.
This says, for example, that the probability of getting a 7 card suit is 7 in 200 hands, ie for every 200 hands you get 7 card suit 7 times - on average. Six card suit turns up much more often - about 17 times in 100 hands. Also it seems that singletons are quite common - 3 times in every 10 hands, while on average there are 5 voids in every 100 hands. And - if you think that flat hands are now very rare, perhaps you would change your mind if I tell you that - on average - there are 47 flat hands in every 100 hands. Sometimes more, sometimes less.
Read also the following:
"Since we started using computer dealt hands, I've been extracting statistics from the hand definition files - the PBN files - and fed them into an Excel spreadsheet. Data from 2007, 2008 and 2009 have been used, 18048 deals in all. The results follow quite closely the theoretically expected values - see Summary.
I also produced a series of graphs which demonstrate random behaviour from set to set. The process has been semi-automated, so it didn't require as much work as one might imagine and it can easily be updated with more data or repeated for another set of data. The spreadsheet itself is also available for download - beware, it's size is about 7Mb.
Summary
High Card Points Graphs
Singletons Graphs
Suit Breaks for 7 and 8 card fits
Suit Break Graphs for 9, 10 and 11 card fits
Hand Patterns Graphs - 1
Hand Patterns Graphs - 2
Hand Patterns Graphs - 3
The Excel Spreadsheet
Mirna
1-March-2009 "
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