# Fair Distribution of NS/EW points on Randomised Boards

Hi All

I have come back to this forum after 3 years. I have one question on which I am seeking an explanation over the fairness of the HCP distributed over the 24 boards previously randomised in the dealing machine. Having done so, , a director subsequently decides to reduce the number of boards of play to say, 18 for whatever reason. When this happens, does the fairness of points received to N/S and E/W get compromised in anyway to the extent it could potentially deemed to be judged as "unfairness" , thereby potentially affecting final rankings/ percentages at the end of an 18 board session. Is there an issue here ? I would be interested to know your views particularly if there is any view from a mathematical/ scientific perspective ?

## Comments

Nothing should be done to randomly dealt boards to try to change the HCP held by NS v EW.

The closest there is to a statement on this is in the White Book

Thank you Robin. Perhaps, I didn't make my points clearer. My point is that when a player argues that the fairness over the distribution of points randomised over 24 boards would deem "unfair" if only 18 boards are played

No, there isn't. You have 24 boards randomly dealt and then the TD takes away the last six boards and you have 18 boards randomly dealt. There is no way of telling (before play) how the HCP are distributed in the 24 boards or in the remaining 18 boards.

If you think that when the duplimator deals a set of 24 boards, the HCP will be even between NS and EW, that is not so. Because every board is randomly dealt, there is no reason why the NS and EW HCP should be equal over any number of boards

Barrie Partridge - CTD for Bridge Club Live

+1

Sorry - I did misunderstand.

The fairness of distribution in any set of boards comes from each deal being (statistically) independent of the other. The dealing process does not attempt to create equal HCP for NS v EW over the set of boards.

Thank you for your expert advice.

I actually think that there may be some relatively small issue at play here... The more boards that you randomly generate, the closer to 10 HCP for each direction you will have.

Deal a million boards and the distribution of points will be very, very close to 10 points average each.

Deal much fewer boards and you are more likely to have skewed distributions...

For example, I just created a single deal and the points were: N 8, S16, E 5, W 11

creating a 5 board deal gave these averages: N 7.2, S 11.6, E 10.2, W 11

A 10 board deal gave: N 12.3, S 9.3, E 7.4, W 11

20 boards: N 9.3, S 11.6, E 9.25, W 9.8

30 boards: N 9.63, S 10.07, E 9.83, W 10.47

As a crazy example, I generated 640 hands (the most possible in Dealer 4 software) and the distribution of points were: N 9.97, S 10.2, E 10.04, W 9.78

So, the more boards dealt/in play, the more evenly the points will be distributed between each direction will be - which could be considered an element of 'fairness'. There will be a small, but not insignificant difference in the distribution of points between the different directions in 18 board sets and 24 board sets.

However, these things do have a habit of evening themselves out, so you might have a week or few with fewer than 10 points on average, but over the weeks, months and years, the 'good' and 'bad' nights will even themselves out. Essentially, most people play bridge over a long period of time, so playing 18 boards once a week for a year is 936 hands, 24 boards every week a for a year is 1,248 boards - there is not going to be much difference between the average HCP over these number of boards.

Kind regards Steve 👍