Generator

Output formats

• html: for viewing on screen
• duplimate: for creating live tournaments
• lin: to import them on bbo for bidding practice/team match
• print: to make a bidding challenge for your partner and you

Freakness

Measuring hand freakness was developed by Richard Pavlicek.

• Add 1 point for each card over four or under three in each suit.
• Add 1 point if the hand contains a singleton, or
• Add 2 points if the hand contains a void.

When deals are generated with uniform distribution, then the expected (average) freakness of a random hand is approximately 2.98.

Importance of statistics

Bridge is a game of probabilities. If you generate deals randomly with uniform distribution, then normal probabilities apply. If you generate then with non-uniform distribution, then it changes the whole game. It is not bridge anymore, although the rules are the same. In order to be successful, you need completely new methods for bidding, play and defence. Everything changes. So it is absolutely vital that participants of the goulash tournament know, how the deals are generated, or at least how freaky they are.

How the generator works

This bridge deal generator is designed to generate freaky deals. Normally, every single deal has the same probability of occurrence. Deals with the same pattern can be grouped. Each pattern occurs with the probability proportional to the number of different deals with that pattern. In order to change the expected freakness of a random bridge hand, a parameter k is cleverly chosen. To change the normal probabilities, a random deal pattern is generated with probability proportional to the k-th power of the normal probability. The deal itself is generated from the deal pattern, with random uniform distribution.

Generator properties

• No deal pattern is completely eliminated (instead, it's probability is reduced gradually to arbitrarily close to 0).
• The pattern of North-South hands is independent from the pattern of East-West hands. Eg: if North-South hold 10-card spade fit, then the probabilities of 2-1 or 3-0 distributions in East-West does not change if they are divided 5-5 or 10-0 in North-South.
• It is possible to calculate the probabilities of each hand pattern and distribution.

If k equals 1, then each deal occurs with same probability (normal random). If k equals 0, then each deal pattern (there are 393197 of them) occurs with the same probability. Eg: 13-0-0-0 in all hands simultaneously occurs with the same probability as 4-3-3-3 in all hands simultaneously.
Some other goulash dealing methods require each hand to have 7 card suit. If you are South, and know that West has exactly 6 spades, then you should think: in which suit does West have 7 cards, and where are his two voids? These types of constraints are very artificial and I don't like these generators.

Author

Comments are welcome: hendrik dot nigul gmail dot com.