Talk:Contract bridge probabilities

Probablities as Percentages

Bridge players always express probabilities as percentages, and so I suggest that all the tables in this article should do that. At the moment only one does, which is inconsistent.

Also the first table is a bit inconsistent about its numerical precision. The probability for a shape is given to 2 decimal places, but then the probability of an individual holding is given to 3 or 4 significant figures followed by a tilde. Surely the level of precision should be the same in each case, and 2 sig figs seems reasonable. Then what's the tilde about? One sometimes sees a tilde before a number to mean approximately, but here all the figures in both columns are approximate. I'd suggest everything in percentages to 2 sig figs and no tildes.

Kestrelsummer (talk) 15:41, 29 October 2014 (UTC)

Good points, although the reason the first table is the way it is is because some of the probabilities are indeed exact. I marked those that are not exact with tilde.Beowulf (talk) 02:29, 20 October 2015 (UTC)

I was going to make exactly the same point as Kestrelsummer. (Many of the numbers in the "Probability" column are approximate but have no tilde.) I'd suggest all probabilities are quoted to three (maybe four) decimal places, with trailing zeros where necessary.---Ehrenkater (talk) 10:32, 14 March 2024 (UTC)

Verification of scope of possible deals

At this writing, the article states:

In total there are 53,644,737,765,488,792,839,237,440,000 (5.36 x 10²⁸) different deals possible, which is equal to $52!/(13!)^{4}$. The immenseness of this number can be understood by answering the question "How large an area would you need to spread all possible bridge deals if each deal would occupy only one square millimeter?". The answer is: an area more than a hundred million times the total area of the earth.

This is simply to verify the foregoing.

Inputs:

• The surface area of the earth: 510 million (or 510 x10⁶) square kilometers. See this reference
• Size of standard bridge card: 2.25 inches by 3.50 inches. See card sizes
  • Accordingly, the surface area of one cards is 7.875 square inches
  • 7.875 square inches is 5,080.64 square millimeters or 5.08064 x10^-9 square kilometers
• Number of possible bridge deals: 53,644,737,765,488,792,839,237,440,000 (5.36447 x 10²⁸). See Number of possible deals

Outputs:

• If the area of one card represents each possible deal, the total surface area of all possible deals would be: 5.08064 x10^-9 times 5.36447 x10²⁸ or 27.25494 x10¹⁹ square kilometers. Dividing 27.25494 x10¹⁹ by 510 x10⁶ gives 534.4 x10⁹ or over 534 billion times the surface area of the earth
• If instead all 52 cards of each deal were to be placed on the earth's surface, they would cover the earth over 27 trillion times (52 times 534.4 x10⁹)
• If instead 1 square millimeter represents each possible deal, the total surface area of all possible deals would be: 534.4 x10⁹ divided by 5,080.64 or 0.107 x10⁹ billion times the surface area of the earth which is also expressed as being over 100 million times the surface area of the earth

Conclusions:

1. the statement is correct
2. a better statement might be something like "if all the cards of all possible deals were placed on the earth's surface, they would cover all its land and water over 27 trillion times"

Comments?

Newwhist (talk) 22:10, 10 July 2012 (UTC)

Pointless comparison.

From the article: The immenseness of this number can be understood by answering the question "How large an area would you need to spread all possible bridge deals if each deal would occupy only one square millimeter?". The answer is: an area more than a hundred million times the surface area of Earth.

Such pointless apples to oranges comparisons don't belong in an encyclopedia. — Preceding unsigned comment added by 45.46.65.46 (talk) 16:58, 9 December 2020 (UTC)

Do probabilities change as you play?

P(a,b,ne,nw) is claimed to give the probability of a split(a.b) when there are (ne, nw) unknown cards outstanding. So P(0,4,13,13)=.09585. Suppose declarer plays 9 tricks and gains no information on the split. So now ne=nw=4, and P(0,4,4,4)=.02857. It seems to me that the probabilities of the various splits have not changed, but the above results seem to contradict this. Rhwoirsham (talk) 16:05, 13 December 2022 (UTC)

Vandalism

As a former contributor to this page, I deplore the insertion of the section currently headed by "Calculation of Probabilities" as an act of mathematical vandalism. The previous derivation of the probabilities (my own) was based on the simple, yet precise, mathematics of vacant places. It has been replaced by what I consider to be advanced probability theory (the hypergeometric formula, if I recall correctly) which few bridge players will know, let alone understand. Such a treatment belongs, if at all, as an appendix to the article. Beowulf (talk) 09:49, 9 October 2023 (UTC)