Combined odds

[helene_t]

Bayes' theorem can be written as

 

posterior_odds = prior_odds x likelihood_ratio

 

For example, in the textbook example of restricted choice, when Alice drops the queen we set the prior odds for her also having the jack to 1:1. The likelihood of her dropping the queen if it was sec is 1, while if she had QJ it would have been 1/2. Hence the likelihood ratio is 1:(1/2) or 2:1 in favour of Alice having the queen sec.

 

More generally, we can combine multiple information sources and write:

 

combined_odds =

odds_from_source_A x

odds_from_source_B x

etc.

 

For example, suppose that we are looking for the queen of trumps. Alice opened a precision 2♣, giving her give or take 12 of the 18 HCPs we don't have (i.e. odds 12:6 of her having a given honour), 7 of the 18 non-clubs (so odds 7:11) and maybe we reckon that if she did not have the queen she would have let a trump 1/3 of the time while she would never lead away from the queen, this would give her odds 1:(2/3) = 3/2 of having the queen. This is odds 42:22 in total.

 

This is of course a bit dangerous since is it is easy to overlook relevant information sources, such as for example the lack of a club lead which might suggest a broken club suit and hence give her more honours outside clubs. And combining information sources assumes independence.

 

Does anyone think this idea has any place in bridge teaching?

[billw55]

Does anyone think this idea has any place in bridge teaching?

Only for mathy people. Which most bridge learners are not. For the few that are, sure. For the rest, expect glassy eyes and blank stares.

[Zelandakh]

The principles, yes; the mathematical details, usually not.

[The_Badger]

Hello helene_t,

 

I personally believe only those at the very top of their game (world class/expert) would want to get involved in number-crunching statistics. It is a useful statistical anecdote to use, but there are simpler ways to get the message across for sure. They won't be so statistically accurate, but they will point a player in the right direction - and even for advanced players (who might have a few years of bridge under their belt) that is what is needed I feel.

 

Bridge is a difficult enough game as it stands: adding (what looks like for most people) complicated statistics into the mix - as opposed to simple statistics gently built upon - will probably have them scratching their head at the best, or running from the class at the worse.

[kenrexford]

"Why did you play for the drop?"

 

"Slight odds advantage."

 

"What took you so long to decide that, then?"

 

"The odds were 45,231 to 43,877."

 

 

 

 

 

[Finch]

Bayes' theorem can be written as

 

[snip Bayes' theorem]

 

Does anyone think this idea has any place in bridge teaching?

 

Only with some very specific students. In fact, only with those students who already know some statistics and are learning bridge.

 

I was originally taught Bayes' theorem at school. At the start of my last year I was applying to various universities to read mathematics, which in some cases involved attending an interview. The interviewer at imperial college london was a bridge player and he'd seen on my application that I played bridge. As an interview question he invited me to explain the principle of restricted choice in the context of Bayes' theorem.

 

Also on the subject of Bayes' theorem, a few months later I was sitting an exam paper related to my application to go to Cambridge university. I still remember the start of one of the questions, which was "This morning I found a body in my fridge...." it continued with some information about various people who might have turned up in the author's fridge that morning, and ended asking 'what is the probability that the body is of person A' ? I found out the following year that the question was written by a bridge-player.

[pigpenz]

MacKinnons book on odds at bridge is an interesting at sometimes boring read but well worth it

[ochinko]

It could still be quite useful for writing a bot :)