Probability of Cold Grand Slam

[pedals]

Let's pretend that me and my partner were to play millions of bridge hands. What percentage of hands would our team have a cold grand slam; that is, a grand slam that can always be made with perfect defense.

[billw55]

I'm no number cruncher, but based on experience I expect it is less than one percent.

[P_Marlowe]

The following may help to get an approximate answer

http://www.rpbridge.net/7z76.htm

 

Assume, that you will always make 13 tricks, if you have 36 / 37

HCP in the combined hands, based on the table you, get the answer,

based on HCP raw power.

 

The shape will play a role, with 10HCP and a 13 carder you will make

13 tricks as well, but how likely is it, that you get this hand.

..., suggestion would be to reduce the cut off, to see, how the cut off

effects affects the result, I would not go below 33.

 

The answer will at least give you a feeling, how many deals, you would

need to test with a DD simulation, to get an reliable answer.

 

With kind regards

Marlowe

[semeai]

Let's pretend that me and my partner were to play millions of bridge hands. What percentage of hands would our team have a cold grand slam; that is, a grand slam that can always be made with perfect defense.

 

I tried Richard Pavlicek's ancient RP Deal Finder program (DOS-based!), found here, which searches through a library of more than 2 million pre-double-dummy-analysed hands.

 

I'll interpret "cold" as double-dummy-makeable.

 

I stopped the program at around 50000 deals. One side having a makeable grand slam of any sort was 1.4% of the 50000 deals and either side having one was 2.8% of them (these numbers looked pretty stable by the time it got out near 50000 deals).

[phil_20686]

I was going to say you expect to make 13 tricks about once every 24 boards, but only about half of those are `good' grand slams.

 

Of course, in RL, you collect 13 tricks quite often when the oppo have an ace and don't lead it.

[CarlRitner]

I tried Richard Pavlicek's ancient RP Deal Finder program (DOS-based!), found here, which searches through a library of more than 2 million pre-double-dummy-analysed hands.

 

I'll interpret "cold" as double-dummy-makeable.

 

I stopped the program at around 50000 deals. One side having a makeable grand slam of any sort was 1.4% of the 50000 deals and either side having one was 2.8% of them (these numbers looked pretty stable by the time it got out near 50000 deals).

 

If we assume, as part of the original question, that their partnership can 1) bid the grand slam,

and 2) also play (declare) perfectly, then yes, you can use the double dummy tool to determine

this. Otherwise, a statistical review (e.g. BridgeBrowser/BBO Records) would be in order. I'd be

curious how close/far apart those two numbers are.

[barmar]

The DD version will include lots of hands missing an honor: all the hands with the K/Q onside and offside singleton K or doubleton Q.

[semeai]

The DD version will include lots of hands missing an honor: all the hands with the K/Q onside and offside singleton K or doubleton Q.

 

Yes, it's sort of a strange statistic with double dummy being used.

 

Better might be to use the GIBson trick as a definition of "cold": Analyse hands (similar to DD analysis) pretending that the defenders get to construct their hands as they go; ie they have a pool of 26 cards and can take any card to play at any time, except that they can't play a suit they've previously shown out of.

 

[Might want to forbid ruffs on opening lead as well or the statistic will be pretty meaningless.]

 

Setting this up would take a decent amount of work I suppose as you'd essentially be writing your own (modified) DD solver as part of it.