Re: In between Law 23

The original  question  arose when I found the word "subset" in 23A2 and
I took a mathematical look on law 23.
(sorry this will be a bit theoretical)

The idea behind law 23 is: "Let the game go on, if there is no harm done
by the withdrawn bid"

And the three parts of law 23 define situations when this is  the case.

Hermann named the important part: "There is little additional
information coming from the withdrawn bid."

And in case this little bit of information is causing damage to the
non-offending side, we have 23C.

Lets have a closer look to this:
We have a set W of hands fitting to the withdrawn bid and the set R of
the hands fitting to the replacement.

Obviously there is no additional information if  R is in  W. (This case
is 23A2)

"R in W"  is the same as "R/W is empty", and this is the  mathematical
equivalent to "there is no information coming coming from the withdrawn
call".

On the other hand W/R is the set of all hands, which are matching the
withdrawn bid, but not the replacement. This set may be huge, without
doing any harm. The information that the offending player does not have
one of these hands is AI from the replacing call. No need to care about
the size of W/R.

"R in W" is an asymmetric relation between the two sets which is
according the fact, that the information from the replacing call is
allowed and the additional information from the withdrawn call is not.

The words of 23A1 (similar meaning) describe the fact that the R≈W.
(With repect to a measurement we still have to define)
This is a symmetric relation.

The sets being "similar" requires R/W to be small, and the SAME  for W/R.

"R/W is small" is a little bit more tolerant than "R/W is empty".
The knowledge, that offenders hand is in W is "additional information".
It becomes more important if R/W is big.

But do we really need W/R to be small? Like above, when we considered
23A2, the information, that the offending player has a hand according to
the replacing call, is AI for his partner. It is not "additional
information". It does not matter that the replacing call does exclude
many of the possibilities included in the withdrawn call.

No harm is done if there are lots of hands, which are suitable for for
the withdrawn call, but not for the replacement.

So the condition that the sets are similar is not necessary for our
purposes. We only need R/W to be small.

And at that point I thought it might be better to have  a law 23A1 not
requiring similarity between the replacement and the withdrawn call and
the replacing one. We need less than similarity.

The three systems A, B and C where only a constructed example to make it
more easy to see the general problem.

Volker


Am 07.11.2017 um 03:28 schrieb Steve Willner:
> On 2017-11-06 6:41 PM, Jan Peach wrote:
>> showing weak hearts or spades or several possible game force hands is
>> similar to showing just hearts or spades (whatever the range).
>
> That wasn't the original question as most of us understood it.  I don't
> think anyone would rule those as similar, and I explicitly mentioned
> that in an earlier message.
>
> The original question as understood was "possible game force" versus
> "possible game force or a hand type that will be dealt twice a decade if
> you play a lot."  Those two meanings seem similar to me, and we have
> L23C if ruling out the rare hand type becomes important.
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> Blml mailing list
> [email protected]
> http://lists.rtflb.org/mailman/listinfo/blml


-- 
Volker Walther
Am 07.11.2017 um 03:28 schrieb Steve Willner:
> On 2017-11-06 6:41 PM, Jan Peach wrote:
>> showing weak hearts or spades or several possible game force hands is
>> similar to showing just hearts or spades (whatever the range).
> 
> That wasn't the original question as most of us understood it.  I don't 
> think anyone would rule those as similar, and I explicitly mentioned 
> that in an earlier message.
> 
> The original question as understood was "possible game force" versus 
> "possible game force or a hand type that will be dealt twice a decade if 
> you play a lot."  Those two meanings seem similar to me, and we have 
> L23C if ruling out the rare hand type becomes important.
> _______________________________________________
> Blml mailing list
> [email protected]
> http://lists.rtflb.org/mailman/listinfo/blml
> 


-- 
Volker Walther
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