# [BLML] once again, UI from allowed source

Jerry Fusselman jfusselman at gmail.com
Thu Aug 29 16:27:46 CEST 2013

```On Thu, Aug 29, 2013 at 7:18 AM, Brian <bmeadows666 at gmail.com> wrote:
> On 08/29/2013 07:36 AM, Alain Gottcheiner wrote:
>
> <snip>
>
>> That's what I like with my fellow mathematicians. They call such a proof
>> 'easy'.
>> But it is correct.
>>
>
> Mathematically correct, maybe - but having been educated as a chemist
> rather than a mathematician, reading something which implies that a
> bridge player can time the accuracy of partner's bid at the table to
> +/- 0.05 of a second makes me automatically sceptical about what's
> being said.

It would have been incompetent of me to supply a proof that works only
because I used continuous random variables.  The proof generalizes to
discrete random variables, but using discrete random variables would
not have been fair to Steve.  He postulated the existence of a point
that provides no UI, and using continuous random variables is the only
way he could possibly be right.  (Actually, he is right if he limits
himself to *two* possible meanings of the bids and he requires the
densities to have overlapping convex supports and to be continuous
with continuous contact with zero---but these assumptions strike me as
unrealistic.)

>
> If Jerry had said "Assume that your partner makes his bid in 4 seconds
> +/- 1 second" then that would seem far more realistic to me. I'm not
> enough of a mathematician to know whether the proof holds up when you
> introduce real-world observational uncertainties.
>

Yes, the proof still holds up if I had said "Assume that your partner
makes his bid in 4 seconds
+/- 1 second" and the numbers are exactly the same, because

p(N|s=4+/-1) = p(s=4+/-1|N)p(N) / (p(s=4+/-1|N)p(N)  + p(s=4+/-1|A)p(A)),

and all the same numbers work---p(s=4+/-1|N) = 1 still, and
p(s=4+/-1|A) = 1/6 still.  The end result of seeing that the bid takes
4 seconds +/- 1 second is still to change your thinking from p(N) =
20% to p(N|s=4+/-1) = 60%.  It's still UI.

Jerry Fusselman
```