[r-t] Proportion of Surprise Methods

[Richard Smith]

Leigh Simpson wrote:

>> What proportion of TD minor grids are surprise methods?  And what
>> proportion of regular or standard methods?  I think "a quarter" is too
>> simplistic...
>
> Well, a probabilistic argument could work as follows:
>
> -----
>
> When the treble hunts 2-3, the following place-notations are possible:
>
> 14
> 1456
> 1458

[big snip]

> (who is now waiting for RAS to say this is all a load of rubbish)

If you insist.  I think your first mistake came when you 
thought that you could get a 1458 place notation in TD minor 
grid.  Note: minor means on six bells.

But that aside, the analysis seems to hold water.  As you 
note, the requirement for no more than two (or four, 
or whatever) consecutive blows in one place will lose you 
the independence between the division ends.  I expect the 
effect will be to further depress the probability of TB and, 
to a lesser extent, of D.  This is because, of the 33 
non-null changes on eight, 20 include a place at lead (and 
by symmetry, the same number include a place in 8ths); but 
only 15 include a place in 3rds (or 5ths) which is the next 
most popular place.  This suppresses the probability of 
external places below what you expect by assuming changes 
can be selected independently.

Requiring a regular lead head (which I didn't in my analysis 
-- I took grid to mean anything, irrespective of whether it 
produced a 1-lead coures) will have a further effect, but I 
can't immediately picture what, if any, systematic bias 
this will add.

RAS