[r-t] Bobs only Erin Triples (was: Composition search)

[Alexander Holroyd]

I assume that the percentage represented here is the percentage of plains 
and bobs of a given length that are true, correct?

If so, it would be very interesting to see it extended much further, 
preferably with a log scale on the vertical axis.  E.g. how long does the 
touch have to be for the truth probability to drop to 1%? 0.1%? 0.01%?

These questions are very relevant to possible new approaches to the 
bobs-only search.

It should not be necessary to do an exhaustive search for this.  One could 
use Monte Carlo sampling.  In the first instance, just sample a large 
number of random touches and see how many are true.  This will cease to 
work when the probabilities become too small, because you won't find any 
true ones.  For this, some kind of importance sampling ought to work...

On Wed, 25 Nov 2015, Richard Smith wrote:

> Alan Burlison wrote:
>
>> On 25/11/2015 15:06, John Harrison wrote:
>> 
>>> There's an anomalous looking plot of ~97% at a depth of 27.5.  Is that
>>> real?
>> 
>> I think it's the graph key, this looks like it might have come out of 
>> gnuplot.
>
> Yes, I used gnuplot to plot the data.  I've just continued it on to depth 35 
> (and removed the key).  The raw data is given below.  The first figure is the 
> length, the second is the number of true touches.
>
> I didn't do anything sophisticated to find this: no rotational pruning, no 
> parallelisation, no hand-written assembler, just the C++ code I gave earlier. 
> The search to depth 35 evaluated 15.9 billion nodes in 201 seconds, or 12.7 
> ns / node.  I ran it on my laptop which has a 1.9 GHz processor, so that 
> works out at 24 clock cycles per node.
>
> RAS
>
>
> 1	2
> 2	4
> 3	8
> 4	16
> 5	32
> 6	62
> 7	122
> 8	236
> 9	456
> 10	878
> 11	1668
> 12	3188
> 13	6092
> 14	11640
> 15	22206
> 16	42234
> 17	80318
> 18	152692
> 19	289864
> 20	550118
> 21	1042604
> 22	1974914
> 23	3737844
> 24	7068528
> 25	13357312
> 26	25216576
> 27	47577386
> 28	89697668
> 29	168973506
> 30	318059706
> 31	598167662
> 32	1124133852
> 33	2110893402
> 34	3960591668
> 35	7425076460
>
>
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