Thanks Mike it formats and reads perfectly… nice job, Rob
> On 20 Jul 2017, at 8:02 am, 'Mike Day' via Programming
> <programm...@jsoftware.com> wrote:
>
> This took me much longer than a lunch-break, partly because we
> were away in France, and I was experimenting with J701 on my
> iPad when Liz would let me.
>
> I came up with a number of variants, of which the following is best.
> It's slower and uses more space than Raul's for small problem-sizes,
> but is perhaps better for larger problems, eg n > 100 or so.
>
> NB. a Boolean verb for whether a player donates, which,
> NB. of course, depends on whether he has any money:
>
> donation =: 1 & <.
>
> NB. This verb lists the indexes of the random donee (? player donated to)
> NB. for each player, whether of not that player CAN donate.
> NB. It assumes that its single argument is i.n where n is the number
> NB. of players, which is why its name ends in i (!):
>
> idoneei=:(#|(+?&.<:@#~@#))
>
> NB. The idea is to concatenate
> NB. (the old state minus donation) and (donation), namely
> NB. ((-, ])donation)
> NB. and sum them as ordered with this left-hand key:
> NB. (i.n) concatenated with (idonee), namely
> NB. (, idoneei)@(i.@#)
>
> NB. Here it is, with a fix, f.
>
> new =: ((,idoneei)@(i.@#) +//. ((-, ])donation )) f.
>
> NB. time & space:
> ts =: 6!:2 , 7!:2@]
>
> NB. where my version is ok:
> ts'orig ^:5000 #~200' NB. Xiao-Yong Jin's original suggestion
> 5.72563 22912
> ts'tick ^:5000 #~200' NB. Raul's revised version
> 1.57339 77824
> ts'new ^:5000 #~200' NB. The best I could manage
> 0.922963 20992
>
> NB. and where it isn't so good:
> ts'orig ^:5000 #~10' NB. Xiao-Yong Jin
> 0.341718 6272
> ts'tick ^:5000 #~10' NB. Raul M
> 0.0445439 3840
> ts'new ^:5000 #~10' NB. Mike D
> 0.0676198 4864
>
> Sorry for this late posting, but it wasn't convenient to
> write up and send until home and with laptop to hand.
>
> Thanks,
> Mike
>
> NB. prepared in notepad, copied to Thunderbird, and trying
> to force fixed width - hope it displays reasonably.
>
>
>
> On 11/07/2017 19:33, Devon McCormick wrote:
>> Reading the page referenced, I see where I was confused. The problem
>> starts out as 100 people each with $100, but then solves a variant of it
>> for 45 people with $45 each, possibly so the animation is legible. It's
>> not clear why they even mention the first set of numbers.
>>
>> On Mon, Jul 10, 2017 at 8:37 PM, Raul Miller <rauldmil...@gmail.com> wrote:
>>
>>> Oops, I did not think about that "reflexive giving" wart.
>>>
>>> Here's a fix for my version:
>>>
>>> tick=: (0 >. <:) + i.@# +/@:(=/)~ I.@:* (] + <:) +/@:* ?@# <:@#
>>> require 'stats'
>>> stddev"1 tick^:(i.10) 45#45
>>> 0 0.977008 1.18705 1.73205 2.01133 2.15322 2.46798 2.86832 2.97719 3.1334
>>> tick^:10000]20#20
>>> 3 20 1 15 10 38 6 8 23 24 11 90 33 67 5 13 7 20 1 5
>>>
>>> Thanks,
>>>
>>> --
>>> Raul
>>>
>>> On Mon, Jul 10, 2017 at 7:50 PM, 'Pascal Jasmin' via Programming
>>> <programm...@jsoftware.com> wrote:
>>>>
>>>> The number of $ available each round is the number of people with >&0.
>>> The number of potential recipients is the population. This simplification
>>> though means its possible for someone to pay himself.
>>>>
>>>> A correction to your version,
>>>>
>>>> /:~@(-&1`]@.(=&0)"0 (#/.~@] + ~.@]{[)`(~.@])`[} >&0 # (?@#~@#@]`]`[} ]
>>> I.@:= i.@#)@?@#~@#)^:21000 #~10
>>>> That assumption would increase the likelihood of eventual
>>> "superconcntration" but that doesn't seem to happen.
>>>> As soon as some have 0, the rest have a "negative return" expectation
>>> each turn.
>>>>
>>>> ________________________________
>>>>
>>>>
>>>> From: Xiao-Yong Jin <jinxiaoy...@gmail.com>
>>>>
>>>> To: "programm...@jsoftware.com" <programm...@jsoftware.com>
>>>>
>>>> Sent: Monday, July 10, 2017 3:43 PM
>>>>
>>>> Subject: [Jprogramming] Everyone giving dollars to random others
>>>>
>>>>
>>>>
>>>>
>>>> I thought this is a good lunch break exercise.
>>>>
>>>>
>>>>
>>>> http://www.decisionsciencenews.com/2017/06/19/counterintuitive-
>>> problem-everyone-room-keeps-giving-dollars-random-others-
>>> youll-never-guess-happens-next/
>>>>
>>>>
>>>> Quote: “Imagine a room full of 100 people with 100 dollars each. With
>>> every tick of the clock, every person with money gives a dollar to one
>>> randomly chosen other person. After some time progresses, how will the
>>> money be distributed?”
>>>>
>>>>
>>>> And I came up with this simulation. (45 people with 45 dollars each,
>>> same as on the webpage.)
>>>>
>>>>
>>>> /:~@(-&1`]@.(=&0)"0 (#/.~@] + ~.@]{[)`(~.@])`[} >&0 # (?@#~@#@]`]`[} ]
>>> I.@:= i.@#)^:_@?@#~@#)^:5000 #~45
>>>>
>>>>
>>>> And I really like to see the mean expectations and the standard
>>> deviation of the mean, I ended up doing this. (Make sure the J sentence is
>>> one long line if you want to try it out.)
>>>>
>>>>
>>>> ((],.[:(+/%#*<:@#)&.:*: -"1)+/%#)}.(/:~@(-&1`]@.(=&0)"0 (#/.~@] +
>>> ~.@]{[)`(~.@])`[} >&0 # (?@#~@#@]`]`[} ]I.@:=i.@#)^:_@?@#~@#)^:10000)^:(<65)
>>> #~45
>>>>
>>>> 0.984375 0.124984
>>>>
>>>>
>>>> 2.01562 0.170335
>>>>
>>>>
>>>> 3.0625 0.180765
>>>>
>>>>
>>>> 4.15625 0.230616
>>>>
>>>>
>>>> 5.21875 0.248476
>>>>
>>>>
>>>> 6.1875 0.306894
>>>>
>>>>
>>>> 7.35938 0.332862
>>>>
>>>>
>>>> 8.64062 0.362809
>>>>
>>>>
>>>> 9.84375 0.380723
>>>>
>>>>
>>>> 10.9688 0.383805
>>>>
>>>>
>>>> 12.125 0.407944
>>>>
>>>>
>>>> 13.6406 0.423964
>>>>
>>>>
>>>> 15.0625 0.457453
>>>>
>>>>
>>>> 16.5312 0.462893
>>>>
>>>>
>>>> 18.1875 0.480717
>>>>
>>>>
>>>> 19.7031 0.464877
>>>>
>>>>
>>>> 21.1562 0.475709
>>>>
>>>>
>>>> 22.7031 0.483702
>>>>
>>>>
>>>> 24.4062 0.516935
>>>>
>>>>
>>>> 26.4062 0.5768
>>>>
>>>>
>>>> 28.1094 0.604266
>>>>
>>>>
>>>> 29.8281 0.617838
>>>>
>>>>
>>>> 31.875 0.61942
>>>>
>>>>
>>>> 33.9375 0.603345
>>>>
>>>>
>>>> 35.7812 0.642211
>>>>
>>>>
>>>> 37.9844 0.647987
>>>>
>>>>
>>>> 40.6562 0.731321
>>>>
>>>>
>>>> 43 0.739342
>>>>
>>>>
>>>> 45.3906 0.723616
>>>>
>>>>
>>>> 48.0469 0.7613
>>>>
>>>>
>>>> 51.6094 0.823639
>>>>
>>>>
>>>> 54.7656 0.873934
>>>>
>>>>
>>>> 57.1406 0.815544
>>>>
>>>>
>>>> 60 0.866598
>>>>
>>>>
>>>> 63.8594 0.898319
>>>>
>>>>
>>>> 68.75 0.918018
>>>>
>>>>
>>>> 73.5781 1.00736
>>>>
>>>>
>>>> 78.3281 1.08128
>>>>
>>>>
>>>> 84.9688 1.25534
>>>>
>>>>
>>>> 93.4688 1.29731
>>>>
>>>>
>>>> 104.578 1.73274
>>>>
>>>>
>>>> 114.922 2.07574
>>>>
>>>>
>>>> 131.938 2.7357
>>>>
>>>>
>>>> 159.359 4.40899
>>>>
>>>>
>>>> 204.766 7.24239
>>>>
>>>>
>>>>
>>>> So, how do I make a fancy animation (like the one in the webpage I
>>> linked in the beginning of this message) with J?
>>>>
>>>> ----------------------------------------------------------------------
>>>>
>>>>
>>>> For information about J forums see http://www.jsoftware.com/forums.htm
>>>> ----------------------------------------------------------------------
>>>> For information about J forums see http://www.jsoftware.com/forums.htm
>>> ----------------------------------------------------------------------
>>> For information about J forums see http://www.jsoftware.com/forums.htm
>>>
>>
>>
>
>
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